helllp 7- Take a system H such that its frequency response in the frequency range of [−π π],is5,H(e) =5,for w≤for 子,0,Otherwise.a) Sketch the frequency response of the system. Can you express this frequency re-sponse as the difference of two low-pass filters with two differenet cut-off frequencies?b) Find the impulse response h(n), of this system.c) Find the output, if the following signal is applied as the input to the systemx(n) = 2 cos(0.4πn) - 3sin(2.1лn) + cos(πn).d) Is this system realizable?(You may assume that for a low-pass filter F, with the cut-off freq. We, the impulseresponse is given as, ƒ(n) = sin(n) when n0, and f(0) = s.)7771

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Answered: 7- Take a system H such that its…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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Let the impulse response of a filter be ℎ[?] = {ℎ[0] = −0.5, 0.5}a) Calculate the frequency response ?(???). Is it a low-pass or a high-pass filter? Plot boththe magnitude and phase responses.b) Obtain the I/O relation for this filter.c) Is this a causal filter? Explain your answer.
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Please provide Handwritten answer. Electrical Engineering It is a common practice to low-pass filter signals before feeding them into an A/D Converter. The purpose of this filter is to eliminate any noise or other frequency components beyond a useful frequency range. For instance, if you are recording ECG, you would low-pass filter it at 100Hz because there is no useful frequency components beyond 100Hz and if there is any component that would be noise. What problem arises during sampling of the signal by the A/D Converter if this pre-filter is not used? How does the sampling frequency need to be adjusted with and without the pre-filter? Answer the question considering Nyquist theorem.
A Digital Filter is defined by the following difference equation: y[n] = 0.99 y[n-1] + x[n] The filter is clearly recursive. a. Determine the impulse response h[n]. b. Is the filter stable? c. Would you classify it as Low Pass, Band Pass ... or what? d. Plot its magnitude |G (w)|?
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3. You have need for a bandpass filter whose passband includes frequencies from 500 Hz up to 1000 Hz. You are planning to implement the filter digitally by first design- ing an analog bandpass filter which is then converted to digital form via the bilinear transformation. (a) If your sampling rate is 4000 Hz, what frequencies are appropriate to specify as the band edges for your analog design? (b) If your sampling rate is 8000 Hz, what frequencies are appropriate to specify as the band edges for your analog design?
Problem 2 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[n]e-inw (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(ew)|, over -27 < w 2π (you may use Matlab). (a) (b) 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) H(ejw) = h[n] 1 1 1 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 h[n] -6 -5 -4 -3 -2 -1 0 1 -6-5-4-3-2-1 0 1 n=-∞ 1 1 1 1 1 2 3 4 5 6 2 3 4 5 6 n n h[n] is real-valued. h[n] is real-valued. h[n] is real-valued.
Q1: For the pole-zero diagram shown in Figure below, the lengths of poles and zeros from the origin are 0.5 and 0.8 respectively: a. Find the transfer function H(z), impulse response h(n) and the difference equation. b. Calculate and plot the magnitude and phase frequency responses. Im(z) Re(z)
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