View source for HW6.3 Kofo Adafin ECE301Fall2008mboutin - Rhea

==Problem 5==
An LTI system has unit impulse response h[n] = u[n] - u[n-2].
  
a) Compute the system's function H(z).


<math>H(z)=\sum_{k=-\infty}^{\infty}h[k]z^{-k}</math>

<math>H(z)=\sum_{k=-\infty}^{\infty}(u[k]-u[k-2])z^{-k}</math>

u[k]=  1, k > 0 and  0, else

u[k-2]= 1, k > 0 and 0, else

h[n] is 1 between 0 and 1; and 0 elsewhere 

<math>H(z)=\sum_{k=0}^{1}z^{-k}</math>


<math>H(z)= 1*z^{-0} + 1*z^{-1}</math>


b) the system's response to the input <math>x[n]=\cos(\pi n)</math>.


<math>\cos(\pi n)=(-1)^n</math>


<math> Y(n)= H(-1)*(-1)^n  = 0</math>