1) Given an LTI system with the real impulse response (i.e. the impulse response has no imaginary part), show that
a) Any real input provides rise to a real output. Employ the convolution sum to show this.
b) If the response to the complex input, , is , then the response to the input is. Employ the convolution integral again to show this.
c) If the response to the complex input, , is , then the response to the input is , and the response to the input is .
Hint: Re{Xn} = [X(n) +x^*(n)]/2