# Mathematics of Signal Representations

## Math4355 - Spring 2013 - Homework

**Assignment 4, due Thursday, February 14**

- Review Sections 1.2.1, 1.2.3 up to Lemma 1.7 and 1.2.4.

- Matlab project

Write an m-file part_sum_fs.m in Matlab code which
helps plot trigonometric polynomials of the form

y(t) = a_0 + a_1*cos(t)+ b_1*sin(t) + a_2*cos(2*t)+ b_2*sin(2*t) + ... +
a_n*cos(n*t)+ b_n*sin(n*t)

The m-file (function) should be called as part_sum_fs(a,b,t) where the vectors containing the
coefficients are

a=[a_0, a_1 ,..., a_n]

b=[b_1, b_2 ,..., b_n]

and the row vector
t contains times at which y(t) is evaluated.

This should work for plotting y=1+2cos(t)+3sin(t)-sin(3t) on
[0,4π]. To do this, we want to type

>>a = [1,2,0,0];

>>b = [3,0,-1];

>>t = linspace(0,4*pi,500);

>>y = part_sum_fs(a,b,t);

>>plot(t,y)

>>xlabel('t'), ylabel('y'),
title('y=1+2cos(t)+3sin(t)-sin(3t)')

Include the plot and your m file in your homework. Also include plots
for the trigonometric polynomials

y=sin(t)+sin(2t)/2+sin(3t)/3+sin(4t)/4

y=cos(t)+cos(3t)/32+cos(5t)/52

- Do Exercises p. 84-85: 12; 13; 21; 22.