It is known that a causal, LTI system has the impulse response: n-1 n-1 h(n) = (-4 (-1) + 5 (-3)^) u (n − 1) - where u(n) is the unit-step signal. a) Write the system-function H(z) that corresponds to the system. Is the system stable (Justify!!!) ? b) Sketch the pole-zero plot of the system c) Using contour integration/method of residues, obtain the time-domain response of the system to the signal whose Z-transform is X(z) = ROC: |Z| >1 (z-1)

It is known that a causal, LTI system has the impulse response: n-1 n-1 h(n) = (-4 (-1) + 5 (-3)^) u (n − 1) - where u(n) is the unit-step signal. a) Write the system-function H(z) that corresponds to the system. Is the system stable (Justify!!!) ? b) Sketch the pole-zero plot of the system c) Using contour integration/method of residues, obtain the time-domain response of the system to the signal whose Z-transform is X(z) = ROC: |Z| >1 (z-1)

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 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.
A) Give the graphical representation and the relationship form of 1) r(-5+n) 2) p(n- 3) u(n).r(-5+n). p(n-3) B) Write the signal in form U(n) by using the basic operation
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.
(b) A ramp discrete time signal of f[n] is given in Figure Q1(b) for n = -3 until n = 4. Modify this signal by applying the concept of basic on transformation to produce a new signal, g[n] that meets all these criteria below: • Time reversal • Advanced time shifting in 2 units • 2.5 times in amplitude scaling You need to sketch the signal g[n]. f[m] 4 3 2 2 3 -1 -2 -3 Figure Q1(b) (c) Prove the obtained answer in (b) by determining the expression for g[n] in tem of f[n].
A second order dynamic system with the states x1 and x2 is represented by the following block diagram as shown in FIGURE Q2. X1 s + 3 S +1 + -2 FIGURE Q2 Obtain a state-space representation of the system in controllable canonical form (phase-variable form). Construct the corresponding signal flow graph in its controllable canonical form.
T1 (t) and r2 (t) are two given signals. r1 (t) is band-limited to 500 Hz and r2 (t) is bandlimited to 2.5 kHz. 1. f. Hz 500 O 500 1 f, Hz -2500 2500 QUESTION 2 These signals are multiplexed by impulse-sampling them at a rate T and combining the samples as shown in the figure. The multiplexer output is given by y (t) = 1 (t) E 5(t – nT') + #2 (t) E 6 (t- nT –5) n=-00 n=-00 (a) demultiplexing? What is the minimum value of T which makes it possible for us to recover the signals after (b) Plot the Fourier transform of r1 (t) E 8 (t – nT'). n=-00 NOTE: F (# (t)] = / (t) e-jut dt 2n FE 8 (t – nT) ) = E 6 (w - kuo) k=-00
review the time-domain solutions for the series and parallel 2nd order switched voltage step responses by showing and discussing their complete derivations. Note the relationship between loaded Q and ringing frequency. Cs Ro 50 +. Vsig V(t)
Consider a negative unity feedback control system KG(s): K(s + 10) s(s+5)(s+ 6) (s+8) Using Matlab, write a code to plot the root locus of this system. Copy and paste your code as well as the root locus graph.
K(s+1) 1. One general feedback system has G(s) = s² (s+3)(s+4) and H(s)=2s Find the value of gain K that causes steady state error ess Equal to 0.01 when the input is a ramp input signal of size 1 unit.
Ex. 449. K*G(s)=K*1/(s(s+3)(s+6)) is the FTF of a unity-feedback closed-loop system. Calculate the asymptote centroid and show it on a professional root locus plot. Draw the asymptote plot separately. Determine the break-away point and K at the break-away point and show both on the plots. Formal documentation required. ans: 3
Obtain the transfer function of the two systems in figures (a) and (b) below. Initial conditions are all zeros. Find the range of values of k, k1 and k2 for which the systems are naturally stable with m= 10 kg. you may use any design method.
Solve All parts or will dislike answer A. Find the open-loop transfer function . Y(S) / R(S)B. Find ?(?) when the input ?(?) is a step function (use expansion of partial fractions).C. State the damping factor ?.D. Indicate whether the system is overdamped, underdamped, or critically damped.E. Indicate the natural frequency of the system ??.F. Indicate the poles and zeros of the system.G. Use the end theorem to find the steady-state value.H. Find ?(?) (use inverse Laplace transform).I. Plot the time response of the system.