Sampling process illustration in Matlab

Here a simple example of sampling process of a signal in matlab is provided. Sampling is effectively applying pulse signal to a transistor that turns it on and off. In matlab this can be stimuated by applying a pulses to an input signal.

Here first impulse(h) is generated using filter and then applied to a sinuoid signal(x) to get the sampled signal(y).

The following line generates an impulse response h.

% generate discrete time impulse signal

a = [1 0 0 0 -1];

d = [1 zeros(1,127)];

h = filter(1,a,d);

n = 0:127;

The following line generates a cosine signal

% generate cosine signal

x = cos(2*pi*n/32);

% generate frequency response for signal x

[X,w] = freqz(x,1,128,whole);

% scale w for plotting properly

wp = fftshift(w)/pi-1;

The frequency spectrum of cosine signal is plotted below,

% plot frequency response of x

figure(1)

plot(wp,X)

Now the cosine signal x is multiplied by h which is effectively the process of sampling.

% sampling with 8 samples/ cycle

y = x.*h;

This sampled signal y is then plotted to get its frequency spectrum

Y = fft(y);

figure(2)

plot(wp,Y);

The overall process is shown in the graph which shows signals and its spectrum at various stages:

The overall matlab code is below,

% generate discrte time impulse signal

a = [1 0 0 0 -1];

d = [1 zeros(1,127)];

h = filter(1,a,d);

n = 0:127;

H = fft(h);

% generate cosine signal

x = cos(2*pi*n/32);

% generate frequency response for signal x

[X,w] = freqz(x,1,128,whole);

% scale w for plotting properly

wp = fftshift(w)/pi-1;

% sampling with 8 samples/ cycle

y = x.*h;

Y = fft(y);

figure

subplot(3,2,1)

plot(n,h)

title(Time Domain Responses)

xlabel(Time)

ylabel(h)

subplot(3,2,2)

plot(n,H);

title(Frequency Responses)

xlabel(Frequency)

ylabel(H)

subplot(3,2,3)

plot(n,x)

xlabel(Time)

ylabel(x)

subplot(3,2,4)

plot(wp,X);

xlabel(Frequency)

ylabel(X)

subplot(3,2,5)

plot(n,y)

xlabel(Time)

ylabel(y)

subplot(3,2,6)

plot(wp,Y);

xlabel(Frequency)

ylabel(Y)

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