Question

What is the dc gain of a filter with difference equation ?[?] = ?[?] + ?[? − 1]? Show your work.

A DT system has frequency response ?(? ??) = 2 (1 − 0.5? −?? ⁄ ). Calculate the magnitude of the frequency response at an input frequency of 2.2 radians.

A DT system has a difference equation ?[?] = 2?[? − 1] + ?[?] − 0.5?[? − 2]. What are the a and b coefficient arrays in the MATLAB filter function?

A periodic DT signal ?[?] = {2, −1, −2, k} (one period shown) has an average power of 9⁄2. What is the numeric value of ??

Answer 1

y[n] = x[n] + x[n-1]

Taking Z tranform of both side,

Y(z) = X(z) + z^-1X(z) = (1 + z^-1)X(z)

=> H(z) = 1 + z^-1

Coefficients of the FIR filter: [1, 1]

DC gain of FIR filter = sum of the coefficients

= 1 + 1

= 2