Q$.3$ an input sequence $x(n)=(-2,1,0+1,-3)$ determine the output sequence $y(n)$ using the convolution sum. Find $y(n)$ for all values of $n,$ and specifically determine $y(-4),y(3).$

$3$n$-$ B$.$ Given the input signal

$x$ the input signal

$x(n)=3cos(n+1)-2sin(2n-0\mathrm{.}5)+2cos(3n-2)-sin(4n+3)$

Find the output signal $y(n)$ for the following frequency response $H(e^{\text{'}\text{'}})=cos(w),$ for $n=0,1,2.$

$3$p Given a sequence $x(n)$ for $0n3,$ where $x(n)=\{0,1,2,3\}.$ Evaluate its DTFT $x(0^0).$