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Accounting Information Systems
How system function is defined for a CT system?
A triangular pulse signal \(x(t)\) is shown in Fig. 1.77a. Sketch the following signals. (a) \(x(4 t)\); (b) \(x(4 t+3)\); (c) \(x(-3 t+2)\); (d) \(x\left(\frac{t}{3}+2ight)\); (e) \(x(3
Sketch the even and odd parts of the following signals shown in Fig. 1.88a and \(\mathrm{b}\).Figure 1.88 a and b (a) 2 0 x(t) 2 (b) 1 + x(t) 0 2 t
Consider the CT signal \(x(t)=\delta(t+4)-\delta(t-4)\). Sketch \(\int x(t) d t\) and find the energy of the signal (Fig. 1.89).Energy \(E=8\).Figure 1.89 -4 [18(1+4)-8(1-4)]dt 0 4 +
Find the energy of the following CT signal. (a) \(x(t)=\operatorname{tri3} t\); (b) \(x(t)=2 \operatorname{tri}\left(\frac{t}{2}ight)\);(c) \(x(t)=\operatorname{rect10t}\); (d) \(2
What is the average power of the triangular wave shown in Fig. 1.90? Average power \(P=\frac{1}{3} \mathrm{~W}\).Figure 1.90 Triangular wave 1 0 x(t) 1 M 3 4 2 5 6 t
(a) The system response requires memory. Hence, it is dynamic.(b) The output depends on the present input only. Hence, it is causal.(c) The output due to the delayed input is not the same as the
(a) The output response depends on present and past inputs. Hence, it is dynamic.(b) The output does not depend on the future input. Hence, it is causal.(c) The output due to the delayed input is
(a) The system response depends on present, past, and future inputs. Hence, it is dynamic.(b) Since the output depends on the future input, it is non-causal.(c) The output due to the delayed input is
The output depends on present, past, and future inputs.(a) The system is dynamic.(b) The system is non-causal.(c) The output due to the delayed input is not the same as the delayed output. The system
(a) The system requires memory and so it is dynamic.(b) The output depends on present and past inputs. Hence, it is causal.(c) The output due to the delayed input is same as the delayed output. The
Consider the system shown in Fig. 1.91. Derive expressions for the impulse response and unit step response of the system. Also determine \(T, t_{r}, t_{d}, t_{s}\) for step input.Figure 1.91 R(s)
Consider the second-order system shown in Fig. 1.92. The system is subjected to unit step input. Derive the expression for the output variable. Determine the time domain specifications \(T, t_{s},
Explain why system is tested for impulse and step inputs.
Consider the mechanical system shown in Fig. 1.93a. Draw the F-V and F-I analogous circuits and verify by writing down the dynamic equations describing the given system and the electric circuit so
What is a Fourier series?
What are the different forms of representing Fourier series?
Give mathematical expression for trigonometric Fourier series?
What is the effect of symmetry in trigonometric Fourier series?
What is half wave symmetry?
Give the mathematical expression for the cosine Fourier series.
Give mathematical expression for the exponential Fourier series?
How the coefficients of exponential Fourier series are related to the coefficients of trigonometric and cosine Fourier series?
Why exponential Fourier series is preferred to represent the Fourier series?
What do you understand by Fourier spectrum?
What do you understand by existence of Fourier series?
What do you understand by convergence of Fourier series in the mean?
What are Dirichlet conditions?
What do you understand by Parseval's theorem as applied to Fourier series?Parseval's theorem anb = [bx + abiz iabjez +abr +.. 12/17 2 1 2 = ab + ab+... (2 b + 0 + 0 + 2;by + ... by + + ...) +* -R
What are differentiating and integrating properties of Fourier series?
Determine the trigonometric and exponential Fourier series representation of the signal \(x(t)\) shown in Fig. 2.14?Figure 2.14(a) Trigonometric or quadratic Fourier series.(b) Exponential Fourier
Consider the following signal:\[x(t)=\cos \left(\frac{1}{3} t+30^{\circ}ight)+\sin \left(\frac{2}{5} t+60^{\circ}ight)\]Determine (a) Whether the signal is periodic, (b) Find the fundamental period
For the signal shown in Fig. 2.15, determine the coefficients of exponential Fourier series. -4 - -3 -2 - 1 2 1 4 x(t) -1 0 | 1 2 93 3 4 5 6 t
Find the exponential Fourier series coefficients for the signal shown in Fig. 2.16a and plot its amplitude and phase spectrum.Figure 2.16a (a) -3 -2 - 1 - x (t) 1 0 et 1 2 4 3 +
Consider the signal shown in Fig. 2.17. Determine the exponential Fourier series coefficients. - 2 x(1) 1 2 --1 - 0 2+1 3 4
What do you understand by Fourier transform pair?
How Fourier transform is different from Fourier series?
How FT is developed from Fourier series?
How Parseval's Energy theorem is defined for the frequency domain signal?
What is the connection between Fourier transform and Laplace transform?
What do you understand by frequency response?
What is the condition required for the convergence of Fourier transform?
What is the Fourier transform of x (t) = d dt2x (t+1)
What is the FT of \(x(t)=[\delta(t+5)-\delta(t-5)]\) ?
Find the FT of \(x(t)=2[u(t+6)-u(t-6)]\) ?
Consider the following continuous time signal.\[x(t)=e^{-5|t|}\]Find the FT. Hence determine the FT of \(t x(t)\).
For the signal \(X(j \omega)\) shown in Fig. 3.43, determine \(x(t)\) ?\[x(t)=5 \frac{\sin 5 t}{\pi t}\] -5 X(jw) 5 0 5 3
Consider the signal shown in Fig. 3.44. Find \(X(j \omega)\). What is the FT for \(x(t-1)\) ? - 1 - +x(t) 2 1 0 1
Using Parseval's theorem evaluate energy in the frequency domain. 8118 anbn = . |aybz + iayb2e-iz iagbjeiz + agb2% + - 27 (2 by + 0 + 0 + 2magby + ...) = ab + agbg + ..
\[x(t)=e^{-2 t} u(t)\]and\[\begin{aligned}h(t) & =e^{-4 t} u(t) \\y(t) & =x(t) * h(t)\end{aligned}\]Using time convolution property find \(Y(j \omega)\) and \(y(t)\) ?
\[\begin{aligned}x(t) & =e^{-2 t} u(t) \\h(t) & =e^{-2 t} u(t) \\y(t) & =x(t) * h(t)\end{aligned}\]Find \(Y(j \omega)\) and hence \(y(t)\) ?
A certain LTIC system is described by the following differential equation.\[\frac{d y(t)}{d t}+2 y(t)=x(t)\]Determine the Frequency response and the Impulse response?
What is Laplace Transform?
What do you understand by LT pair?
What is bilateral Laplace transform?
What is unilateral Laplace transform?
What do you understand by LT of right-sided and left-sided signals?
What is the connection between LT and FT?
What do you understand by Region of convergence?
How do you identify the ROC of a causal signal?
How do you identify the ROC of a non-causal (left-sided) signal?
How do you identify the ROC of a bilateral Laplace transform?}
State any three properties of ROC.
Identify the ROCs for the following signals and sketch them in the \(s\)-plane?
Sketch the ROC of the following T.F. of a certain causal system and mark the poles and zeros.
Sketch the ROC of a non-causal system whose T.F. is given as\[H(s)=\frac{(s+2)(s-2)}{s(s+1)(s-3)}\]Mark the poles and zeros of \(H(s)\).
What are initial and final value theorems?
Find the initial and final values of \(x(t)\) whose LT is given by\[X(s)=\frac{(s+5)}{\left(s^{2}+3 s+2ight)}\]
Define transfer function.
Define poles and zeros of the transfer function.
What do you understand by eigenfunction of a system?
What do you understand by causality of an LTIC system?
What do you understand by stability of an LTIC system?
What do you understand by impulse response and step response of a system?
What do you understand by zero state response and zero input response?
What do you understand by natural response and forced response of a system?
Are zero input response and natural response and zero state response and forced response same?
Comment on the solutions of the differential equations obtained by the application of LT and by classical method?
What do you understand by asymptotic stability of an LTIC system?
What do you understand by marginal stability of the system?
What do you understand by zero input stability and zero state stability?
What do you understand by bounded input and bounded output (BIBO) stability?
Find the transfer function of LTI system described by the differential equation\[\frac{d^{2} y(t)}{d t^{2}}+3 \frac{d y(t)}{d t}+2 y(t)=2 \frac{d x(t)}{d t}-3 x(t)\]
Find the LT of \(x(t)=e^{-a t} u(t)\).
Given \(\frac{d y(t)}{d t}+6 y(t)=x(t)\). Find the T.F.
Find the LT of \(\boldsymbol{u}(\boldsymbol{t})-\boldsymbol{u}(\boldsymbol{t}-\boldsymbol{a})\) where \(\boldsymbol{a}>\mathbf{0}\).
Find the LT of \(x(t)=+e^{-3 t} u(t-10)\) ?
Find the LT of \(x(t)=\delta(t-5)\) ?
What is the output of a system whose impulse response \(h(t)=e^{-a t}\) for a delta input?
Find the LT of \(\boldsymbol{x}(\boldsymbol{t})=\boldsymbol{t} \boldsymbol{e}^{-\boldsymbol{a t}} \boldsymbol{u}(\boldsymbol{t})\) where \(\boldsymbol{a}>\mathbf{0}\) ?
Determine the LT of\[\begin{array}{rlrl}x(t) & =2 t & 0 \leq t \leq 1 \\& =0 & & \text { otherwise. }\end{array}\]
Determine the output response of the system whose impulse response \(h(t)=e^{-a t} u(t)\) for the step input?
Find the LT and sketch the pole-zero plot with ROC for \(x(t)=\) \(\left(e^{-2 t}+e^{-3 t}ight) u(t)\).
Find the LT of \(x(t)=\delta(t+1)+\delta(t-1)\) and its ROC.
Find the LT of \(x(t)=u(t+1)+u(t-1)\) and its ROC.
Using convolution property determine \(y(t)=x_{1}(t) * x_{2}(t)\) where \(x_{1}(t)=e^{-2 t} u(t)\) and \(x_{2}(t)=e^{-3 t} u(t) ?\)
Find the zero input response for the following differential equation.
Find the LT \(\frac{d}{d t}[\delta(t)]\).
Find the LT of \(x(t)=\delta(2 t)\).
Find the LT of integrated value of \(\delta(t)\).
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