EE348 Homework Assignment #4: FIR Filters
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This homework assignment #4 is due on Wednesday, March 4, 2015, by 11:59 PM.
1. Filter Impulse Response:
Consider a filter with the di?erence equation y[n] = 4x[n]? 3x[n? 1] + 2x[n? 2]? x[n? 3] relating its input x[n] and its output y[n].
What is the impulse response h[n] of this filter?
2. MA Filter and Convolution:
Answer the following questions for a moving-average (MA) filter. This 4-point MA filter has impulse response
h[n] =14 ?[n] +14 ?[n? 1] +14 ?[n? 2] +14 ?[n? 3].
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(a) Is this filter causal? Explain why or why not.
(b) Write the di?erence equation of this filter; the di?erence equation expresses y[n] in terms of scaled and delayed versions of the input x[n]. (See question 1 for example of a di?erence equation).
(c) The input to this filter is x[n] = ?[n] + 5?[n? 1]? ?[n? 2] + 3?[n? 3].Use the tabular method ofconvolution to find the filter output y[n]. Be sure to write an expression fory[n].
(d) Plot the output y[n] (on the y-axis) vs. n (on the x-axis).
3. Linearity and Time-Invariance:Consider the system described by the equationy[n] =nx[n].
(a) Is this system linear? Show why or why not. You must prove whether the system is or is not linear.
(b) Is this system time-invariant? Show why or why not. You must prove whether the system is or is not time-invariant.
(c) Is this system causal? Explain why or why not.