Question

Part 1: One mark for questions 1-14, two marks for questions 15-17 || Ifx(n) = {17,0,1} and y(n) = {-1,11), calculate the following expressions: 1 1.x(n)(n-1) =........................ 2.x(n) + y(n) =..... 3.>x(n)*8(n +1) =.. . ngan ang ang nanay na nangan. . 4.>x(n) * y(n) = ***. ... og en min. 5. Crosscorrelation rxy (n) =....... . . . 6. Autocorrelation rxx(n) =...... 7.-x(n) *y-n) = . om commem.... 8.-x(n) * u(n) =....... 9.-8(n-3)* 8(n+1) =..... 10. Crosscorrelation between x(n) and 8(n): =....... 11. Find the value k such that the signal 8(n + k) 8(n+k2 – 2) is not zero everywhere ..... .1 12. Fourier transform of rxy (n). 13. Fourier transform of n w(n) in term of Fourier tansform of w(n), w (jw). 14. Why if x(n) is a causal signal then lim X(Z) = x(0)? If x(n) = {...,11,0,1,...} is periodinc signal and y(n) = acos(in/3) is stochastic process where a is gaussian distribution with mean two and variance 4.1 15. Find the two autocorrelations Tax(n) and ryy(n) ......... 16. Find autocovariance of y(n). 17.Find fourier transform of y(n)= =-. *(n) in terms of X(jw).......

Answer 1

2 (M)= 1,0,'y in terms of Sony' function am) = S(N) + sin-2) yem = (-1] in terms of 'son' fucking yon 2-(n+1) +809) o aen) Sen-1) = By The product property ain) sin-nol = x(no) Srn-no) Shok son) Sin-1) = x (1) Senande xin) +yin) A todos 210) , in yim + $7/13 = -1,2,0,13 3 X.) * &in +1) = 261+1) = { 0,1,0,1 (: By convolution property acn) * Sin-na) = a1n-no

X( 1, xon) - Sin) + Sin-27 yon) - - Sim + 1) + son) acn* y(n) = (scn) + S(1-2))*(-sen +0+sm) = S(N)*-5(n+1) + Sco*sin) - SCN-2)* Stn 1) + Sin-2)* Sm) = - SON+1) + Son) – 516-1) + S(1-2) = [ , -1,0)

x(n) *yen Flule = (4.169 1 I 1 0 I- - O -1 sit 1. -1] © acn) furn) xin) yan[S(n) + 8 (n.- 2) ) *uin) = Scotuin) + sin-27 *urn) und turn-22 ſi,,2,2,2,2, .... ] © scn-3) * sin +1) = sin-3+1) = sin-2)