Question 4: This question relates to z-transform.a)A digital system is described by the following difference equationy[n]+2y[n− 1] + y[n − 2] = x[n − 1]-(i)Find the transfer function H(z).(ii) Determine the stability of the system.(iii) Determine the system output response y[n] for the input x[n] = u[n].

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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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When the unit step function is applied to the input of the control system given below, the peak time of the output signal is 0.59 s and the settlement time is 0.88 s. It is also known that the steady state error of the system is 10% for the same input. So what is the unknown K2 value in the transfer function? calculate.
1. Sketch the following discrete-time signals. a. xn] = u[n– 5]–uln – 6] b. x[n]=10u[-n + 2]– Su[n – 2] x[»] = 48[n + 5]+ (n+5)u[n + 3]– mu[n] c.
Obtain the transfer function of the system and find the unit step response. Show all intermediate operations in detail. m=1 kg b=20 Ns/m k=125 N/m ww k m
For the signal x[n] shown in the following figure, sketch y[n] = x[-2-n] x [n] ... ... -3 F1 J0 1 2 3 4 5 6 7
B) A signal f(t) = 2e-atu(t) is applied to the input of system have frequency transfer function Determine the required relations between the constant a and b such that exactly |H(w) = %3D Vw² +b? 50% of the input energy on a 1 ohm basis, is transferred to the output.
4. Find N-point DFT for the signal h: hy = 8[k – 1] + 1.9 8[k – 6].
Discrete Signals and Discrete Time systemsx[n1] = (values) 9 random integer values from -10 to 5x[n2] = (values) 9 random integer values from -5 to 5 a. Plot the graph setting the middle integer value at n = 0 showing the all samples.b. Plot the graph x[-n] showing all the samples.c. Plot the graph x[n-3] showing all the samples.d. Plot the graph x[n+2] showing all the samples.e. Plot the graph x[2n] showing all the samples.f. Plot the graph x[n/3] showing all the samples.g. Evaluate the convolution of x[n1] and x[n2].
12 - When the unit step function is applied to the input of the control system given below, the peak time of the output signal is 0.59 s and the settlement time is 0.88 s. It is also known that the steady state error of the system is 10% for the same input. So what is the unknown K2 value in the transfer function? calculate.A) 5.7B) 4.9C) 3.7D) 7.3E) 6.4
3. given the system coefficients below. The initial conditions are given as y(-1) = 1 and y(-2) = 1, and x(n) = 3u(n). Solve for the zero-input, zero-state responses, and the total response of the system b, =[1 -2 1] a = [1 -0.77178 0.7225]
1) y(t) = 3e-2tu(t)The function above defines the model of a signal from the braking activities of a vehicle.a)sketch the signal using the information above.b)Determine the power & energy of the signal. 2) A sensor is used to capture voltage signal y(t) from a volcanic eruption & passed through an active highpass filter system for processing.a)Make a circuit diagram sketch for the process.b) Derive an expression for the transfer function of the system. c)Cut-off frequency = 2.5kHz & Input voltage = 20mVUse the above data to determine the values of the circuit components needed to produce an output of five volts. d) Suppose a two volts input voltage is applied to the filter system, In terms of unit step function, i) what is the expression for this input? ii)Determine the output z(t) of the system. Assumption: All the circuit components in the transfer function equation have unity values.
Question 3: Consider the simple signal processing system shown in the figure. The sampling period of A/D and D/A converters are T= 5 ms and T1= 1 ms, respectively. Determine the output ya(t) of the system if the input is Xa(t) = 3cos100nt + 2 sin250xt (t in seconds) x.(t) A/D T x(n) D/A T1 Postfilter y.(t) The postfilter removes any frequency component above F/2.
A sinusoid signal v(n) = 5 sin( @₂ .n) with f=5 Hz and fs = 10 kHz has to be quantized @ (Vq(n) = Q[v(n)]) with a midtreat quantizer. The range of the signal is ±5 V and the word length of the quantizer 4 bits. The quantizer is at digital full scale. (a) How many quantization levels L does the quantizer have? What is the value of A? (b) Sketch the input-output characteristic of the quantizer. How different is a midtreat quantizer to a midrise quantizer. (c) For time index n = 1250 calculate the quantized value v₁ (n), the quantization error eq(n) and represent vą (n) using RZ code. (d) Calculate the power P of the quantization noise. (e) Determine the SNR in dB.

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