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Each of the following figures shows the impulse response of a LTI system h[n]. For each figure in (a), (b), (c) and (d): (i) Firstly write an expression of h[n] and then find an expression of the frequency response of the system: H(ew) = h[n]e-jnw, (ii) say whether H(e) as a function of w is even or odd or neither (iii) and sketch/plot the magnitude of the frequency response, i.e., |H(e³w)|, over - 27 < w 2π (you may use Matlab). (a) In each figure, the value indicated for each impulse means the amplitude of that impulse. For example, if the value of an impulse at n = 3 is indicated to be 2j, it means 2jd[n - 3]. The value of h[n] is zero for all n outside the range shown in the figure. h[n] n=-∞ 1 1 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 n h[n] is real-valued.

Each of the following figures shows the impulse response of a LTI system h[n]. For each figure in (a), (b), (c) and (d): (i) Firstly write an expression of h[n] and then find an expression of the frequency response of the system: H(ew) = h[n]e-jnw, (ii) say whether H(e) as a function of w is even or odd or neither (iii) and sketch/plot the magnitude of the frequency response, i.e., |H(e³w)|, over - 27 < w 2π (you may use Matlab). (a) In each figure, the value indicated for each impulse means the amplitude of that impulse. For example, if the value of an impulse at n = 3 is indicated to be 2j, it means 2jd[n - 3]. The value of h[n] is zero for all n outside the range shown in the figure. h[n] n=-∞ 1 1 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 n h[n] is real-valued.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Each of the following figures shows the impulse response of a LTI system h[n]. For each figure in (a), (b), (c) and (d): h[n]e-jnw, (ii) say whether H(e) as a function of w is even or odd or neither (iii) and sketch/plot the magnitude of the frequency response, i.e., |H(e³w)|, over - 27 < w 2π (you may use Matlab). (a) (b) (i) Firstly write an expression of h[n] and then find an expression of the frequency response of the system: In each figure, the value indicated for each impulse means the amplitude of that impulse. For example, if the value of an impulse at n = 3 is indicated to be 2j, it means 2jd[n - 3]. The value of h[n] is zero for all n outside the range shown in the figure. h[n] (c) (d) (e) H(ew) = h[n] -6 -5 -4 -3 -2 -1 0 1 2 h[n] 1 1 1 h[n] -6-5-4-3-2-1 0 −1 n=-∞ -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 1 j 1 4 5 1 1 6 2 3 4 5 6 。 -6-5-4-3-2-1 0 1 2 3 4 5 6 n h[n] is real-valued. h[n] is real-valued. h[n] is real-valued. h[n] is purely imaginary. -j Among the four systems defined in (a), (b), (c) and (d), which system would you choose if you need to use it as a causal low pass filter?
Transcribed Image Text:Each of the following figures shows the impulse response of a LTI system h[n]. For each figure in (a), (b), (c) and (d): h[n]e-jnw, (ii) say whether H(e) as a function of w is even or odd or neither (iii) and sketch/plot the magnitude of the frequency response, i.e., |H(e³w)|, over - 27 < w 2π (you may use Matlab). (a) (b) (i) Firstly write an expression of h[n] and then find an expression of the frequency response of the system: In each figure, the value indicated for each impulse means the amplitude of that impulse. For example, if the value of an impulse at n = 3 is indicated to be 2j, it means 2jd[n - 3]. The value of h[n] is zero for all n outside the range shown in the figure. h[n] (c) (d) (e) H(ew) = h[n] -6 -5 -4 -3 -2 -1 0 1 2 h[n] 1 1 1 h[n] -6-5-4-3-2-1 0 −1 n=-∞ -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 1 1 j 1 4 5 1 1 6 2 3 4 5 6 。 -6-5-4-3-2-1 0 1 2 3 4 5 6 n h[n] is real-valued. h[n] is real-valued. h[n] is real-valued. h[n] is purely imaginary. -j Among the four systems defined in (a), (b), (c) and (d), which system would you choose if you need to use it as a causal low pass filter?
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