A first-order low-pass analog filter has a transfer function H(s) = 1/(s + 1). (a) If for
Question:
(a) If for this filter, the input is x(t) and the output is y(t) what is the ordinary differential equation representing this filter.
(b) Suppose that we change this filter into a discrete filter using the bilinear transformation
Obtain the transfer function H(z). If for the discrete filter, the input is x[n] and the output y[n] obtain the difference equation representing the discrete filter.
(c) Suppose x(t) = u(t) u(t 0.5) find the output of the analog filter.
(d) Let K = 1000, so that Ts = 2/K is used to sample x(t) to get the discrete signal x[n]. Use the difference equation to solve for the output y[n]. Compare your result with the one obtained by solving the ordinary differential equation for the first three values.
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