Question

A wireless service provider transmits a signal s(t) = 5 cos(2π fc t) to a receiver, where fc is a variable carrier frequency. The impulse response of the channel linking transmitter and receiver is

c(t) = 0.80δ(t − Td ) − 0.47δ(t − T1 )

where Td = 270 nsec, T1 = 430 nsec, and “nsec” = 10 ^{− 9} sec.

(a) Compute the simplest math expression for the magnitude-squared frequency response |C(f)|².
(b) Suppose the service provider is allocated the spectrum range from 15 ≤ f ≤ 25 MHz. Plot |C(f)|² over this range.
(c) Over this range, which carrier frequency would provide the strongest signal at the receiver? Which carrier frequency would provide the weakest signal at the receiver?

Answer 1

Question b)

MATLAB code is given below to plot the square of magnitude.

clc;
clear all;
close all;

% define frequency
f = 15e6:1e3:25e6;

% define the frequency response
C = 0.8*exp(-1j*f*270e-9)-0.47*exp(-1j*f*430e-9);

% Plot the square of magnitude of frequency response
figure;
plot(f,abs(C).^2,'linewidth',2);grid on;
xlabel('f');ylabel('Square magnitude');
title('|C|^2');

Question C)

from the above plot it is observed that the magnitude is highest at the frequency of 19.96 * 10^6 Hz and the magnitude is 1.613

the magnitude is lowest at the frequency of 25 * 10^6 Hz and the magnitude is 1.35

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