Question

From the book Practical Signals Theory with MATLAB application (RICHARD J. TERVO)

Chapter four problem 4.3:

Consider the signal a(t)=cos(t) and the signal b(t), which is an even square wave with period 2? seconds and amplitude going +or- 1V

(a) Use the signal inner product to find the best approximation to a(t) in terms of b(t). In other words, find B to optimize the approximation a(t)=Bb(t).

(b) Use the signal inner product to find the best approximation to b(t) in terms of a(t). In other words find A to optimize the approximation b(t) =Aa(t).

(c) Should you expect A=1/B?   Why or why not? Discuss the difference between the values A and B found above.

PLEASE PLEASE SHOW ALL STEPS! i AM NEW TO SIGNALS

Answer 1

clc; clear; close all;

% a(t) = cos(t);
% b(t) is a function square wave with a time period of 2.
% the inner product for approximation of a(t) = Bb(t).
% B = integral of (a(t)*b(t)) / integral of (b(t)^2).
p = integral(@(t) cos(t),0,0.99);
q = integral(@(t) -cos(t),1,2);
r = integral(@(t) cos(t).*cos(t),0,2);
% (p+q) = integral of (a(t)*b(t))
B = (p+q)/r

% the inner product for approximation of b(t) = Aa(t).
% B = integral of (a(t)*b(t)) / integral of (a(t)^2).
s = 2; % integral of (a(t)^2).

A = (p+q)/s