1. Prove the six convolution sum properties enumerated in Sec. 5.5.1. 2. (a) Find the zero-state response y[n] of an LTID system with input x[n] = e−nu[n] and impulse response h[n] given by (−2)nu[n]....

2. (a) Find the zero-state response y[n] of an LTID system with input x[n] = e−nu[n] and impulse response h[n] given by (−2)nu[n].

(b) Repeat part (a) using impulse response

(c) We showed in Eq. (5.28) that

To derive this result, we used the LTID system property that if x[n] =⇒ y[n], then x[n] =⇒ y[n]. Derive this result without using this property.