problem 3 15 points a commonly used method for converting discrete tim

Question

Problem 3 [15 points] A commonly used method for converting discrete-time signals to continuous-
time signals is zero-order hold, in which z(t) is held constant between its known samples at t = nTg.
Zero-order hold interpolation of samples is illustrated in the following figure
a. [10 points] Zero-order hold is a low pass filter. Compute its frequency response H(w).
Hint: The sampled signal is z, (t) = a[n]d(t-nT) and the zero-order hold signal is
equivalent to convolving the sample signal r(t) with a rectangular pulse of with T.
b. [5 points] Zero-order hold is used to reconstruct cos(0.1t/T.) from its samples at t = nT,.
The first copy of the spectrum induced by sampling lies in