Digital Signal Processing

Lab 1

Exercise 1

Read and write sounds in .wav format.

Some sound files: piano.wav, alligators.wav, bird.wav

Use the command

[y,fs,bits] = wavread(‘filename.wav’);

to read a WAVE file.

Then use the command to play the sound.

sound(y,Fs);

Finally, output the vector y to a new WAVE file

wavwrite(y,fs,bits,’filename.wav’);

Exercise 2

Discrete-time sequences.

1. Discrete-time impulse (Page 11)

n = -10:20;

y = zeros(1, 31);

n0 = 10;

y(n0-n(1)+1) = 1;

stem(n, y);

2. Unit-step sequence (Page 11)

n = -10:20;

y = zeros(1, 31);

n0 = 10;

y(n0-n(1)+1:31) = 1;

stem(n, y);

3. Exponential sequence (Page 13)

n = -10:20;

y = 2*exp(-0.5*n);

stem(n, y);

4. Sinusoidal sequence (Page 13-14)

n = -10:20;

y = 2*cos(pi/4*n);

stem(n, y);

y = 2*sin(pi/7.3*n);

stem(n, y);

        y = exp(j*pi/6*n);

        subplot(211)

stem(n, real(y));

        subplot(212)

stem(n, imag(y));

5. Combined

n = -10:20;

        y = exp(-0.1*n+j*(pi/6*n+pi/4));

        subplot(211)

stem(n, real(y));

        subplot(212)

stem(n, imag(y));

Exercise 3

Linear constant-coefficient difference equations

1. An accumulator (Page 34, Example 2.14)

n = -10:20;

        x = (0.9).^n.*cos(pi/6*n+pi/4);

        a = [1 -1];

        b = [1];   

y = filter(b, a, x);

        subplot(211)

stem(n, x);

        subplot(212)

stem(n, y);

2. An accumulator with an impulse input

n = -10:20;

x_impulse = zeros(1, 31);

n0 = 0;

x_impulse(n0-n(1)+1) = 1;

        a = [1 -1];

        b = [1];   

y = filter(b, a, x_impulse);

        subplot(211)

stem(n, x_impulse);

        subplot(212)

stem(n, y);

3. A moving-average system (Page 35, Example 2.15)

n = -10:20;

        x = (0.9).^n.*cos(pi/6*n+pi/4);

        M2 = 6;   

a = [1];

        b = (1/(M2+1))*ones(1,M2);   

y = filter(b, a, x);

        subplot(211)

stem(n, x);

axis([-10 20 –3 3])

subplot(212)

stem(n, y);

axis([-10 20 –3 3])

4. A moving-average system with an impulse input

        M2 = 6;   

a = [1];

        b = (1/(M2+1))*ones(1,M2);   

y = filter(b, a, x_impulse);

        subplot(211)

stem(n, x_impulse);

        subplot(212)

stem(n, y);

5. Recursive computation of difference equations (Page 37, Example 2.16)

n = -10:20;

        x = (0.9).^n.*cos(pi/6*n+pi/4);

a = [1 -0.9];

        b = [1];   

y = filter(b, a, x);

        subplot(211)

stem(n, x);

axis([-10 20 -5 5])

subplot(212)

stem(n, y);

axis([-10 20 -5 5])

6. Recursive computation of difference equations with an impulse input

a = [1 -0.9];

        b = [1];   

y = filter(b, a, x_impulse);

        subplot(211)

stem(n, x_impulse);

axis([-10 20 -2 2])

subplot(212)

stem(n, y);

axis([-10 20 -2 2])

Exercise 4

Convolution (Page 24)

n = -10:20;

x = zeros(1, 31);

x(-2+10+1) = 0.8;  x(0+10+1) = 1;  x(3+10+1) = -0.5;

h = [1 2/3 1/3];

y = conv(h,x);

stem(-10:22, y);

Sources:

Fundamentals of Digital Signal Processing, by Joyce Van de Vegte, Prentice Hall, 2002.