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)
Wednesday, April 8, 2015
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