Signals and Systems - Electrical Engineering

436 CHAPTER 7: Sampling Theory

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Analog signal

Sampled signal

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FIGURE 7.9

Sampling ofx(t)= 2 −cos( 500 πt)−sin( 1000 πt)with (a) no aliasing (fs= 6000 samples/sec) and (b) with

aliasing (fs= 800 samples/sec).

y1(1:delta:L) = x(1:delta:L);

y = x(1:delta:L);

% analog FT and DTFT of signals

dtx = 1/fsim;

X = fftshift(abs(fft(x)))∗dtx;

N = length(X); k = 0:(N−1); fx = 1/N.*k; fx = fx∗fsim/1000−fsim/2000;

dty = 1/fs;

Y = fftshift(abs(fft(y)))∗dty;

N = length(Y); k = 0:(N−1); fy = 1/N.*k; fy = fy∗fs/1000−fs/2000;

The following function computes the sinc interpolation of the samples.

function [t,xx,xr] = sincinterp(x,Ts)

%

% Sinc interpolation

% x sampled signal

% Ts sampling period of x

% xx,xr original samples and reconstructed in range t

%

N = length(x)

t = 0:dT:N;

xr = zeros(1,N∗ 100 +1);

for k = 1:N,