2. LTI SystemSuppose a system with y[n] as the output and x[n] as the input is defined byy[n] = x[n] – x[n – 1] – x[n – 2]a) Please find the frequency response using Discrete Time Fourier transform. Plotmagnitude and phase vs frequency ob) Is the systems linear phase, why?c) Derive system impulse response h[n]. Let input be x[n] - {1, 2 }. Find the output ofthe system y[n].d) Assume the input x[n] = cos (En) u[n] + cos n) u[n] is applied to this system, whatis the steady state output?

"Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

LTI System Suppose a system with y[n] as the output and x[n] as the input is defined by yim) = x[m] – x[n – 1- x[n – 2] a) Please find the frequency response using Discrete Time Fourier transform. Plot magnitude and phase vs frequency . b) Is the systems linear phase, why? c) Derive system impulse response h[n]. Let imput be x|n] - L 21. Find the output of the system y(n]-

LTI System Suppose a system with y[n] as the output and x[n] as the input is defined by yim) = x[m] – x[n – 1- x[n – 2] a) Please find the frequency response using Discrete Time Fourier transform. Plot magnitude and phase vs frequency . b) Is the systems linear phase, why? c) Derive system impulse response h[n]. Let imput be x|n] - L 21. Find the output of the system y(n]-

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...

See similar textbooks

Similar questions

a. Show that 2-D discrete Fourier Transform of a M × N digital image is periodic.That is, you must prove that F(u + M, v + N) = F(u, v). b. Suggest two methods to bring the frequency origin of a discrete Fourier Transform of an image to the center ofthe 2-D array of frequency plane.
For the causal discrete-time LTI system implemented using thedifference equation y[n] =-0.25y[n-1]+0.15y[n-2]+4x[n]+0,25x[n-1] where x[n] is the input signal, and y[n] is the output signal. a) Draw the direct form-II block diagram of the system. b) Find the transfer function of the system, H(z). c) Sketch the pole-zero diagram and indicate the ROC. Determine if the Fouriertransform of the system H(ejw) exists. If the Fourier transform exists, write H(ejw).
Suppose that we have the LTI system defined by the differential/integralequations given below, where x(t) and y(t) denote the system input andoutput, respectively. Find the frequency response ?(jw) and the impulseresponse (h(t)) of the system. ******Only use Fourier Transform properties for the solution, the othersolutions will not be considered.
a. Which of the following is true? The Fourier transform of a unit rectangular pulse is A. real. B. not oscillating. C. complex. D. neither real nor complex. b. Which of the following is true? For system and signal operations, the symbol “*” is typically shared between A. convolution and complex conjugate. B. linear combination and complex conjugate. C. orthogonality and complex conjugate. D. multiplication and complex conjugate. c. Which of the following is true? The Fourier transform is based on A. The Fourier series by substituting the signal x(t) into Fourier coefficient’s expression. B. The Fourier series by substituting the Fourier coefficient’s expression into a random signal which is periodic over a defined period. C. The Fourier series by substituting the Fourier coefficient’s expression into x(t). D. The Fourier series because this is a logical process.
Briefly explain the behavior of the transfer function of an ideal low-pass filter with a bandwidth of 2ωc in Fourier domain, i.e explain how H(w) of an ideal low pass filter with a bandwidth of 2ωc is.
a) Make a plot of the normalized fft magnitude as a function of frequency (real frequency in Hz). Only display the frequency range between -1kHz and 1kHz. b) On the same figure as part (c), superimpose the magnitude of the Fourier series coefficients, |??|, as a function of frequency as a stem plot. Again, only display the frequency range between -1kHz and 1kHz. How well do they compare? Hint*: Consider making a frequency vector containing only the Fourier harmonic frequencie
x(0)=4, x(1)=3, x(2)=2, x(3)=1, x(4)=0, x(5)=0 give as, x(n) series ( 0≥ ? ≥ 5 ). a) calculate x(k) with discrete fourier transform coefficients (every calculation step must be given)
a continuous time signal x(t) = cos(400*pi*t) is sampled at Ts = 1/300s. a) draw the continuous time fourier transform Xs(j omega) of the sampled signal. b) aslo draw DTFT spectrum c) does aliasing occur? what is the reconstructed signal? d) can the sampled signal be unsampled by a rate L = 3? give the new sampling frequency.
A signal given by m(t) = 3cos(20πx103t) frequencymodulates a 1MHz carrier signal to produce a frequency deviation of 40KHz. Assume the carrier amplitude is 5V. a) Determine the modulation index. b) Write the time domain expression for the resulting FM signal ΦFM(t). c) What is the bandwidth of the signal.
The following finite digital signal x[n] was acquired during sampling. The samples outside of the finite bounds of the given signal are x[n] = [0.5,-0.7,0.3,-0.2,1.5] a. Write the expression for the Discrete Fourier Transform (DFT) of the given signal as a function of discrete frequency Be sure to expand the summation over all n, but you DO NOT have to substitute the k values. Simply state what the k values are. You DO NOT have to compute the actual values of b. Compute the magnitude of the DC component of the given signal using the appropriate k value and X(k) determined in (a).
expressed by P(??Ω), G(??Ω), K(??Ω)Find the Fourier transform (DTFT) of the signals p [n], g [n] and k [n].
What is the bandwidth of an AM signal whose carrier is 2.1 MHz modulated by a 1.5-kHz square wave with significant harmonics up to the fifth? Calculate all the upper and lower sidebands produced? (Our lesson is AMPLITUDE MODULATION FUNDAMENTALS) (Please box the answer )