Problem $1[]$ is a real valued discrete time signal with fundamental period $=5.$ The nonzero Fourier series

coefficients of $[]$ are given by

$$

$$

$2=2$

$=24$

$=4,$

$$

$$

$4=4$

$=8$

Express $[]$ in the form

$[]=+$ sin $(+)$

$=1$

$$

Hint cos$(+)=$ sin $(++)$

$2$

Problem $2$

Determine the Fourier series coefficients for each of the following discrete time signals

$2$

a$.[]=$ cos $($

$3$

$2$

$)$ cos $(4)$

b$.[]$ is periodic with period $=3$ and given by the following expression in one period