b3 Digital signal rpocessıng question. 3) Impulse response of an FIR and LTI system with linear phase is given as: h(n)={1, -1/2, 2, -1/2, 1},n=0,1,2,3,4.a) Calculate the frequency response of the system using DFT. Write the magnitude response, phaseresponse and the group delay of the system.b) Let h'(n)={1, -1/2, 2, -1/2, i, 0} signal be the periodic version of h(n) with period N=6. Find DFScoefficients of h'(n). Find and compare the computational loads of DFT and FFT algorithms.(Computational load for DFT is N²,and for FFT is Nlog2N.)c) The input signal x(n)={1, 2} is applied to the system in (a). Find the 5 points circular convolutionof x(n) and h(n) in time domain: c(n) = x(n) *s h(n)d) Now, calculate the output of the system, y(n), firstly with linear convolution: yı(n) = x(n) * h(n),then calculate the output with 6 points in time domain: yz2(n) = x(n) *6 h(n). Compare the results.

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3) Impulse response of an FIR and LTI system with linear phase is given as: h(n)={1, -1/2, 2, -1/2, 1}, n=0,1,2,3,4. a) Calculate the frequency response of the system using DFT. Write the magnitude response, phase response and the group delay of the system.

3) Impulse response of an FIR and LTI system with linear phase is given as: h(n)={1, -1/2, 2, -1/2, 1}, n=0,1,2,3,4. a) Calculate the frequency response of the system using DFT. Write the magnitude response, phase response and the group delay of the system.

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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The impulse response of a linear phase FIR and LTI system is given as h(n)={1, -1/2, 2, -1/2, 1}.a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.b) Let h'(n)={1, -1/2, 2, -1/2, 1, 0} be the periodic form of h(n) with N=6. Give the DFS coefficients of h'(n). Compare the computational load for DFT and FFT algorithms. (The calculation load for DFT is N2,For FFT, N is calculated as log2 N)c) The input sign x(n)={1, 2} is applied to the system in (a). Calculate the 5-point circular convolution of x(n) and h(n) in the time or frequency domain: c(n) = x(n) *5 h(n)d) Now calculate the output y(n) of the system first by linear convolution: y1(n) = x(n) * h(n), then by circular convolution of 6 points, in the time or frequency domain: y2(n) = x(n) *6 h(n). Compare the results.
PleaseThe input-output relationship of a discrete-time LTI system is given as follows?[n] = 2x[n − 4] − 3x[n − 6].a) Determine the impulse response of the system, h[n].b) Using h[n], show that the system is causal.c) Using h[n], show that whether the system is BIBO stable or not.d) Determine the transfer function H(z). Plot pole-zero diagram. Indicate ROC.e) Using H(z), show that whether the system is stable or not.f) Determine the frequency response of the system, if exists. Why?g) Determine the impulse response of the inverse system calculated in f).
1. Show that if the high-pass filter illustrated is scaled inboth magnitude and frequency, the transfer function is the same with s replaced by s/kf, where kf is the frequency scalefactor.2. In the prototype version of the high-pass filter circuit ,ωc=1 rad/s, R1=1 Ω, C=1 F, and R2=K ohms. What is the transferfunction of the prototype circuit?3. Using the result in (a), derive the transfer function of the scaledfilter.
Compute 8-point DFT of the discrete time signal , x(n)={1,2,1,2,1,3,1,3} using radix-2 DIF FFT Also sketch the magnitude and phase spectrum
The input-output relationship of a discrete-time LTI system is given as follows?[?] = 2?[? − 4] − 3?[? − 6].a) Determine the impulse response of the system, ℎ[?].b) Using ℎ[?], show that the system is causal.c) Using ℎ[?], show that whether the system is BIBO stable or not.d) Determine the transfer function ?(?). Plot pole-zero diagram. Indicate ROC.e) Using ?(?), show that whether the system is stable or not.f) Determine the frequency response of the system, if exists. Why?g) Determine the impulse response of the inverse system calculated in f).
Consider the output voltage measured across the resistor in the circuit shown below. a. Find the transfer function for the filter circuit above (??/??) as a function of jω. (Leave R and C as variables) b. Transpose the transfer function to a Magnitude and Phase , that is |?(??)|??? form. c. Approximate the magnitude and phase of H(jω) as ω approaches 0; and as ω approaches infinity. d. If R = 4000 ohms, C = 2.5uF what is the corner frequency ω0 in rad/s. e. What is the corner frequency, f0 in Hz? f. Is this a high pass or low pass filter? g. What is the passband gain of the circuit in [dB]. h. Assuming C does not change, choose R for a cut off frequency of 50Hz.
The impulse response of an LTI system is h(n) = 3δ(n) + (1/4)n u(n). Find the frequency response, H(e jω), and the difference equation of this system. An input signal x(n) = (1/3)n u(n), is applied to this system and an output signal y(n) is observed. Find the output signal, y(n), using DTFT methods. Give the system function H(z) using the frequency response H(ejω). Find the zeros, poles and ROC of this system and show them on the complex plane. Discuss the stability, causality, FIR/IIR and memory properties of this system.
The voltage transfer function of either low-pass prototype filtershown isH(s)=1s+1. Show that if either circuit is scaled in both magnitude and frequency, thescaled transfer function isH′(s)=1(s/kf)+1.
The impulse response of a linear phase FIR and LTI system is given as h[n]={2, -1, 3, -1, 2}.a) Calculate the frequency response of the system with DFT. Give the amplitude and phase responses and the group delay.b) Let h'[n]={ 2, -1, 3, -1, 2, 0} be the periodic state of h[n] with N=6. Give the DFS coefficients of h'[n]. Compare the computational load for DFT and FFT algorithms.c) The input sign x[n]={1, 2} is applied to the system in (a). Calculate the 5-point circular convolution of x[n] and h[n]: c[n] = x[n] ⊗ 5 h[n]d) Now calculate the output y[n] of the system first by linear convolution: y1[n] = x[n] * h[n], then by circular convolution: y2[n] = x[n] ⊗ h [n]. Compare the results.
In the circuit shown in the figure, Vcc = 12 V, Vin = 10 mV, β = 100, r0 = 40 kΩ, RB = 360 kΩ, RC = 3.3 kΩ, RE = 220 Ω, Rs = 0.5 kΩ and RL = 7.1 kΩ . Accordingly, find the voltage gain (Vout/Vin) of the circuit. NOTE-1: The output impedance of the transistor r0 will be taken into account in the calculations.NOTE-2: Capacitors are negligible at midband frequency.
1. Show that if the low-pass filter circuit illustrated isscaled in both magnitude and frequency, the transfer function of thescaled circuit is the same with s replaced by s/kf, wherekf is the frequency scale factor.2. In the prototype version of the low-pass filter circuit ,ωc=1 rad/s, C=1 F, R2=1 Ω, and R1=1/K ohms. What is the transferfunction of the prototype circuit?3. Using the result obtained in (a), derive the transfer function of thescaled filter.
In the circuit shown in the figure, Vcc = 12 V, Vin = 10 mV, β = 100, r0 = 40 kΩ, RB = 360 kΩ, RC = 3.3 kΩ, RE = 220 Ω, Rs = 0.5 kΩ and RL = 42.1 kΩ . Accordingly, find the voltage gain (Vout/Vin) of the circuit.NOTE-1: The output impedance of the transistor r0 will be taken into account in the calculations.NOTE-2: Capacitors are negligible at midband frequency.