Consider a first-order system with transfer function where K > 0 is a gain, z 1 is
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where K > 0 is a gain, z1 is a zero, and p1 is a pole.
(a) If we want unity dc gain, i.e., |H(j0)| = 1, what should be the value of K.
(b) What types of filters (lowpass, bandpass, band-eliminating, all-pass, and high-pass) can you obtain with this first-order system?
(c) Let H1(s) = 1/(s + 1), corresponding to a low-pass filter, determine the dc gain of this filter and use it to find the half-power frequency of the filter.
(d) Determine the magnitude response of a filter with transfer function H2(s) = (s 1)/(s + 1). Plot the poles and zeros of this filter. What type of filter is it?
(e) What type of filter has the transfer function H3(s) = s/(s + 1) ?
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