Loose Leaf for Engineering Circuit Analysis Format: Loose-leaf
9th Edition
ISBN: 9781259989452
Author: Hayt
Publisher: Mcgraw Hill Publishers
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Chapter A5.2, Problem 4P
(a)
To determine
The value of
(b)
To determine
The value of
(c)
To determine
The value of
(d)
To determine
The value of
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a) Show whether the following signals are periodic, if so find the fundamental periods. x [n] = 4 * cos (0.3π * n) + 3 * sin ^ 2 (0.2π * n) x (t) = 2 * cos (10π ^ 2 * t) + sin (3π * t)
b) Show whether the system given the input-output relation y (t) = βx (t) + u (t) is linear, memoryless, time invariant, causal and stable. Here β is constant.
Step functions can be used to define a window function. Thusu(t −1)−u(t−4) defines a window 1 unit high and 3 units wide located on the time axis between 1 and 4. A function f(t) is defined as follows: f(t)=0,t≤0;=−20t,0≤t≤1 s= −20,1 s≤t≤2 s=2 cosπ2t,2 s≤t≤4 s;=100−20t,4 s≤t≤5 s=0,5 s≤t<∞.
1. Sketch f(t) over the interval −1 s≤t≤6 s.
2. Use the concept of the window function to write an expression for f(t).
given that vc=q/C. derive the expression for q in terms of time t.
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- 1. a) Assume the voltage impulse response of a circuit is h(t)={0,t<0;10e−4t,t≥0. Use the convolution integral to find the output voltage if the input signal is 10u(t) V. 2. b) Repeat (a) if the voltage impulse response is h(t)={0,t<0;10(1−2t),0≤t≤0.5 s;0,t≥0.5 s. 3. c) Plot the output voltage versus time for (a) and (b) for 0≤t≤1 s.arrow_forwardIf the roots of the characteristic equation are -3,0 then the system is _________________________. Marginally stable Conditionally stable Stable Unstablearrow_forwarda) f(t) = 5 −3 sin(πt) sin (2πt) −sin(πt) cos (πt) on the interval [−1,1]. b) f(t) = cos (πt + π/3)+ sin (3π/2*(t) + π/6) on the interval [−2,2].arrow_forward
- s ( s+1 ) ( s+2) (s+3)+k =0 Draw the root-locus curves of the characteristic equation . (Note: Find the equation that gives the separation points of the root locus curves, but without solving the equation, give roughly the location of these points on the axis)arrow_forwardA system has the following characteristic equation: s + s + 3 + 2s + 2 = 0 Using the Routh-Hurwitz method, checkarrow_forwardWhen the root locus curve of the given system is drawn, which is the K value that provides s = -0.6 + 1.62j pole value?arrow_forward
- A DSP system is described by the following differential equation with zero initialcondition:y(n)+0.1y(n-1)-0.2y(n-2) =x(n)+x(n-1)a. Determine the impulse response y(n) due to the impulse sequence x(n) = (n).b. Determine system response y(n) due to the unit step function excitation, where u(n)= 1 for n 0.arrow_forwardThe response of a system, h(t) is given as in Figure 1 below where the amplitudeof this signal is 7. Then,this system is excited by an input of x(t) = (u(t) × (u(-t)+u(t))) /1. 1)Illustrate the input signal, x(t). 2)Calculate the convolution output of the system y(t) = x(t) ∗ h(t). Nextdetermine y(t) when t is 1 sec 2)Prove the solution in Q2 is comparable when solving in frequency domain(Laplace). Next, sketch the signal for convolution output.arrow_forwardIf x(n)={1, 2, 0, -1} and h(n)={1, 2, 0, -1} find y(n). don't care where n=0.arrow_forward
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Routh Hurwitz Stability Criterion Basic Worked Example; Author: The Complete Guide to Everything;https://www.youtube.com/watch?v=CzzsR5FT-8U;License: Standard Youtube License