GROUP MEMBERS: _____________ WORKSTATION NO: _________

LAB NO.

Introduction to Digital Signal Processing Fundamental Concepts Using Matlab Functions .

• Attach snap-shots in each of tasks.

• Attach snap-shots for post –task questions if necessary ,write equation or theoretical answer otherwise.

• Task H is home task.

• Attach Snapshot in each of the remaining task.

• Questions related to each task being uploaded in the meantime ,which are to be ,mentioned along each task.

CODE ANALYSIS:

SIGNAL GENERATION AND VISUALIZATION:

Task F :

Voltage Controlled Oscillation:

Another function generator is the vco (Voltage Controlled Oscillator) which generates a signal oscillating at a frequency determined by the input vector. Let's look at two examples using vco with an triangle and rectangle input.

Generate 2 seconds of a signal sampled at 10kHz whose instantaneous frequency is a triangle (respectively a rectangle) function of time:

Code :

fs = 10000;

t = 0:1/fs:2;

x1 = vco(sawtooth(2*pi*t,0.75),[0.1 0.4]*fs,fs);

x2 = vco(square(2*pi*t),[0.1 0.4]*fs,fs);

Plotting the spectrogram :

Plot the spectrograms of the generated signals:

subplot(211)

spectrogram(x1,kaiser(256,5),220,512,fs,'yaxis');

title('VCO Triangle')

subplot(212)

spectrogram(x2,256,255,256,fs,'yaxis')

title('VCO Rectangle')

hgcf = gcf;

hgcf.Color = [1,1,1];

Questions :

1. Mention the Syntax of Spectrogram Command ?

2. What does ‘Kaiser’ word in the above spectrogram ,specify?

TASK G :

To generate pulse trains, we can use the pulstran function. Below, we'll showcase two examples on how to use this function.

Rectangular Pulse Train :

Construct a train of 2 GHz rectangular pulses sampled at a rate of 100 GHz at a spacing of 7.5nS.

fs = 100E9; % sample freq

D = [2.5 10 17.5]' * 1e-9; % pulse delay times

t = 0 : 1/fs : 2500/fs; % signal evaluation time

w = 1e-9; % width of each pulse

yp = pulstran(t,D,@rectpuls,w);

Gaussian Pulse Train Generation :

Generate a periodic Gaussian pulse signal at 10 kHz, with 50% bandwidth. The pulse repetition frequency is 1 kHz, sample rate is 50 kHz, and pulse train length is 10msec. The repetition amplitude should attenuate by 0.8 each time. The example uses a function handle to refer to the generator function.

Code :

T = 0 : 1/50E3 : 10E-3;

D = [0 : 1/1E3 : 10E-3 ; 0.8.^(0:10)]';

Y = pulstran(T,D,@gauspuls,10E3,.5);

subplot(211)

plot(t*1e9,yp);

axis([0 25 -0.2 1.2]);

xlabel('Time (ns)');

ylabel('Amplitude');

title('Rectangular Train');

subplot(212)

plot(T*1e3,Y)

xlabel('Time (ms)');

ylabel('Amplitude');

title('Gaussian Pulse Train');

hgcf = gcf;

hgcf.Color = [1,1,1];

Questions :

1. Use the rectangular train code above to obtain a pulse separated by 1 micro-second ,keep all other parameters same.

2. Use the Gaussian code above to obtain a Gaussian pulse which increases by 0.8 each time and keep all other parameters un-changed.

TASK H :

Design Example :

This example shows how to estimate a speaker's fundamental frequency using the complex cepstrum. The example also estimates the fundamental frequency using a zero-crossing method and compares the results.

Load the speech signal. The recording is a woman saying "MATLAB". The sampling frequency is 7418 Hz. The following code loads the speech waveform, mtlb, and the sampling frequency, Fs, into the MATLAB® workspace.

load mtlb

Use the spectrogram to identify a voiced segment for analysis.

segmentlen = 100;

noverlap = 90;

NFFT = 128;

spectrogram(mtlb,segmentlen,noverlap,NFFT,Fs,'yaxis')

Extract the segment from 0.1 to 0.25 seconds for analysis. The extracted segment corresponds roughly to the first vowel, /ae/, in "MATLAB".

dt = 1/Fs;

I0 = round(0.1/dt);

Iend = round(0.25/dt);

x = mtlb(I0:Iend);

Obtain the complex cepstrum.

c = cceps(x);

Plot the cepstrum for times ranging from 2 to 10 ms corresponding to a frequency range of approximately 100 to 500 Hz. Identify the peak in the cepstrum and find the frequency corresponding to the peak. Use the peak as the estimate of the fundamental frequency.

t = 0:dt:length(x)*dt-dt;

plot(t(15:75).*1e3,c(15:75))

xlabel('ms')

[~,I] = max(c(15:55));

fprintf('Complex cepstrum F0 estimate is %3.2f Hz.\n', 1/(t(I+15)))

omplex cepstrum F0 estimate is 231.81 Hz.

se a zero-crossing detector on a lowpass-filtered and rectified form of the vowel to estimate the fundamental frequency.

[b0,a0]=butter(2,325/(Fs/2));

xin = abs(x);

xin = filter(b0,a0,xin);

xin = xin-mean(xin);

x2 = zeros(length(xin),1);

x2(1:length(x)-1) = xin(2:length(x));

zc=length(find((xin>0 & x2