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DSP HW1, Engineering, Other Engineering
With x[n] denoting the input signal and y[n] denoting the output signal, give the difference equation relating the input signal to the output signal in the discretetime domain, give the initial conditions and their values, and find the transfer function in the zdomain and the associated region of convergence for the ztransform function, for the following linear timeinvariant discretetime systems:
(a) Causal averaging filter with three coefficients. See lecture slide 310. 12 points.
(b) Causal discretetime approximation to firstorder differentiator. See lecture slide 321.
12 points.
(c) Causal discretetime approximation to firstorder integrator. See online hints. 12 points.
(d) Causal bandpass filter with center frequency ?0 given by the inputoutput relationship
y[n] = (2 cos ?0) r y[n1] – r2 y[n2] + x[n]  (cos ?0) x[n1]
where 0 < r < 1. Here, r is the radius of the two pole locations. 12 points.
Posted Date: 2/2/2012 12:47:23 AM  Location : United States
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