Question

Recall the problem from lecture iavolving an information signal betweea (-100, 100) Iz and a noise signal with positive spectrum between (500,700) Hz and negative spectrum between (-700-500) Hz. a) Suppose we want the reconstructed signal to equal the information signal. Suppose also that we would like to VIOLATE the Syquist criterion. If we can use a reconstruction ilter different than the ideal lowpass filter considered ia lecture, then find the minimum sampling frequency which violates Nyquist but still gives ) Also give the design specifications for the recoustruction fiter. Explain your solution. b) Assume the sampling frequency is fixed at .200 Hz and suppose you are limited to using the two filters shown below. Design a sampling and reconstruction system that recovers t) and uses each filter only once. Note: this is possible! Draw a block diagram for your synterm and specify the gains K, and K.

Answer 1

Given that noise signal with Positive Spectrum b/w (500, 700)Hz noise signal with negative spectrum b/w (- 700, - 50)Hz information signal b/w (- 100, 100) Hz a)the minimum Sampling frequency which voltes Nyquist but still gives x_r (t) = x_info (t) H(z) = sigma^z_0_n = z h(n) * z^-n = 1 - 1^z-n H(z) = z^n - 1/z^n So h(n) = {1, n = 0 - 1, n = 4 \r\n 4 repeated pole at �0� 4 repeated zeros at �1� b)Sampling frequency is fixed at F_S = 200 H_z reconstruction system that recovers x_r (t) = x_info (t) X(K) = H(z) Vertical-bar _z e^-j pi k/N H(z) = 1 - z^-4 H(e^jw) = H (e^jw) Vertical-bar _z e^jw rate of equal to length of DFF H(k) = 1 - e^-J 4w Vertical-bar _w = k 2pi/N \r\n H(k) = 1 - e^-J 2pi k/N 4k H(0) = 0 H(128) = 0, H(256) = 0, H(384) = 0 H(k) = sigma^127_n = 0 h(n) e^-2pi times n/r 2 = 1 - w^4k_512 H(0) = 1 - 1 = 0