Comparative Study of Analysis Filter Bank Designs for AC-3 Encoding

Undergraduate Student Project

Mark Joseph L. Tan

2002-22034

B.S. Computer Engineering

Adviser

Franz A. de Leon, MS EE

University of the Philippines, Diliman

Approval Sheet In partial fulfillment of the requirements for the degree of Bachelor of Science in

Computer Engineering, this project entitled “Comparative Study of Analysis Filter Bank

Designs for AC-3 Encoding” prepared and submitted by Mark Joseph L. Tan, is hereby

recommended for approval.

__________________

Franz de Leon

Adviser

Accepted in partial fulfillment of the requirements for the degree of Bachelor of

Science in Computer Engineering

Approved by:

__________________

Panel

__________________

Panel

__________________

Reader

__________________

EEE190 Handler

Abstract

Several high-fidelity digital audio formats have been developed with the challenge of

developing audio coding techniques intended for low cost, limited bandwidth and storage

capacity.

AC-3 is one of these international standards. It has been widely used as the audio

coding standard for laserdiscs, cinemas and DVD films. AC-3 has been accepted by the

Advanced Television Systems Committee (ATSC) as the audio coding standard for US

Grand Alliance High Definition Television (HDTV) system.

This project is a comparative study of analysis filter bank designs for AC-3 encoding.

The standard algorithm will first be implemented in stereo mode using software.

Different optimization techniques on the analysis filter bank designs will then be

performed. Finally, listening and speed performance tests will be done to compare the

optimized codes with the standard implementation.

The project will aid in future designs concerning the AC-3 audio coding standard,

with the goal of improving performance and efficiency for high-quality digital audio

compression.

Table of Contents

1. Introduction

1.1. Background of the Project

1.2. Project Objectives

1.3. Overview

2. Literature Review

2.1. Standard Digital Audio Format

2.1.1. Standard Formatss

2.1.2. MPEG-Based Proprietary Formats

2.1.3. Non-MPEG Proprietary Formats

2.2. AC-3 Audio Coding Standard

2.2.1. History and Development

2.2.2. AC-3 Compression Features

2.2.3. AC-3 Comparative Advantages

2.2.4. AC-3 Bit Stream

2.3. AC-3 Encoding Algorithm

2.3.1. Analysis Filter Bank

2.3.2. Spectral Envelope Encoding

2.3.3. Encode Bit Allocation

2.3.4. Mantissa Quantization

2.3.5. Frame Formatting and Bit Stream Packing

2.4. AC-3 Decoding Algorithm

2.4.1. Frame De-Formatting and Bit Stream Unpacking

2.4.2. Spectral Envelope Decoding

2.4.3. Decode Bit Allocation

2.4.4. Mantissa De-Quantization

2.4.5. Synthesis Filter Bank using IMDCT

2.5 Related Works

2.5.1 The ATSC Standard

2.5.2 FFmpeg Multimedia System

3 Methodology

3.1 Design

3.1.1 Direct Method

3.1.2 Indirect Method using DCT-IV

3.1.3 Indirect Method using FFT

3.1.4 Recursive Method

3.2 Implementation

3.3 Testing

3.3.1 Preliminary Test

3.3.2 Objective Tests

3.3.3 Formal Listening Test

3.3.4 Playback

3.3.5 Listening Conditions

4 Results and Analysis

4.1 Objective Measurements

Chapter 1

Introduction

Digital Audio Compression (AC-3) is the 3

rd generation audio coding algorithm

developed by the Digital coder group at Dolby Laboratories which eventually became the

audio coding standard for the US Grand Alliance HDTV system. The primary motivation

in developing the AC-3 audio coding standard was the need for a superior multi-channel

audio coder. AC-3 became one of the most successful proprietary digital audio formats

available in the market. It is usually integrated with video applications and is rarely used

as stand alone. Thus, even though it has been around since 1990’s, it is not as prominent

as the other consumer audio formats such as MPEG Layer III (mp3).

AC-3 has a wide variety of applications. It can found in laserdiscs, digital cable

and even satellite transmissions. But it is famous for being the audio format used in

cinemas and DVD’s. Like other popular codecs, it has a perceptual coding algorithm that

uses minimal digital information and lower data rates which allows minimum

degradation of quality. Thus, the sound almost exactly the same as the original sound

when decoded for playback providing true surround.

Currently, there are several audio decoders that are capable of AC-3 playback.

However, it is very rare to find audio encoders and decoders that are solely dedicated to

handling the AC-3 format.

1.1 Background of the Project

Figure 1-1 Project Overview

The project is a comparative study of the analysis filter bank designs for the AC-3

encoding which will be subdivided into two major parts. The first part would be the

software development of the AC-3 audio coding standard’s encoding algorithm while the

second part would be the implementation of analysis filter bank designs that will modify

the traditional algorithm. The project overview is shown in Figure 1-1.

Traditional

Encoding Algorithm

Modified Encoding

Algorithms

Final

Code Comparative

Analysis Objective

Analysis

For the development of AC-3 encoding algorithm, each of the different coding

blocks of this audio format will be identified, implemented and tested. Modification will

then be carried out in order decrease the amount of computations, thus, minimizing the

complexity. This will be verified by testing procedures which will include listening tests

to assess the quality of the audio file and tests to verify computational complexity.

The implementation of the encoding algorithm as well as the optimization

techniques will be based on various researches that deal with the AC-3 audio coding

standard.

1.2 Project Objectives

One of the major factors considered in creating perceptual audio coders is the

need for real-time processing. The speed of the encoding algorithm is directly related to

the computational complexity and the number of cycles it takes to process an audio

block. Since a large part of the calculation occurs in the filter bank, the interest of the

project lies on having a comparative analysis of different filter bank designs for the AC-3

encoding algorithm.

This will be done by implementing each block of the coding process to create an

encoder that operates in stereo mode and applying different methods for optimizing the

performance. The project aims to optimize a traditional AC-3 encoding algorithm to

reduce its computational complexity.

Lastly, it is of great importance to characterize AC-3 compression features since

this will be the first AC-3 related project to be conducted by DSP Laboratory. The project

aims to look into particular AC-3 features that make it one of the most powerful

perceptual audio standards.

1.3 Overview

The components of the AC-3 encoding algorithm can be grouped into five major

blocks. These are the: (1) analysis filter banks which perform the time-frequency

transformation of the input signal, (2) spectral envelope encoding where the power

spectral density is analyzed, (3)-(4) bit allocation and mantissa quantization that use

psychoacoustic models to manipulate the mantissa component of the input signal and (5)

formatting & bit stream packing that prepares the audio data for encoding. [1]

Several of the AC-3 related studies that have been carried out focused on

implementing the encoding algorithm and improving its performance such as those in [8]

[11] [12]. The emphasis of the optimization methods have been put mainly on the

analysis filter bank which aims to minimize complexity by decreasing the number of

computations needed by the encoding algorithm. This is because it is one of the most

calculation intensive processes in the algorithm. Thus, this project will compare the

optimization methods on the analysis filter bank design.

The project will be an implementation of the AC-3 audio coding standard’s

encoding algorithm using software. The entire standard algorithm along with the analysis

filter bank designs will be implemented using the C/C++ programming language.

Testing will be done using two methods, first would be objective tests that will

measure accuracy and speed to check the number of computations made. Second would

be subjective audio listening tests to examine quality and check if there are noticeable

differences on the generated AC-3 audio format.

Chapter 2

Literature Review

2.1 Standard Digital Audio Formats

The introduction of the audio compact disc (CD) technology in 1982 set off the

transformation of audio media from analog to digital format. The single purpose of CD

back then was to hold music in digital form. However, huge amount of data is required to

represent the digital audio file which made it necessary to develop audio coding

techniques for efficient transmission and storage. [1]

The goal of these coding techniques is to efficiently use the least amount of bits to

represent a digital audio file without making any obvious changes in the original data

through transparent coding. Audio coding technology has experienced tremendous

development that it has become possible to successfully remove as much as 90% of audio

data during compression without noticeable changes in the original from.

There are several international and commercially available audio coding standards

which can loosely be classified as Standard Formats, MPEG-Based Proprietary Formats,

and Non-MPEG Proprietary Formats. Table 2-1 shows some examples of each. [2]

Standard Formats MPEG-Based

Proprietary Formats

Non-MPEG

Proprietary Formats

Pulse Code Modulation (PCM) AT&T’s a2b AC-3

Differential PCM MP4 EPAC

Adaptive Differential PCM Liquid Audio Windows Media Audio (WMA)

u-law Compression Apple QuickTime Real Audio

ISO/MPEG Family Transparent Audio Compression (TAC)

TwinVQ (VQF)

Table 2-1 – Audio Coding Standards

2.1.1. Standard Formats

PCM is a type of format that can be read by several audio applications. DPCM,

APCM and u-law compressions are simple variations of lossy compression formats that

store only the difference between consecutive samples instead of the entire information.

[2]

The Moving Pictures Experts Groups (MPEG) under the International

Organization for Standardization (ISO) has developed several standards under the

ISO/MPEG Family. These include the MPEG-1 Layers I, II, and III - which can operate

in mono or stereo modes; MPEG-2 Layers I, II, III, and AAC - which can operate in

multi-channel; and MPEG-4 – which can operate in multi-channels low-bit rates.

2.1.2. MPEG-Based Proprietary Formats

The ISO/MPEG Family consists of notable open standards which have become

widely used. Because of this, several proprietary formats have been developed which are

MPEG-based. These enhancements in the ISO/MPEG standards paved way for the

development of sophisticated audio formats that support several features. [2]

2.1.3. Non-MPEG Proprietary Formats

There are also several Non-MPEG Proprietary Formats available in the market.

These formats offer a wide array of applications and claim to produce quality audio

sound that is indistinguishable from the original CD. Among all of these, AC-3 has

emerged to be the de facto standard found on the latest generation of laserdiscs, cinemas,

and DVD films because of its audio coding technique that makes it capable of delivering

high-fidelity audio content. [2]

2.2 AC-3 Audio Coding Standard 2.2.1. History and Development

In 1987, the Federal Communications Commission (FCC) formed the Advisory

Committee on Advanced Television Service (ACATS) in the United States.[6] ACATS

formally started the High Definition Television (HDTV) standardization process with the

aim of creating a an excellent multi-channel audio format for HDTV sound.

Dolby AC-1, a low-cost delta-modulation based coding technology was

developed. By 1989, advances in the audio coding technology allowed the development

of AC-2, a higher quality audio coding standard with reduced bit-rate. [6]

A real-time implementation of AC-3 was first conducted in multiple DSP cards.

By 1991, Star Trek VI became the first AC-3 encoded film. This multi-channel audio

compression standard was accepted by ATSC in 1994.

2.2.2. AC-3 Compression Features

One of the key features of the AC-3 audio standard is the use some very

sophisticated psychoacoustic models which allow channels to be combined and

separated. By using a global bit allocation technique, it allows for any channel to borrow

bits which are not being used.

It has been designed to take maximum advantage of human auditory masking in

that it divides the audio spectrum of each channel into narrow frequency bands of

different sizes optimized with respect to the frequency selectivity of human hearing. This

makes it possible to sharply filter coding noise so that it is forced to stay very close in

frequency to the frequency components of the audio signal being coded. By reducing or

eliminating coding noise wherever there are no audio signals to mask it, the sound quality

of the original signal can be subjectively preserved. [3]

AC-3 provides only full range channels so the sounds are much better in terms of

quality and allows monophonic up to 5.1 audio channels to provide the necessary

channels needed for a digital film audio system. The configuration for a 5.1 channel setup

is composed of five full bandwidth channels: Left, Right, Left Surround, Right Surround,

Center, and the Subwoofer is shown in Figure 2-1. Details of the AC-3 audio coding

standard are also shown in the table below. [4]

Figure 2-1 – AC-3 5.1 channel configuration

General Characteristics of AC-3 Audio Standard

Sample frequency 32 kHz, 44.1kHz, 48 kHz

Bit Depth 16 – 24 bits

Bit Rate (B) 32 – 640 kbps

Frame Size 1536 samples

Compression 10:1

DVD Characteristics of AC-3 Audio Standard

Maximum Sampling Frequency 192 kHz

Maximum Samples per second 192,000

Maximum Bit Depth 24-bits

Table 2-2 – AC-3 Characteristics

2.2.3. AC-3 Comparative Advantages

Evaluating audio compression is complicated because there is no objective quality

parameter. Instead, comparison of AC-3 with two other popular digital audio formats, CD

Quality (PCM) and MPEG Layer III (MP3) is shown in the Table 2-3.

RIGHT

SURROUND

LEFT

SURROUND

RIGHT LEFT

CENTER

(SUBWOOFER)

CD Quality MPEG Layer III* AC-3*

Precision Sampling Accuracy

(Bits/sample/channel)

16-bit 16-bit 24-bit

Gradiation Levels 65,536 65,536 16,777,216

Rate Sampling Rate ( Freq ) 44.1kHz 44.1 kHz 96 kHz

Samples per second 44,100 44,100 96,000

Bit Rate in bits/sec 1,411,200 128,000 192,000

Bit Rate in Kbytes/sec 176 16 24

Size MB/min 10 1 1.5

Compression 1:1 1:12 1:10 * Most commonly used configuration

Table 2-3 - Compares Attributes of AC-3 versus CD audio and MPEG Layer III

Precision values clearly show that AC-3 has a more accurate signal representation

in Figure 2-2. The 24-bit depth allows it to have 256 times more gradiation levels than

the CD quality. Despite of this, AC-3 can still compress audio data by a factor of 10 due

to its very high compression technique. Although this is not evident in stereo mode (since

AC-3 is designed to be most advantageous in multi-channel configurations), its

compression factor is still comparable to MPEG Layer III.

Figure 2-2 – Graphical Comparison of CD Audio with AC-3

2.2.4. AC-3 Bit Stream

An AC-3 Bit Stream is composed of a series of frames representing a constant

time interval of 1536 PCM samples across all coded channels. Each frame is an

independent entity and no data are shared with previous frames aside from the inherent

transform overlap. The frame has a fixed size and depends only on the sample rate and

coded data rate. It consists of 6 audio blocks with 256 samples each. The structures of the

AC-3 Frame and Audio Block are shown in Tables 2-4 and Figure 2-5.

SYNC CRC1 SI BSI AB0 AB1 AB2 AB3 AB4 AB5 AUX CRC2

SYNC It maintains synchronization with the encoder / decoder.

CRC1 and CRC2 These are means of error detection.

SI and BSI The Sync Information (SI) and Bit Stream Information (BSI) include

sample rate, data rate, and number of coded channels.

AB0-AB5 These are the 6 audio blocks, each representing 256 PCM samples

per coded channel.

AUX optional aux data for embedding private control or status

information

Table 2-4 – AC-3 Frame Structure Block

Switch

Flags

Dither

Flags

Dynamic

Range

Control

Coupling

Strategy

Coupling

Coordinates

Exponent

Strategy

Exponents Bit

Allocation

Parameters

Mantissa

Table 2-5 – AC-3 Audio Block Structure

2.3 AC-3 Encoding Algorithm

The AC-3 encoding algorithm is composed of five major blocks as shown in

Figure 2-7. These are the Analysis Filter Bank, Spectral Envelope Encoding, Encode Bit

Allocation, Mantissa Quantization, and Frame Formatting and Bitstream Packing. The

block diagram below shows the AC-3 encoding process.

Figure 2-7 – AC-3 Encoder Block Diagram

2.3.1. Analysis Filter Bank

This block is subdivided into two smaller blocks which are the frequency domain

transformation and the block floating points as shown in Figure 2-8.

Analysis Filter Bank

Mantissa Quantization Spectral Envelope Encoding

Exponents

Encode Bit Allocation

PCM time samples

Frame Formatting and Bitstream Packing

Quantized Mantissa

Mantissa

Encoded Spectral Envelope

Encoded AC-3 bit stream

Figure 2-8 – Analysis Filter Bank Block Diagram

Frequency Domain Transformation using MDCT

The PCM time samples are best examined in the frequency domain due to the

frequency masking properties of human hearing. To transform the signal from a sequence

of PCM time samples to a sequence of frequency coefficient blocks, a 512-point

Modified Discrete Cosine Transform (MDCT) with 50% overlap is first performed.

The result is then multiplied by a time window to transform the input signal to

frequency domain. This MDCT is based on the idea of Time Domain Alias Cancellation

(TDAC) introduced by Princen and Bradley. [11] Normally, the analysis filter bank uses

the 512-point MDCT (long transform). But in the event of transient signals, this method

can be improved by using two 256-point transforms (short transforms) instead.

The 512 x 256 matrix that transforms the 512 windowing samples results in 256

frequency coefficients. The equation of this matrix is shown below:

cos( (2 1)(2 1_ (2 1))1024 4

512 256

nkL n k k

where L x matrix

nk each entry of L

π π+

+

−

< > = + + + +

=

=

The 256 x 128 matrices that transforms the 512 windowing samples results in two

sets of 128 frequency coefficients. The equations of these matrices are shown below:

1

1

1

cos( (2 1)(2 1))512

256 128

nkS n k

where S x matrix

nk each entry of S

π+

+

+

< > = + +

=

=

2

2

2

cos( (2 1)(2 1) (2 1))512 2

256 128

nkS n k k

where S x matrix

nk each entry of S

π π+

+

+

< > = + + + +

=

=

PCM time samples

Analysis Filter Bank

Frequency Domain

Transformation

Block Floating-Point Mantissa Exponent

Block Floating-Point

The input to this block is the set of all transform coefficients that have been

computed in the frequency domain transformation block. The floating point block simply

breaks down each of the frequency transform coefficients into binary exponent and

mantissa parts which will be analyzed separately in the succeeding blocks. [1]

2.3.2. Spectral Envelope Encoding

The Spectral Envelope Encoding involves two main processes, the power spectral

mapping and frequency banding. The exponents are first encoded according to time and

frequency resolution where they are mapped to the power spectrum so that the

computation of this spectrum can be simplified.

The frequency banding then maps the MDCT frequency domain to Fourier

Frequency domain where the psychoacoustic model is used to determine the perceptual

resolution.

Figure 2-9 – Spectral Envelope Encoding Block Diagram

2.3.3. Encode Bit Allocation

The goal of bit-rate reduction is to remove bits from a representation of an audio

signal in a manner that is inaudible to humans. The bit allocation block of the AC-3

coding standard uses the spectral envelope to determine the bit allocation required to

encode the individual mantissa. This block performs a convolution of the power spectral

density with the spreading function matching the ear’s masking curve. The bit allocation

block can be subdivided into smaller blocks as shown in Figure 2-10 below. [1]

Figure 2-10 – Encode Bit Allocation Block Diagram

Bit

Assignment

Transform

Coefficient

Exponents

Spectral Envelope Encoding

Power Spectrum

Mapping

Frequency Banding

Power

Spectral

Density

Encoded Spectral Envelope

Encode Bit Allocation

Spreading

Function

Hearing

Threshold

Masking

Comparison

Power

Spectral

Density

There are two broad classes of bit-allocation strategy. These are the forward

adaptive bit allocation and the backward adaptive bit allocation. AC-3 uses hybrid

forward/backward bit allocation, a fusion of these two methods. [1]

Forward Adaptive Bit Allocation

This is a method where the encoder may precisely calculate an optimum bit

allocation and explicitly code this allocation into the bit stream. It is the most accurate

allocation technique since the encoder has full knowledge of the input signal. Also, since

the psychoacoustic model is in the encoder itself, this can be changed without affecting

the installed encoders. The block diagram is shown in Figure 2-11.

However, there is a need to utilize a portion of the available bit-rate to deliver the

explicit bit allocation to the decoder. Transient conditions require fine time resolution

while steady state conditions require fine frequency resolution. These improved

resolutions require higher allocation in the data rate. Thus, forward adaptive puts

practical limitation on performance at very low bit rates.

Figure 2-11 – Forward Adaptive Bit Allocation Encoder Block Diagram

Backward Adaptive Bit Allocation

This is a method where the encoder calculates bit allocation from the coded audio

data without explicit information from the encoder. It does not require utilization of a

portion of the available bit-rate, thus all of the bits can be allocated to audio coding. It is

more efficient in transmission and allows the bit allocation to have superior time and

frequency resolution. The block diagram is shown in Figure 2-12.

However, the bit allocation must be calculated in the decoder from the

information contained in the bit stream, thus of limited accuracy and may contain small

errors. Also, psychoacoustic model may not be updated since the bit allocation algorithm

in the encoder is fixed.

Bit Allocator

Filter Bank Quantize

Multiplex Input signal

Bit allocation

Coded bit stream

Figure 2-12 - Backward Adaptive Bit Allocation Encoder Block Diagram

Hybrid Forward/Backward Bit allocation

The Hybrid Forward/Backward Bit allocation is the method implemented by the

AC-3 encoding algorithm. It uses the core backward adaptive bit allocation process found

in both the encoder and the decoder. This core routine is accurate and based on the

psychoacoustic model which has assumptions on the masking properties of signals. The

block diagram is shown in Figure 2-13. The input to the core routine is a spectral

envelope which is part of the encoded audio. In AC-3, the spectral envelope has

time/frequency resolution equal to the analysis filter bank.

Figure 2-13 – Hybrid Forward/Backward Bit Allocation Encoder Block Diagram

2.3.4. Mantissa Quantization

The results of the parametric bit allocation model are used along with the raw

mantissa to perform the mantissa quantization. The mantissas are quantized with a

variable number of bits based on the results of the bit allocation block.

The resulting values in this quantization block are not just composed of a

specified number of significant bits. The mantissa values are scaled and offset to provide

zero-centered, equal-width and symmetrical quantization levels. [5]

Encode Spectral Envelope

Filter Bank Quantize

Core Bit Allocator

Input

signal

Bit allocator Multiplex

Bit Allocation

Side Information

Encode

Spectral

Envelope

Filter Bank Quantize

Multiplex

Input

signal

Bit allocator

Encoded Spectral

Envelope Coded

Bit-stream

Quantized

Samples

Coded

Bit-stream

2.3.5. Frame Formatting and Bit Stream Packing

The frame formatting and bit stream packing is the final stage in the AC-3

encoding algorithm. All information in each of the six blocks is placed in a series of array

and scalar values.

This information includes the bit allocation information, exponents, mantissas,

coupling coefficients and dither flags. [5] This data packing stage places all information

in a single block along with all the necessary data such as the synchronization, header,

and wrapper information. The data is coded logically for the decoder to easy unpack the

bit stream data.

2.4 AC-3 Decoding Algorithm

The AC-3 decoding algorithm is composed of five major blocks as shown in

Figure 2-14. The major blocks are basically the same as those in the encoding process

implemented inversely. These are the Frame De-Formatting and Bit Stream Unpacking,

Spectral Envelope Decoding, Decode Bit Allocation, Mantissa De-quantization, and the

Synthesis Filter Bank. The block diagram of the decoding algorithm is shown below:

Figure 2-14 - AC-3 Decoder Block Diagram

2.4.1. Frame De-Formatting and Bit Stream Unpacking

The AC-3 Frame De-Formatting block shown consists of frame synchronization,

error detection and frame de-formatting stages. The frame synchronization ensures that

the decoder maintains the sync with the incoming input data stream. [7] The encoded

digital audio input enters an input buffer before proceeding to the error detection stage.

Each of the decoder input data block is checked in the error detection stage for

consistency. In the case that an error is found and it cannot be resolved, the last known

correct block can be used as a substitute for the erroneous block. The substitution can be

Frame De-Formatting and Bit Stream

Unpacking

Mantissa De-Quantization Spectral Envelope Decoding

Encoded Spectral Envelope

Decode Bit Allocation

Encoded AC-3 bit stream

Synthesis Filter Bank

Mantissa

Quantized Mantissa

Exponents

PCM Time Samples

done several times until a consistent block is found, unless there are extended error

conditions which forces the decoder to mute or revert to analog. [5]

After the synchronization and error checking, the data can now be unpacked. This

process is simply a reverse of the frame formatting stage. All audio data information are

taken out to recover the bit information.

2.4.2. Spectral Envelope Decoding

The purpose of the spectral envelope decoding block is to recover the exponents

from the original encoded data input after it has undergone the frame de-formatting stage.

This will allow the data to be analyzed together with the de-quantized mantissa in the

synthesis filter bank to get the original PCM samples.

2.4.3. Decode Bit Allocation

The result of the decode bit allocation block together with the quantized mantissa

are analyzed to get the raw mantissa information. This block uses transmitted

intermediate result for less decoding time. It also allows modification of the derived bit

allocation for computation of each channel one at a time.

2.4.4. Mantissa De-Quantization

After the decoded bit allocation process, the mantissa is recovered from the

quantized state. This is done by using the specified information on the size of each

mantissa which can be taken from the decoded bit allocation output.

2.4.5. Synthesis Filter Bank using IMDCT

This is the final stage in the AC-3 decoding process. Before the synthesis filter

bank takes place, data is first converted to fixed point. This means that the mantissa and

exponent are combined to reconstruct the original frequency coefficients. Each of the

channel’s recovered transform coefficients are then inversed transformed back to time

domain using the Inverse Modified Discrete Cosine Transform (IMDCT), windowed and

overlap added to produce the original PCM time samples.

The Synthesis Filter Bank is represented by the following equations:

1

0

'( , ) ( , ) cos[ (2 1)(2 1) (2 1) ]4 4

M

k

X m n Y m k k n kM

π π−

=

= + + + +∑ n = 0,1,… 2M-1 (3)

'( ) ( ) '( 1, ) ( ) '( , )x n h n M X m n M h n X m n= + − + + n = 0,1,… M-1 (4)

where:

x’(n) = reconstruction signal from the synthesis filter bank

h (n) = window function

2.5 Related Works This project intends to implement the AC-3 audio coding standard by reviewing related

studies on filters and fast algorithms for efficient implementation. Comparison of filter

bank designs will be the main focus of this project.

2.6.3. The ATSC Standard: Digital Audio Compression (AC-3), Revision A

For technical guidelines on AC-3 encoding and specifications, the ATSC

Standard: Digital Audio Compression Revision A will be used. The AC-3 bit stream is

specified mainly by the syntax and decoder processing, thus the encoder is not precisely

defined. The only normative requirement on the encoding algorithm is that it is able to

produce a bit stream that follows the AC-3 syntax. ATSC documentation will be checked

for consistency of the encoder implementation.

2.6.4. FFmpeg Multimedia System

For the source code reference, the AC-3 encoder included in the codec library of the

FFmpeg project will be used. FFmpeg Multimedia System is a complete solution to

record, convert and stream audio and video. It is a trademark of Fabrice Bellard,

originator of the FFmpeg project and is an experimental and developer-driven project.

However, there are no formal releases yet.

The project is made of several components:

• ffmpeg – command line that converts video format to another

• ffserver – http multimedia streaming server for live broadcasts

• ffplay – simple media player

• libavformat – library containing parsers and generators for all common

audio/video formats

• libavcodec – the leading audio/video codec library that contains all

encoders/decoders. Most of codecs were developed from scratch to ensure quality

performances and high code reusability.

It is developed under Linux but it can be compiled under most operating system including

Windows.

Chapter 3

Methodology

The overview of the project is shown in Figure 3-1. For the first part, a reference

code was used which was modified to create a standard encoding algorithm. Different

designs were then implemented to come up with modified encoding algorithms. Finally,

quality performance of these encoder designs were then compared and analyzed using

different objective and perceptual tests to arrive at an optimum code which will be

selected among all of the implementations.

3.1 Design The AC-3 encoder consists of the following information:

• AC3_encode_init – sets the correct parameters for the AC-3 encoder

• AC3_encode_close – outputs the correct AC-3 bit stream

• AC3_encode_frame – contains the actual AC-3 encoding processing

The main encoding process takes place in the AC3_encode_frame. It contains several sub

functions that perform the different encoder processing requirements which can be

summarized in Figure 3-2. These include:

• mdct512 – calculates the MDCT of the 512 input time samples

• compute_exp_strategy– along with its sub blocks, this computes the exponent

strategy that will be used by the encoder

• compute_bit_allocation – along with its sub blocks, calculate the number of

bits needed by the encoder using mantissa information

• output_frame_header, output_frame_end, output_audio_block – frame

packing and bit stream formatting

Figure 3-1 AC-3 Encode Frame

Since the project deals with comparing different filter bank designs, it is

necessary that the other parts of the encoder will not be modified so as not to affect its

performance. Therefore, the different designs directly refer to the filter bank

implementations. As mentioned previously, the AC-3 filter bank uses an oddly-stacked

TDAC. The general equation that characterizes TDAC is shown below:

( ) ( )( )

( )( )

0

0

cos ( ) 1 cos2 2

sin ( ) 1 sin2 2

( )

( )

cos( ) sin( )2 2

k k

n

k

n

k

m mKX m x n h P n w n n

m mKx n h P n w n n

where K blocksize

x n time domain sequence

X m frequency data of band k in time block m

m mand swit

π

π

π π

∞

=−∞

∞

=−∞

= − + − +

+ − + − +

=

=

=

=

∑

∑

( )( ) ( )( )0 0

0

cos sin

( ) & ( )

k k

ches deciding which path according to block number

w n n and w n n analysis and synthesis filters

n phase delay

h n f n windows with size P

+ + =

=

=

By setting wk = (2 ( 1/ 2) )k Kπ + , replacing –r=mK/2-n and performing deductions, we

can rewrite the equation as a general form of MDCT.

exponent_min

output_frame_header

encode_exp

compute_exp_strategy

compute_bit_allocation

mdct512

output_frame_end

output_audio_block

calc_exp_diff

bit_alloc_masking

bit_alloc

compute_mantissa_size

AC3_encode_frame

The analysis filter bank is the processing of 512-time sample from time to

frequency domain where the current 256 input time samples are concatenated with the

256 time-sample of the previous set. The filter bank is completed in two major processes:

windowing and MDCT implementation.

The PCM samples are windowed through a normalization procedure by using a

Kaiser-Bessel window with 50% overlap between adjacent blocks. The Kaiser-Bessel

window can be described as:

0

0

[ , ]

[ ] , 02

[ , ]

n

p

KBD Left n

p

w pN

W n n

w p

α

α

=

−

=

= ≤ <∑

∑

[ ]

2/ 4

1.0/ 4

N where [ , ] , 0 n

2

o

o

n NI

Nw p

I

πα

απα

− −

= ≤ ≤

2

0

and( / 2)

[ ]!

k

o

k

xI x

k

∞

=

=

∑

For AC-3, α =4. The window characteristic described above is shown graphically

in Figure 3-2. The figure represents the transform window sequence whose values are

specified by the ATSC standard shown in Table 3-1.

Figure 3-2 AC-3 Window Sequence

Due to the window specification, the design modification now depends on the

type of MDCT implementation. This can be classified as (1) Direct (2) Indirect (3)

Recursive. Direct method, or traditional method, is the straightforward execution of the

MDCT block. The indirect method refers to the use of fast algorithms such as Fast

Fourier Transforms (FFT). The third method simply refers to algorithms that are

recursive in nature.

Table 3-1 AC-3 Transform Window Sequence (w[10A+B])

3.1.1 Direct Method

Given the time domain signal samples in a signal block ( ) x n where n=0 to N-1

windowed by an N sample real Kaiser-Bessel derived window w(n) to obtain x(n) , the

complete MDCT of x(n) is:

1

0

2 2( ) ( ) cos[ (2 1)(2 1) (2 1)(1 )] k=0,1,2,...(N/2)-1

4 4

1 for the first short transform

0 for the long transform

1 for the second short transform

N

D

n

X k x n n k kN N

π πα

α

−

=

= − + + + + +

−

= +

∑

Removing the scale factor and setting α =0 simplifies the MDCT to:

1

0

(2 1 / 2)(2 1)( ) ( )cos k=0,1,2,...(N/2)-1

2

N

n

n N kX k x n

N

π−

=

+ + +=∑

3.1.2 Indirect Method using DCT-IV

The direct or traditional method can be accomplished by K/2 points DCT-IV by

using a series of trigonometric identities:

If cos( + )=cos cos sin sin ,

cos (2 1) 2(2 1 ) 1 cos (2 1)(2 1)4N 4

sin (2 1) 2(2 1 ) 1 sin (2 1)(2 1)4N 4

X(m,n) input mth block signal consisting of 256

k N n k nN

k N n k nN

α β α β α β

π π

π π

−

+ − − + = − + +

+ − − + = + +

=

D

new input points and 256 old input points

Y(m,k) = output X ( )

h(n) = window function

x(n) = X(m,n)h(n)

The MDCT of x(n) can be rewritten as:

( ) ( ) ( , ) cos 2(2 1)(2 1) cos (2 1)4 4

D

k

X k h n X m n n k kN

π π

= + + +1

0

1

0

sin 2(2 1)(2 1) sin (2 1) k=0,1,2,...(N/2)-14 4

( , ) cos (2 1) ( ) ( , )cos (2 1)(2 1)4 2

-sin (2 1)4

N

n

N

n

n k kN

Y m k k h n X m n n kN

k

π π

π π

π

−

=

−

=

− + + +

= + + +

+

∑

∑1

0

/ 2 1

0

( ) ( , ) sin (2 1)(2 1) k=0,1,2,...(N/2)-12

( , ) cos (2 1) [ ( ) ( , ) (4

N

n

N

n

h n X m n n kN

Y m k k h n X m n h N

π

π

−

=

−

=

+ +

= + −

∑

∑/ 2 1

0

1 ) ( , 1 )]cos (2 1)(2 1)2

-sin (2 1) [ ( ) ( , ) ( 1 ) ( , 1 )] sin (2 1)(2 1) k=0,1,2,...(N/2)4 2

N

n

n X m N n n kN

k h n X m n h N n X m N n n kN

π

π π−

=

− − − − + +

+ + − − − − + +∑ -1

The final analysis filter bank equation can be recognized as a DCT-IV whose

implementation structure is illustrated above. This implementation structure is illustrated

in Figure 3-3.

Figure 3-3 256-point DCT-IV Implementation Structure

0 256 0

1 DCT 1

: :

254 254

255 255

z-1

z-1

z-1

z-1

z-1

h(0)

z-1

z-1

z-1

h(1)

h(254)

h(255)

-1

-1

-1

-1

Co Y(m,0)

C1 Y(m,1)

C254 Y(m,254)

C255 Y(m,255)

x(n)

3.1.3 Indirect Method using FFT Rewriting the direct implementation of the MDCT gives the form shown by the equation

below:

0

2 1 2 21( )2 2

0

[ ] Re [ [ ] [ ] ]

n knNj n k j jN N N

n

X k e x n w n e e

π π π−− + − −

=

=

∑

This can be implemented using a series of steps: pre-twiddle, N-point FFT, post-twiddle.

The pre-twiddle step is the complex multiplication of the input samples by

2

2

nj

Ne

π−

. A 512-

point FFT is then performed on the pre-twiddled data. The post-twiddle step then takes

the real part of the transformed data and multipliying it by a factor 0

2 1( )

2j n k

Ne

π− +

.

( ) ( )( ) ( ) ( )( )2 ( 1 / 8) /

2 ( 1 / 8) /

( ' )

'

( 3 / 4) 0 k n/4-1'( )

( / 4) n/4 k n-1

' 2 ' 2 1 ' / 2 2 ' / 2 2 1 , 0 k n/4-1

'

(2 ) Re( '( ))

(2 1) Im( '

m k

m m

k

i k n

k k

i m n

n

FFT f

F F e

f k nf k

f k n

f f k f n k i f n k f n k

f f e

F

F m F m

F m F

π

π

+

+

=

=

− + ≤ ≤=

− ≤ ≤

= − − − + + − − + ≤ ≤

=

=

+ =

/ 4 1

0 to n/4-1)

m

m− −

=

3.1.4 Recursive Method The direct method can also be implemented recursively. One traditional recursive method

is as follows:

Let ' ( / 4) and '' ( 3 / 4)n n N n n N= + = −

[ '] [ ' / 4] for n'=N/4,...N-1

[ ''] [ '' 3 / 4] for n''=0,...N/4-1

y n x n N

y n x n N

= −

= +

The direct implementation can then be written as,

/ 2 1

0

1[ ] ( [ ] [ 1 ])

(2 1)2cos

2

(2 1)( 1)[ ] [ ]cos

N

n

u n y n y N nn

N

n kU k u n

N

π

π−

=

= − − −+

+ += ∑

[ ] [ 1] [ ]X k U k U k= + +

This previous equations also represents the DCT-IV. By applying trigonometric

identities, we get

/ 4 / 4 1 / 4 2

/ 4 / 4 1 / 4 2

[ ] [ ] ( 1) [ / 2 1 ]

[ ] cos ( [ ] [ 1]) 2cos [ ] [ ]2

[ ] sin ( [ ] [ 1]) 2cos [ ] [ ]2

k

k

N k k k N N

k

N k k k N N

p n u n u N n

D k p j p j D k D k

S k p j p j S k S k

θθ

θθ

− −

− −

= + − − −

= − − + −

= − − + −

Finally, the output X[n] can be derived by using these equations:

/ 2

/ 4 1 / 4 1

( 1) / 2

/ 4 1 / 4 1

[ ] ( 1) ( [ ] [ 1])for k is even

[ ] ( 1) ( [ 1] [ ])for k is odd

k

n n

k

n n

X k D k S k

X k D k S k

− −

−

− −

= − + +

= − + +

Clenshaw’s Recurrence Formula

The proposed algorithms based on a traditional recursive implementation can be

formally obtained using Clenshaw’s recurrence formula which is an elegant and efficient

way of evaluating the sum of the coefficients.. The formula states that the sum of a given

function f(x) can be obtained using this equation:

1 1 2 2 1 3( ) ( ) ( 1, ) ( ) ( )N n N N N N

f x c F x N x F x y F x yβ− − − − − −= − − −

Applying it for the MDCT implementation, let 1

2k k

M

πθ

= +

and define

2 1

1 2

0

( ) 2cosn k N N

a a

a x n a aθ− −

− −

= =

= + −

( ) ( ) ( )1 2 2 1 3( ) ( 1) N k N k N N k NX k x N F F a F aθ θ θ− − − − −= − + −

Appplying mathematical transformation to the direct method finally gives the output X(k)

as:

1 2( ) cos ( 1) cos ( 1)2 2

k k

N NX k M a M a

θ θ− −

= − − + +

The implementation structures of the traditional recursive transform and the recursive

solution using Clenshaw’s recurrence formula are shown in Figures 3-4(a) and 3-4(b)

respectively.

(a)

(b)

Figure 3-4 (a) Implementation structure for (a) traditional recursive method (b)

recursive based on Clenshaw’s recurrence formula

3.2 Implementation

FFmpeg Multimedia System was the main reference used for implementing the

designs using the C programming language. The code modification was done in an IDE

environment using Microsoft Visual Studio 2005.

However, the reference can only be compiled in Windows using selected software

that can complete the actual compiling and producing of the win32 binaries. Thus, the

compilation was done in a command line Linux environment using the MingGW and

Minimal SYStem (MSys) system with an integrated gcc compiler. MSys is a branch of

Cygwin used in Windows OS for creating configuration and packages. It also offers user

environment for MinGW development and allows users of MinGW version of GCC to

port and build packages in a GNU familiar way without the UNIX complexities brought

about by Cygwin.

The implementation procedure involves a direct application of the different

methods for the MDCT processing block.

3.3 Testing

There were initial tests done to evaluate the performance of the designs. A

preliminary listening test was already implemented to determine the test samples to be

used for the objective test. A formal listening test will be done during the last phase of the

project.

Figure 3-5 Flowchart of the Testing Procedure

3.3.1 Preliminary Test

The main objective of the preliminary test was to determine the type of audio

samples that are best suited for the objective tests. Different types of audio vary in

frequency contents. Thus to produce rational results for the objective analysis, worst case

scenario must be considered. This scenario implies that the encoded audio sample should

be far from the original PCM audio. If the difference between the quality of the encoded

audio sample and the original audio is almost unnoticeable, we can immediately expect

that the results will be almost identical.

The International Telecommunication Union [ITU-R BS.1284] provides the

appropriate guidelines and scale to be used for quality assessment. In determining the

relative difference of two samples with quality far from each other, the seven-grade

comparison scale shown in the figure below is recommended.

Grade Comparison

3 Much Better

2 Better

1 Slightly Better

0 The Same

-1 Slightly Worse

-2 Worse

-3 Much Worse

The system used was the Multiple Stimulus with Hidden Reference and Anchors

(MUSHRA) method. It is a double blind multiple stimulus test method with hidden

Preliminary

Test

Objective Tests Formal

Listening Test

Traditional

and Modified Designs

Listening and

Objective Test Results

reference. This setup involves a reference audio that can be compared against multiple

test samples, wherein one of the test samples is the actual same copy of the reference

sample unknown to the listener. Ideally, the user must be able to give a grade of zero

since one of the test samples is its duplicate.

For this project, the reference audio used was the original PCM audio. One of the

test samples was a copy of the original and the rest of the test samples were the different

designs used for implementing the AC-3 encoding algorithm.

The preliminary listening test was then performed using three different PCM

audio (plain speech, a pop music, and an instrumental song) using randomly selected AC-

3 encoder designs (direct method, MDCT using DCT-IV and MDCT using FFT).

In addition to this, preliminary objective test was done to assess the frequency

response of the selected audio.

3.3.2 Objective Tests

After getting the results of the preliminary listening test, the audio sample was

selected and the objective tests were performed using MATLAB 7.0. However, since

MATLAB is unable to directly read AC-3 formats, the encoded audio sounds were first

recorded to raw PCM format that MATLAB recognizes.

The software used was Audacity, an open source program capable of recording

sounds without the need for microphone and speaker set-up. This ensures that there is no

degradation in audio quality and the characteristics of the encoded audio format can truly

be analyzed.

Moreover, stereo separation into left and right channels was done in order to study

the correlation and frequency response of the encoded AC-3 audio. The autocorrelation

of the original PCM audio was plotted against the correlation between the original audio

and each design. This will illustrate whether or not the encoded AC-3 audio and the

original PCM are highly correlated.

The frequency response of each design was then determined to verify if there are

noticeable differences compared to that of the original PCM audio. The flowchart below

summarizes the procedure done for the objective tests.

Figure 3-6 Flowchart of the Objective Test Procedure

3.3.3 Formal Listening Test

Formal listening test is considered the ultimate measurement of audio quality. The

test was done in a similar manner to that in the preliminary listening tests.

However, the scale used for the formal listening test is the five-grade impairment

scale. This is defined by the [ITU-R BS.562-3] as the scale used for systems with small

impairments. This is related to the five-grade quality scale as shown below. The test

method used is still a double blind multiple stimulus test method with hidden reference.

Grade ITU-R Grade

5 Imperceptible

4 Perceptible, but annoying

3 Slightly annoying

2 Annoying

1 Very annoying

3.3.4 Playback

The open source encoder AC3Filter developed by Alexander Vigovsky on August

2006 [9] will serve as the AC-3 main decoder. AC3Filter is a high quality free

DirectShow AC-3 filter that allows decoding of videos with AC3-encoded surround

audio.

The source is composed of the filter and an audio processing library. The filter

implements all interfaces and logic required by DirectShow while the audio processing

Objective Analysis

- frequency response and correlation

Objective Test Results

Channel Separation

- to left and right channels in MATLAB

AC-3 recording

- to PDCM audio using Audacity

Traditional and Modified Designs

library implements all audio decoding and processing algorithms. It supports

configuration settings that allow control of audio sound intensity and can decode AC-

3/DTS/MPEG1/2 Audio Layer I/II formats. Some of the features include decomposition

to six channels, full information about the audio track format, per channel amplification

for all input/output channels and per channel delays.

3.3.5 Listening Conditions

The listening tests were performed with the listeners having direct control on the

listening conditions. The direct control includes being allowed to repeat the audio

samples and change the audio volume level for. They were asked to use headphones

throughout the duration of testing.

Chapter 4

Results and Analysis 4.1 Objective Measurements

The preliminary objective test done showed that the different encoder designs

produced an encoded audio with frequency characteristics similar to that of the original

PCM input audio.

The test was done on three different audio inputs namely pop music, pure speech, and

an instrumental song. Initially, three encoder designs were considered. These are the

direct implementation, and two modified encoder designs. The first modified design is

the filter bank implementation based on DCT-IV and the other one is based on FFT. The

frequency responses of the designs show minimal differences. The low frequency

components of the encoded audio show unnoticeable changes from the original input

PCM but some high frequency artifacts were present after the encoding process. The

encoder design with an MDCT implementation using FFT showed more visible artifacts

than the other designs. The frequency response of the original instrumental audio PCM

input (electric piano) is plotted in Figure 4-1 followed by those of the modified designs in

Figure 4-2.

(a) (b)

Figure 4-1 Frequency Response of the Original Input

for (a) Left (b) Right Channels

(c) (d)

(e) (f)

(g) (h)

Figure 4-2 Frequency Response of the Different Designs using:

(c) - (d) Direct Method , (e) –(f) Indirect Method DCT-IV ,

(g) - (h) Indirect Method FFT for both left and right channels

The crosscorrelation of the original input PCM and the encoded audio for each design

was also determined and is illustrated in Figure 4-3.

(a) (b)

Figure 4-3 Autocorrelation of the Original Input

for (a) Left (b) Right Channels

(c) (d)

(e) (f)

(g) (h)

Figure 4-4 Correlation of the Different Designs and Original Input PCM

using: (c) - (d) Direct Method , (e) –(f) Indirect Method DCT-IV ,

(g) - (h) Indirect Method FFT for both left and right channels

The results above show that there is a high correlation between the encoded audio and

the original input PCM. Though frequency response and correlation present a general

insight on the frequency components present in an audio sample and its correlation with

the original input, it shows little or no information on the quality of the encoded audio

aside from the noticeable appearance of frequency artifacts.

4.2 Audio Test Samples

The preliminary listening test done reveal that the listener was not be able to

recognize the impairments among the different designs immediately for ordinary pop

music, but it became more obvious when the input audio sample used contains high

frequency components, and thus, high pitch. This is in line with the result of the

frequency response mentioned earlier when frequency artifacts appear after encoding.

It is also more noticeable when the audio sample is made up of a single instrument or

speech. The ensemble of musical instruments masks the impairments brought about by

the encoder design. Table 4-1 shows the average grade given by 10 listeners.

Test Sample Encoder Design Arithmetic Mean

Pop Music Original -0.3333

Direct 0

Indirect using DCT 0.6667

Indirect using FFT 1.125

Speech Original 0.3333

Direct -1

Indirect using DCT -1.1111

Indirect using FFT -1.5556

Table 4-1 Result for the preliminary listening tests

Having realized this, the selections of critical material used are listed in Table 4-2.

The test samples are composed primarily of different musical instruments expect for

speech and pop music.

Input Test Samples

1. CLARINET

2. DRUMSET

3. GUITAR_CONCERT

4. GUITAR_ELECTRIC

5. PIANO_CONCERT

6. PIANO_ELECTRIC

7. POP MUSIC

8. SAXOPHONE

9. SPEECH

Table 4-2 List of critical materials to be used

Chapter 5

Project Schedule

5.1 Revised Gantt Chart

Week no. 01 02 03 04 05 06 07 08 09 10 11 12 13 14 15 16

A B C D E F G H

Tasks

A Implementation and Testing of the analysis filter bank

B Implementation and testing other encoder blocks

C Implementation and Testing of the 1st and 2

nd modified filter bank designs

D Implementation and Testing of the 3rd

and 4th

modified filter bank designs

E Listening tests and comparative analysis of the designs

F Testing of other optional AC-3 compression features

G Final Comparative analysis and Listening Tests

H Documentation

5.2 Halfway-Point Deliverables The standard integrated code, test results and documentation for each of the following

individual blocks in the encoder:

• Implementation of four different filter bank designs

• Objective test results

• Preliminary listening test results

5.3 Final Deliverables

Task

The final deliverables include four filter bank designs and analysis of AC-3 audio

compression feature. The comparative analysis of four different filter bank

implementations before the conclusion of the optimum final code will also be presented,

stating grounds for selecting the design. All functional and listening test results will also

be presented along with the full documentation of the project implementation.

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University, Taiwan.

[2] Digital Audio Formats. http://www.teamcombooks.com/mp3handbook/12.htm

Feb 10, 2007

[3] Dolby AC-3 Audio Coding. http://www.fedele.com/website/hdtv/dolbyac3.htm

Feb 10, 2007

[4] Dolby AC-3. http://www.mp3-tech.org.htm. Feb 10, 2007

[5] M. Davis. “The AC-3 Multichannel Coder”. Dolby Laboratories Inc., San

Francisco, 1993.

[6] C. Todd, G. Davidson, M. Davis, L. Fielder, B. Link, and S. Vernon. “AC-3:

Flexible Perceptual Coding for Audio Transmission and Storage”. Dolby

Laboratories Inc., San Francisco, 1994.

[7] A. Alvarez, S. George, H. Yang, and K. Das. “SGS-Thomson DSP D950-Core

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[8] Y. Chen, C. Tsai, and J. Wu. “Fast Time-Frequency Transform Algorithms and

their Applications to Real-Time Software Implementation of AC-3 Audio Codec”.

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[9] AC3Filter Project. http://ac3filter.net/ Feb 10, 2007

[10] AC3Decode. http://www.users.on.net/%7Ersobon/ac3dec.html Feb 10, 2007

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Institute of Electronic Engineering, Hangzhou China.

[12] S. Lee and C. Liu. “Transformation from 512-point transform coefficients to 256-

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