stest1-2000 - Name BME 171, Fall 2000 - TEST #1 1. The...

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Unformatted text preview: Name BME 171, Fall 2000 - TEST #1 1. The response of an FIR filter is given by a following difference equation: y [n] = x[n] + 2 x[n − 1] + 3 x[n + 2] + 4 x[n − 3]. (a) Find and sketch impulse response h[n] of this filter. What is the length and order of this filter? (b) Consider an input x[n], which has nonzero samples for index n in the range from 5 to 25. Determine the range of indices of nonzero samples in the response of this FIR filter to input x[n]. 2. An LTI system has an impulse response h(t) = a e−t/τ u(t). Compute the response of this system to an input x(t) = δ (t − 1) + u(t). Sketch this response, assuming that τ = 0.2. Label all pertinent features. 3. IGNORE THIS ONE: An LTI system is characterized by a differential equation τ dy dx +y =a + b x. dt dt Find the frequency response of this system by steady-state analysis. 4. Consider an analog signal: x(t) = cos(2.5πt + π/4) + 1.5 cos(7πt − π/16). (a) Is signal x(t) periodic? Justify your answer. (b) Signal x(t) is sampled with frequency fs = 7 Hz. Is this sampling frequency adequate to reconstruct x(t)? Justify your answer. ...
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This note was uploaded on 05/25/2010 for the course BME 171 taught by Professor Izatt during the Spring '08 term at Duke.

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