A causal discrete time filter has a z-domain description of (22+0.82 +0.64)(z-1.5) Ĥ(z) = 23 a.) Is this filter FIR or IIR? Briefly justify your answer. b.) Is is filter stable or not? Briefly justify your answer. c.) Find the impulse response, h[n], for this filter. d.) Find the transfer function of the filter as function of normalized radial fre- quency, W. e.) For your answer in part d.), find the value of the transfer function at = -2π/3, = 0 and ŵ= +2/3. If the answer is complex, specify the magnitude and angle (in degrees).

A causal discrete time filter has a z-domain description of (22+0.82 +0.64)(z-1.5) Ĥ(z) = 23 a.) Is this filter FIR or IIR? Briefly justify your answer. b.) Is is filter stable or not? Briefly justify your answer. c.) Find the impulse response, h[n], for this filter. d.) Find the transfer function of the filter as function of normalized radial fre- quency, W. e.) For your answer in part d.), find the value of the transfer function at = -2π/3, = 0 and ŵ= +2/3. If the answer is complex, specify the magnitude and angle (in degrees).

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Concept explainers

Filter

A filter is a device or process which removes some of the unwanted features or components like frequencies from a signal in signal processing. The feature of filters is the complete or partial suppression of some part of the signal, and filtering is a class of signal processing. This most often means removing some frequency bands or some frequencies. In the frequency domain, the filters do not exclusively act, especially in the image processing field many other targets for filtering exist. Without having to act in the frequency domain, the correlations can be removed for certain frequency components and not for others. The filters are widely used in electronics and telecommunication, in television, radio, radar, audio recording, music synthesis, control systems, computer graphics, and image processing.

Question

4.)
A causal discrete time filter has a z-domain description of
(22+0.82 +0.64)(z-1.5)
Ĥ(z)
a.) Is this filter FIR or IIR? Briefly justify your answer.
23
b.) Is is filter stable or not? Briefly justify your answer.
c.) Find the impulse response, h[n], for this filter.
d.) Find the transfer function of the filter as function of normalized radial fre-
quency, .
e.) For your answer in part d.), find the value of the transfer function at =
-2π/3, = 0 and = +27/3. If the answer is complex, specify the magnitude
and angle (in degrees).

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