Let x[n] be an input of a discrete time linear shift invariant system while its impulseresponse and output are denoted by h[n] and y[n] respectively. The umpulse response of this system isgiven ash[n] =(1)where d[n] denotes the discrete time unit impulse signal. Obtain the step response (ie. yn] for xin]=4/n]) of this system via convolution summation.

h(n) = ∑K=-∞∞δn-khn = .............δn+5+δn+4............δn+δn-1..........δn-5.....hn = 1 when n is…

Let xịn] be an input of a discrete time linear shift invariant system while its impulse response and output are denoted by h[n] and y[n], respectively. The impulse response of this system is given as h|n] =) 8[n -k] (1) %3D where 6 n] denotes the discrete time unit impulse signal Obtain the step response (i.c. yn for xfn] = u|n]) of this system via convolution summation.

Let xịn] be an input of a discrete time linear shift invariant system while its impulse response and output are denoted by h[n] and y[n], respectively. The impulse response of this system is given as h|n] =) 8[n -k] (1) %3D where 6 n] denotes the discrete time unit impulse signal Obtain the step response (i.c. yn for xfn] = u|n]) of this system via convolution summation.

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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Q1) Impulse response and the input of a discrete time LTI system are respectively h[n] = 28[n] – 8[n – 1] + d[n – 2] and x[n] = 28[n] + 8[n – 1] – 8[n – 2]. (a) Plot the impulse response h[n] versus n (b) Plot the input x[n] versus n (c) Determine and plot the output of the LTI system, y[n] = x[n] * h[n] (d) Find and plot y[n] = x[n] * h[3n] Hint: Do the convolution and plot the results for steps for n = -2,–1,0,1, 2, 3,4.
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Consider the first-order discrete-time system given by the difference equation: y[n] = -ay[n-1]+xn] The impulse response is the output of this system when the input is set to the unit pulse, so that a[n] = [n]. Similarly, the step response is the output of this system when the input is set to the unit step sequence, such that a[n] = u[n]. Calculate the impulse response and step response for the system given Assume the system is causal so that for n < 0 both x[n] = 0 and y[n] = 0. HINTS. There are a variety of approaches to solving for the step response and impulse response. Perhaps the easiest approach is to calculate the step response first, and then note the relationship between the step response and the impulse response. These are: 72 u[n] = Σ 6[m], _and_§[n] = u[n] — u[n — 1] m=-00 - The particular solution then for the step response is easier to determine than the particular solution for the impulse response.
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(a) Digital Convolution Consider an LTI system that has an impulse response h[n] given in the figure below (and is zero everywhere else): h[n] 3 2 1 -1 1 n -1 -2 -3 Suppose the input to the system is x[n] = u[n + 1] + u[n – 1] – 2u[n – 2]. Determine the output of the system, y[n]. You may provide your answer either as sample values and their corresponding sample number (n) or using a plot, remem- bering to label your axes.
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1. Show that x[n] + u[n] = xlk]. k=-00 2. The impulse response h[n] of a discrete-time LTI system is shown in Figure 1(a). Determine and sketch the output y[n] of this system to the input x[n] shown in Figure 1(b) without using the convolution technique. for h[n] |x[n] 0 23 -1 (a) (b) Figure 1.
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4. a) Find the complete solution for the difference equation y[n] – 0.9y[n-1] = x[n] with the input x[R]= (-1/4)"u[n] and initial condition y[-1]= 1. b) An LTI system has an impulse response h[n] and input x[n] displayed in Figure 2 below. (b.i) Apply the method of convolution by superposition to find and sketch the convolution output y[n] of the system. (b.ii) Determine and sketch the step response of this LTI system.