DIGITAL SIGNAL PROCESSING

LECTURE # 1: INTRODUCTION

Muhammad Rzi Abbasmuhammadrziabbas@uet.edu.pk

Department of Mechatronics and Control Engineering University of Engineering and Technology, Lahore

WHAT???

Digital

Signal

Processing

Digital Signal Processing

SIGNAL

A signal conveys information about the state or behavior of a physical system

It is a measured quantity that varies with time (or position)

Examples:

Voltage: Represented as a function over time -> 1D signal

Image signal: Represented as an intensity function of two spatial variables -> 2D signal

Video signal: A sequence of images spanning over a period of time -> 3D signal

SIGNAL

Information is always contained in some pattern of variation..

What did I just said?????

SIGNAL PROCESSING

Signal processing is concerned with the representation, transformation, and manipulation of signals and the information they contain.

TYPES OF SIGNALS

Continuous-Time (CT) or Analog signal:

Example: Voltage, Current, Speech signal, etc.

Discrete-Time (DT) signal:

Example: Daily stock market price, Daily average temperature, Sampled continuous signals

What type of signal our eyes are providing? Video is what type of a

signal?

IDENTIFY THE SIGNAL TYPE

Voltmeter Wall Clock

Thermometer

IDENTIFY THE SIGNAL TYPE

Population Data

Stock Market Data

IDENTIFY THE SIGNAL TYPE

Hourly Temperature Measurement Data

TYPE OF SIGNALS

So what about the word Digital???

What are digital signals???

What is sampling???

What is Quantization???

Why are you here???

Zain MehdiSticky NoteQuantization, in mathematics and digital signal processing, is the process of mapping a large set of input values to a smaller set such as rounding values to some unit of precision. A device or algorithmic function that performs quantization is called a quantizer. The round-off error introduced by quantization is referred to as quantization error.

Zain MehdiSticky NoteIn signal processing, sampling is the reduction of a continuous signal to a discrete signal. A common example is the conversion of a sound wave (a continuous signal) to a sequence of samples (a discrete-time signal).A sample refers to a value or set of values at a point in time and/or space.A sampler is a subsystem or operation that extracts samples from a continuous signal.A theoretical ideal sampler produces samples equivalent to the instantaneous value of the continuous signal at the desired points.

DISCRETE TIME SIGNAL PROCESSING (DTSP)

Discrete time processing of Continuous Signals

DIGITAL SIGNAL PROCESSING (DSP)

Digital signal processing is derived from DTSP

DIGITAL SIGNAL PROCESSING (DSP)

Converting analog signal into a digital signal

Perform signal processing operations in the digital form

Convert back the digital signal to analog one when necessary

Analog InputAnalog Filter

ADCDSP

ProcessorDAC

Analog Filter

Analog Output

WHY PROCESS THE SIGNALS DIGITALLY?

Digital data storage and transmission is more effective than in the analog form

Flexibility: Processing function can be modified or adjusted

Can implement very complex processing functions

Speed of digital operations tends to grow rapidly with the years of technical progress

A very high accuracy and reliability is possible

Dynamic range can be increased

Simultaneous (Parallel) processing

WHY DO DSP PROCESSORS NEED TO DO WELL? Most DSP tasks require:

Repetitive numeric calculations

Attention to numeric fidelity

Fixed- vs. floating-point

Standards

High memory bandwidth

Streaming data

Real-time processing

Processors must perform these tasks efficiently while minimizing:

Cost

Power consumption

Memory use

Development time

BENCHMARK

Implementation of Complex Block FIR Filter

DSP vs. High Performance CPU (lower is better)

EXAMPLE DSP APPLICATIONS Digital cell phones Automated inspection Vehicle collision avoidance Voice -over-Internet Motor control Consumer audio Voice mail Navigation equipment Audio production Videoconferencing Toys, games consoles Music synthesis, effects Satellite communications

Seismic analysis Secure communications Tapeless answering machines Sonar Cordless phones Digital cameras Modems (POTS, ISDN, cable, ...) Noise cancellation Medical ultrasound Patient monitoring RadarAnd many more to come..

SPEECH PROCESSING

Original

Down sampleHigh Pass Filter

Low Pass Filter

EQUALIZATION

Selectively enhance/attenuate some parts of the frequency spectrum

Applications

Coding & compression

Room simulation

Echo or chorus effects

SPEECH TRANSMISSION

IMAGE PROCESSING

IMAGE PROCESSING

SIGNAL INTERPRETATION

The objective of the processing is not to obtain an output signal but to obtain a characterization of the input signal

Example: Speaker Identification

Signal Interpretation

Attribute Matching

Database of Attributes

Attributes

SPEAKER

DISCRETE TIME SIGNAL (DTS)

Sequence: It is simply a function whose domain is the set of integers.

Practically such sequences may arise from periodic sampling of an Analog Signal.

x[n] = xa(nT) - < n <

T = Sampling Time, whiles its reciprocal is called Sampling Frequency.

DISCRETE TIME SIGNAL (DTS)

A sequence of numbers, x, in which nth number in the sequence is denoted by x[n]

x = {x[n]}, - < n <

Note: x[n] is defined only for integer values of n. Moreover, it is not correct to think that x[n] is zero for non-integer values of n

DISCRETE TIME SIGNAL (DTS)

We want to convert the following Analog Signal into a DTS

BASIC TYPES OF DTS

Unit Impulse Sequence or an Impulse

[n] = 0, 01, = 0

Unit Step Sequence

u[n] = 0, < 01, 0

BASIC TYPES OF DTS

Sinusoidal Sequence

x[n] = cos (won)

Exponential Sequence

x[n] = an

BASIC OPERATIONS

Ideal delay: A sequence y[n] is said to be a delayed or shifted version of a sequence x[n] if

y[n] = x [n-n0]

where n0 is an integer

BASIC OPERATIONS

Note that if n0 is negative the sequence will be shifted towards left by n0samples, corresponding to Time Advance

BASIC OPERATIONS

Sum Difference

y[n] = x1[n] x2[n]

Multiplication

y[n] = x1[n].x2[n]

BASIC OPERATIONS

x[n] via Impulse function

x[n] = = [][nk]

BASIC OPERATIONS

Unit Step Sequence

u[n] = [n] +[n1] + [n2]

u[n] = =0 [nk]

Impulse Sequence

[n] = u[n] u[n-1]

RESOURCES

Discrete-Time Signal Processing by Alan V. Oppenheim, Ronald W. Schafer & John R. Buck. 2nd Edition, Pearson Education Prentice Hall, 1999

https://groups.google.com/forum/#!forum/mct413_dsp

Lectures slides, assignments (computer/written), research papers, projects, lab manuals, and announcements will be uploaded to group repository and will be notified to all group members through email

REFERENCES

Chapter # 1, Discrete-Time Signal Processing by Alan V. Oppenheim, Ronald W. Schafer & John R. Buck. 2nd Edition, Pearson Education - Prentice Hall, 1999