Digital Signal Processing PROJECT...

Digital Signal Processing

PROJECT REPORT Amplitude Modulation – Single Sideband Signal Generation

Using TMS320C5515 eZDSPTM USB Stick

April, 28th 2014

Đại học Duy Tân

Khoa Điện – Điện tử

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Table of Contents

I) Table of Contents ..................................................... 1

II) Abstract .................................................................... 2

III) Introduction ............................................................. 3

1) MODULATION ............................................. 3

2) DOUBLE SIDEBAND MODULATION ............. 4

3) SINGLE SIDE-BAND (SSB) ............................ 5

a)The Benefits of SSB .................................. 6

b)The Cost of SSB ........................................ 6

IV) Related theories ....................................................... 7

1) FAST FOURIER TRANSFORM (FFT) .............. 7

2) HILBERT TRANSFORM ................................. 7

3) SINGLE SIDEBAND MODULATION ............... 8

V) Implementation ....................................................... 10

1) 1) MATLAB .................................................... 10

2) 2) TMS320C5515 eZDSPTM USB Stick ............ 13

VI) Conclusion ............................................................... 17

VII) References ............................................................. 21

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Abstract

This project studies one variant of Amplitude Modulation: Single Sideband (SSB) Modulation. In this report, we will discover the concept of amplitude modulation, double sideband and single sideband signals and their applications. We will then build a demonstration of SSB modulation using Matlab and TMS320C5515 eZDSPTM USB Stick Development Tool. The underlying theories used to build this demonstration are also explained in details.

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Introduction

1) MODULATION

In electronics and telecommunications, modulation is the process of varying one or more

properties of a periodic waveform, called the carrier signal (high frequency signal), with a

modulating signal (low frequency signal) that typically contains information to be

transmitted.

A modulator is a device that performs modulation. A demodulator (sometimes detector or

demod) is a device that performs demodulation, the inverse of modulation. A modem

(from modulator–demodulator) can perform both operations.

There are 2 kinds of modulation: digital and analog. In our group project, we only concern

about continuous wave analog modulation. Common analog modulation techniques are:

Amplitude modulation (AM) (here the amplitude of the carrier signal is varied in accordance to the instantaneous amplitude of the modulating signal)

o Double-sideband modulation (DSB) o Single-sideband modulation (SSB, or SSB-AM) o Vestigial sideband modulation (VSB, or VSB-AM) o Quadrature amplitude modulation (QAM)

Angle modulation o Frequency modulation (FM) o Phase modulation (PM)

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2) DOUBLE SIDEBAND MODULATION

Double sideband modulation is the original form of amplitude modulation, in which the modulating signal containing the message of interest is multiplied with the sinusoidal carrier signal of frequency wc for transmitting. This process results in two copies of the spectrum of the modulating signal in the DSB spectrum, one shifted to wc and the other shifted to - wc. The frequencies on either side of the carrier are called the sidebands. The bandwidth of a DSB signal is thus twice the bandwidth of the modulating signal.

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3) SINGLE SIDE-BAND (SSB)

Conventional AM transmission has several problems:

Bandwidth is wasted by having two identical side-bands on either side of the carrier The efficiency is limited to 33% to prevent distortion in the receiver when

demodulating. The carrier signal is present even if nothing is being transmitted

In radio communications, single-sideband modulation (SSB) or single-sideband

suppressed-carrier (SSB-SC) is a refinement of amplitude modulation that more efficiently

uses transmitter power and bandwidth. Amplitude modulation produces an output signal

that has twice the bandwidth of the original baseband signal. Single-sideband modulation

avoids this bandwidth doubling, and the power wasted on a carrier, at the cost of increased

device complexity and more difficult tuning at the receiver.

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a) The Benefits of SSB

By eliminating the duplicated side-band and carrier from transmission, the bandwidth has been reduced by half. By reducing the bandwidth transmitted, you may put double the number of channels (or stations) in the same frequency band.

Because the carrier if also filtered out, there is no transmission unless information is being sent. This is useful if you are trying to be covert. The efficiency is also improved considerably. In theory, since you are only transmitting side-band information then the efficiency is 100 %. In practice, including losses in the circuitry and antenna, a more typical efficiency would be 80 -> 95 %.

b) The Cost of SSB

To make the SSB system work, every receiver must now contain its own carrier oscillator. An oscillator that can cover the range of all possible frequencies in your band and be stable does not come cheaply. Therefore, SSB systems are usually limited to things that already are expensive and/or costly or situations where the improved performance is essential (like the military).

This is what the SSB transmitter looks like:

The SSB receiver looks like:

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Related theories

1) FAST FOURIER TRANSFORM (FFT)

In summary, the Fast Fourier Transform (FFT) is an algorithm to compute the Discrete

Fourier Transform (DFT) and its inverse. A Fourier transform converts time (or space) to

frequency and vice versa; an FFT rapidly computes such transformations by factorizing the

DFT matrix into a product of sparse (mostly zero) factors.

2) HILBERT TRANSFORM

In AC circuit theory we use complex exponentials to represent real sinusoidally varying quantities with the understanding that the real part of the complex exponential gives the physical quantity of interest. The analytic signal of a real function plays the same role for

more general waveforms. Given a real function f(t) with Fourier transform , the analytic signal fa(t) is defined by

This is just the inverse Fourier transform of the positive frequency part of F(w). The Fourier

transform of fa(t) is given by

The Hilbert transform of f(t) is defined to be the imaginary part of fa(t) and is denoted by

Thus

The Fourier transform of this relationship is

where is the Fourier transform of . Solving this yields

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3) SINGLE SIDEBAND MODULATION

For any signal g(t), let

be two complex-valued signals associated with g(t). The significance of these two signals can be seen from their Fourier transforms. We have

where u (f) is the unit step function, and, similarly,

Thus g+(t) has spectral components (equal to those of g(t)) at positive frequencies only, i.e., g+(t) has a right-sided spectrum. Similarly, g−(t) has spectral components (equal to those of g(t)) at negative frequencies only and hence has a left-sided spectrum. These spectra are illustrated in the following figure

It is now straightforward to express upper- and lower-sideband signals in terms of g+(t) and g−(t). Let g(t) be the modulating signal, assumed bandlimited to W Hz, and let fc > W be the carrier frequency. In the frequency domain, the upper sideband signal is given by

and the lower sideband signal is given by

as sketched in the figure below:

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It follows from the frequency-shifting property of the Fourier transform that

A similar derivation shows that

Thus we see that single-sideband modulation can be regarded and implemented as a form of quadrature amplitude modulation (QAM), with the modulating signal g(t) placed in the in-phase channel and the Hilbert transform of g(t) (or its negative) placed in the quadrature channel. A block diagram illustrating this approach is given in the following figure

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Implementation

1) MATLAB

In Matlab, we used another approach to the model presented above. This second method

uses Hilbert Transformer and Spectral Shifter and can be used interchangeably with the

first method. Later on when implement SSB modulation on TMS320C5515 eZDSPTM USB

Stick we will use the first method. This is to show the flexibility of implementing SSB

modulation, i.e. different models can be used depending on resources and tastes.

The SSB modulated signal is

where ma denotes the analytic signal and the Hilbert transform of m.

Note that this simple mathematical transformation returns the same final result as the first

method, yet now we have a different way to obtain it:

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Matlab code is as shown:

% Target frequencies

Fm = 400; % base frequency

Fc = 4000; % carrier frequency

Fs = 48e3; % sampling frequency

% Base sine signal

nsample = 4 * Fs / Fm;

n = 0 : nsample;

signal_m = sin(2 * pi * n * Fm / Fs);

% Number of samples

NFFT = 4096;

% Generate the double side band signal

carrier = sin(2 * pi * n * Fc / Fs);

xcarrier = exp(1i * 2 * pi * n * Fc / Fs);

dsbSig = signal_m .* carrier;

% Apply transformer, get the result

mc = hilbert(signal_m);

% Shift the signal frequency to desire Fc

mcm = mc .* xcarrier;

% Plotting the result

%Set axis limit

Xlim = [0 6];

Ylim = [-80 -20];

% Plotting the double side band

subplot (3,1,1);

periodogram(dsbSig, [], 4096, Fs);

title({'Double Side Band AM'});

set(gca,'XLim',Xlim,'YLim',Ylim)

set(gcf,'Color','white');

% Ploting the single side band obtain by hilbert

subplot(3,1,2);

periodogram(real(mcm), [], 4096, Fs);

title({'Single Side Band AM'});

set(gca,'XLim',[0 6],'YLim',[-80 -20])

set(gcf,'Color','white');

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Using the above Matlab codes, we obtain the result:

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2) TMS320C5515 eZDSPTM USB Stick

The the AIC3204_tone_headphone.c is modified as follows: /*

* Copyright 2010 by Spectrum Digital Incorporated.

* All rights reserved. Property of Spectrum Digital Incorporated.

*/

/*

* AIC3204 Tone

*

*/

#include "stdio.h"

#include "usbstk5515.h"

extern Int16 AIC3204_rset( Uint16 regnum, Uint16 regval);

#define XmitL 0x10

#define XmitR 0x20

#define Fs 48000

#define Fa 500

#define Fc 4000

#define PI 3.141592654

#include "math.h"

/* ------------------------------------------------------------------------ *

* *

* AIC3204 Tone *

* Output a 1 kHz tone through the HEADPHONE jack *

* *

* ------------------------------------------------------------------------ */

Int16 aic3204_tone_headphone( )

{

double* signal;

short ptsig1[480];

short ptsig2[480];

int x;

int nsample = 480;

signal = (double*) malloc( nsample * sizeof(double));

for ( x = 0; x < nsample; x++)

{

signal[x] = cos (2*PI*x*Fa/Fs) * cos (2*PI*x*Fc/Fs);

}


{

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ptsig1[x] = 1333 * signal[x];

}


{

signal[x] = cos (2*PI*x*Fa/Fs -PI/2) * sin (2*PI*x*Fc/Fs);

}


{

ptsig2[x] = 1333 * signal[x];

}

free(signal);

short ptsig3[480];


{

ptsig3[x] = ptsig1[x] + ptsig2[x];

}

/* Pre-generated sine wave data, 16-bit signed samples */

Int16 sinetable[48] = {

0x0000, 0x10b4, 0x2120, 0x30fb, 0x3fff, 0x4dea, 0x5a81, 0x658b,

0x6ed8, 0x763f, 0x7ba1, 0x7ee5, 0x7ffd, 0x7ee5, 0x7ba1, 0x76ef,

0x6ed8, 0x658b, 0x5a81, 0x4dea, 0x3fff, 0x30fb, 0x2120, 0x10b4,

0x0000, 0xef4c, 0xdee0, 0xcf06, 0xc002, 0xb216, 0xa57f, 0x9a75,

0x9128, 0x89c1, 0x845f, 0x811b, 0x8002, 0x811b, 0x845f, 0x89c1,

0x9128, 0x9a76, 0xa57f, 0xb216, 0xc002, 0xcf06, 0xdee0, 0xef4c

};

Int16 j, i = 0;

Int16 sample;

/* Configure AIC3204 */

AIC3204_rset( 0, 0 ); // Select page 0

AIC3204_rset( 1, 1 ); // Reset codec


AIC3204_rset( 1, 8 ); // Disable crude AVDD generation from DVDD

AIC3204_rset( 2, 1 ); // Enable Analog Blocks, use LDO power

AIC3204_rset( 0, 0 );

/* PLL and Clocks config and Power Up */

AIC3204_rset( 27, 0x0d ); // BCLK and WCLK are set as o/p; AIC3204(Master)

AIC3204_rset( 28, 0x00 ); // Data ofset = 0

AIC3204_rset( 4, 3 ); // PLL setting: PLLCLK <- MCLK, CODEC_CLKIN <-PLL

CLK

AIC3204_rset( 6, 7 ); // PLL setting: J=7

AIC3204_rset( 7, 0x06 ); // PLL setting: HI_BYTE(D=1680)

AIC3204_rset( 8, 0x90 ); // PLL setting: LO_BYTE(D=1680)

AIC3204_rset( 30, 0x88 ); // For 32 bit clocks per frame in Master mode ONLY

// BCLK=DAC_CLK/N =(12288000/8) = 1.536MHz = 32*fs

AIC3204_rset( 5, 0x91 ); // PLL setting: Power up PLL, P=1 and R=1

AIC3204_rset( 13, 0 ); // Hi_Byte(DOSR) for DOSR = 128 decimal or 0x0080

DAC oversamppling

AIC3204_rset( 14, 0x80 ); // Lo_Byte(DOSR) for DOSR = 128 decimal or 0x0080

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AIC3204_rset( 20, 0x80 ); // AOSR for AOSR = 128 decimal or 0x0080 for

decimation filters 1 to 6

AIC3204_rset( 11, 0x82 ); // Power up NDAC and set NDAC value to 2

AIC3204_rset( 12, 0x87 ); // Power up MDAC and set MDAC value to 7

AIC3204_rset( 18, 0x87 ); // Power up NADC and set NADC value to 7

AIC3204_rset( 19, 0x82 ); // Power up MADC and set MADC value to 2

/* DAC ROUTING and Power Up */


AIC3204_rset( 0x0c, 8 ); // LDAC AFIR routed to HPL

AIC3204_rset( 0x0d, 8 ); // RDAC AFIR routed to HPR


AIC3204_rset( 64, 2 ); // Left vol=right vol

AIC3204_rset( 65, 0); // Left DAC gain to 0dB VOL; Right tracks Left

AIC3204_rset( 63, 0xd4 ); // Power up left,right data paths and set channel


AIC3204_rset( 0x10, 0x00 );// Unmute HPL , 0dB gain

AIC3204_rset( 0x11, 0x00 );// Unmute HPR , 0dB gain

AIC3204_rset( 9, 0x30 ); // Power up HPL,HPR


USBSTK5515_wait( 100 ); // wait

/* ADC ROUTING and Power Up */


AIC3204_rset( 0x34, 0x30 );// STEREO 1 Jack

// IN2_L to LADC_P through 40 kohm

AIC3204_rset( 0x37, 0x30 );// IN2_R to RADC_P through 40 kohmm

AIC3204_rset( 0x36, 3 ); // CM_1 (common mode) to LADC_M through 40 kohm

AIC3204_rset( 0x39, 0xc0 );// CM_1 (common mode) to RADC_M through 40 kohm

AIC3204_rset( 0x3b, 0 ); // MIC_PGA_L unmute

AIC3204_rset( 0x3c, 0 ); // MIC_PGA_R unmute


AIC3204_rset( 0x51, 0xc0 );// Powerup Left and Right ADC

AIC3204_rset( 0x52, 0 ); // Unmute Left and Right ADC

AIC3204_rset( 0, 0 );

USBSTK5515_wait( 200 ); // Wait

/* I2S settings */

I2S0_SRGR = 0x0;

I2S0_CR = 0x8010; // 16-bit word, slave, enable I2C

I2S0_ICMR = 0x3f; // Enable interrupts

/* Play Tone */

for ( i = 0 ; i < 1000 ; i++ )

{

for ( j = 0 ; j < 1000 ; j++ )

{

for ( sample = 0 ; sample < nsample ; sample++ )

{

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while((XmitR & I2S0_IR) == 0); // Wait for transmit

interrupt to be pending

// I2S0_W0_MSW_W = (sinetable[sample]) ; // 16 bit left channel

transmit audio data

// I2S0_W1_MSW_W = (sinetable[sample]) ; // 16 bit right channel

transmit audio data

//DSB

// I2S0_W0_MSW_W = (ptsig1[sample]) ; // 16 bit left channel

transmit audio data

// I2S0_W1_MSW_W = (ptsig1[sample]) ; // 16 bit right channel

transmit audio data

//X

// I2S0_W0_MSW_W = (ptsig2[sample]) ; // 16 bit left channel

transmit audio data

// I2S0_W1_MSW_W = (ptsig2[sample]) ; // 16 bit right channel

transmit audio data

//SSB

I2S0_W0_MSW_W = (ptsig3[sample]) ; // 16 bit left channel

transmit audio data

I2S0_W1_MSW_W = (ptsig3[sample]) ; // 16 bit right channel

transmit audio data

}

}

}

/* Disable I2S */

I2S0_CR = 0x00;

return 0;

}

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Conclusion

In this project, we successfully built the demonstration of AM-SSB modulation on both Matlab and

TMS320C5515 eZDSPTM USB Stick. This helps us to have a deeper insight of AM-SSB in application

and to understand the underlying theories leading to this method of broadcasting signals.

The results captured from Scope are as shown:

Double sideband signal

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Double sideband frequency spectrum

Single Sideband signal

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Zooming version of Single Sideband signal

Single Sideband Frequency spectrum

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Low Single Sideband signal

Low Single Sideband Frequency spectrum

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References

[1] S.M. Tan, Chapter 5: The Hilbert transform and linear modulation theory, Linear

Systems, The University of Auckland, retrieved on April 28th 2014

[2] Frank R. Kschischang, The Hilbert Transform, University of Toronto, October 22, 2006,

retrieved on April 28th 2014

Software used: Soundcard Scope v1.41, C. Zeitnitz

Illustrating images of C5515 eZDSP USB Stick Development Tool are taken from http://www.ti.com/tool/tmdx5515ezdsp.

All source codes in this report are taken from the usbstk5515_v1 library associated with C5515 eZDSP USB Stick Development Tool, provided by Spectrum Digital Inc..

http://www.ti.com/tool/tmdx5515ezdsp

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