A signal x (t) is periodic and one period of the signal is described by



Find the samples of this signal over one period sampled at a rate of 1 samples/sec (beginning at time, t=0). Then graph, on the same scale, two periods of the original signal and two periods of a periodic signal which is bandlimited to 0.5 Hz or less that would have these same samples.








% Solution to Exercise 65 in Sampling and the DFT

close all ;

fs = 1 ; Ts = 1/fs ; T = 8 ; N = T/Ts ;

% Set up a vector of sampling times, ts.

ts = [0:Ts:(N-1)*Ts]’ ;

% Set up a vector of corresponding sample values, xs.

xs = 3*ramp(ts).*rect((ts-2.75)/5.5) ;

% Set up vectors of times and signal values much closer

% for plotting the continuous signal, x.

nPts = 256 ; dt = T/nPts ; t = [0:dt:(nPts-1)*dt]’ ;

x = 3*ramp(t).*rect((t-2.75)/5.5) ;

% Find the CTFS of the signal, x(t).

[Xs,k] = CTFS(xs,ts,k) ;

% Generate the bandlimited signal, xbl, which passes through

% all the samples, xs[n]. Sum all the complex frequency components

% from n = -N/2 to n = +N/2.

xbl = zeros(nPts,1) ; f0 = 1/T ;

for nn = -N/2:N/2-1, xbl = xbl + Xs(nn+N/2+1)*exp(j*2*nn*pi*f0*t) ; end

% Clean up any small imaginary parts left over due to

% round off error.

xbl=real(xbl) ;

% Form two periods from the one period computed so far for

% each time-domain function computed; s, x and sbl.

xbl2 = [xbl;xbl] ; t2 = [t;t+T] ; x2 = [x;x] ;

xs2 = [xs;xs] ; ts2 = [ts;ts+T] ;

% Plot the original signal, samples and bandlimited signal.

p = xyplot({t2,t2,ts2},{x2,xbl2,xs2},[0,16,0,20],’\itt’,...

‘x({\itt}),x_b_l({\itt}) and x[{\itn}]’,’Times’,18,’Times’,14,...

“,’Times’,24,{’n’,’n’,’n’},{’c’,’c’,’d’},{’k’,’k’,’k’}) ;

set(p{1},’LineWidth’,0.5) ;

Trades & Technology

You might also like to view...

Which of the following should you do before leaving your vehicle unattended?

A. Chock the wheels. B. Put on the parking brakes. C. Remove the keys. D. All of the above.

Trades & Technology

An electrical circuit is composed of a power source, a path for current to flow, and:

A) Load. B) Switch. C) A means of regulating power. D) Element.

Trades & Technology

Technician Asays the  brake pedal position sensor is a potentiometer. Technician B says it can inform the BCM that the brake lamps need to be illuminated. Who is correct?

A. A only B. B only C. Both A and B D. Neither A nor B

Trades & Technology

Which of the following is not a valid type of 3D object?

a. Swept 3D solid b. Loft with cross sections only surface c. Cone surface d. 3D solid cylinder

Trades & Technology