Question: Consider an FIR system whose impulse response is This system is an example of a class of filters known as frequency-sampling filters, problem 6.37 discusses
Consider an FIR system whose impulse response is
This system is an example of a class of filters known as frequency-sampling filters, problem 6.37 discusses these filters in detail. In this problem, we consider just one specific case.
(a) Sketch the impulse response of the system for the cases n0 = 0 and n0 = 15/2.
(b) Show that the system function of the system can be expressed as,
(c) Show that if n0 = 15/2, the frequency response of the system can be expressed as
Use this expression to sketch the magnitude of the frequency response of the system for n0 = 15/2. Obtain a similar expression for n0 = 0. Sketch the magnitude response for n0 = 0. For which choices of n0 does the system have a generalized linear phase?
(d) Draw a signal flow graph of an implementation of the system as a cascade of an FIR system whose system function is 1 − z−15 and a parallel combination of a first-and second-order IIR system.
![0 <n< 14, otherwise. hlnl = { i3 (1 + cos[(2r/15)(n – no)]), 0, Part B je-i2an0/15 1 – ei2n/157-1 jei2ano/15 1 – e](https://dsd5zvtm8ll6.cloudfront.net/si.question.images/images/question_images/1550/1/4/0/3065c654392783301550140305328.jpg)
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