Q$.3$

$3$pt A$.$ Given an LTI system with impulse response sequence $h(n)=\{1,-1$larr,$0,2,1\}$ and an input sequence $x(n)=\{-2,1,0$larr,$1,-3\}$ determine the output sequence $y(n)$ using the convolution sum. Find $y(n)$ for all values of $n,$ and specifically determine $y(-4),y(3).$

$3$pt B$.$ Given 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 $H(e^{jw})=cos(w),$ for $n=0,1,2.$

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