Reference no: EM13866778

1) You are given two continuous time functions: x(t)=cos(t) and y(t)=sin(t)

Find the convolution of these two signals using time domain convolution. You may need to use a trigonometric identity to solve this or equivalently Euler's formula.

z(t)=x(t)*y(t).

Prove that multiplication in the frequency is the same as convolution in the time domain by finding the multiplication of the Fourier series of the signals of x(t) and y(t), transforming the result to the time domain.

2) The triangle wave shown in example 3.7 (page 207) will be called x(t). Find the Fourier series of this signal if it is shifted to the right by one second (x(t-1)) First find it by using the time shifting property.

Prove this is true by finding the even portions of the signal of x(t-1) and the Fourier series of it, and the odd portion and add the Fourier series components together.