lDiscreteTime Signal Processing Alan V Oppenheim Ronald W S

EENG 751 MTE OW 1. (15)Calculate the sequences in angle bracket notation: (b) The even and odd parts of yb[n]=R,[n+1]+R,[n-1] 2.(15)Calculate the convolutio n of the following sequences : x[n] = (2-n)R4[n]and h[n]=-u[n-2] 3.(15) Calculate the frequency response of ybr] = 0.25x[n]_ 0.5x[n-3] + 0.25x[n-6] Which frequencies are completely blocked by this system?

Solution

1(a) y(z) = zR(z)

ROC Z<4

(b) even part = yb[n] + yb[-n]/2 = R5[n+1] + R4[n-1] + R5[-n+1] + R4[-n-1]/2

odd part = yb[n] - yb[-n] / 2 = R5[n+1] + R4[n-1] - R5[-n+1] - R4[-n-1]/2

2.convolutio sequuence

y(z) = x(z)*h(z)

= 2/(1-z^-1)* 1/(1-z^-1 )² z^{-2 R(z)}