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Questions and Answers of Accounting Information Systems

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 \(\delta(t)\).
Why integrators are preferred to differentiators in structure realization?
What are the components required in structure realization?
Mention the steps to be followed to realize a transposed structure from canonic form structure.
Find the LT of \(x(t)=e^{-2|t|}\) and ROC.
Find the LT of \(x(t)=e^{2|t|}\) and ROC.
Find the LT of \(x(t)=\left(e^{2 t}+e^{-2 t}ight) u(t)\) and the ROC.
Find the LT of \(x(t)=\left(e^{2 t}+e^{-2 t}ight) u(-t)\) and the ROC.
Find the LT of \(x(t)=\left(e^{-6 t}+e^{-4 t}ight) u(t)+\left(e^{-3 t}+e^{-2 t}ight) u(-t)\)
Find the LT of\[x(t)=\left(e^{-6 t}+e^{-3 t}ight) u(t)+\left(e^{-4 t}+e^{-2 t}ight) u(-t)\]
Find the LT and ROC of\[x(t)=e^{-3 t}[u(t)-u(t-4)]\]
Find the inverse LT of the following \(X(s)\) for all possible combinations of ROC.\[X(s)=\frac{4}{(s+1)(s-3)}\]
Find the inverse LT of \(X(s)\) X (s) = 8(s + 2) s(s + 4s + 8) ROC: Re s> -2
Find the inverse LT of X (s) = s + 2s + 4) (s + 2) (s + 4) ROC: Res> -2
Find the inverse LT of X (s) = (s + 3s + 1) (s + 5s + 6) ROC: Re s> -2
Find the inverse \(\mathbf{L T}\) of X (s) = S +85 +21s + 16 (s + 7s +12) ROC: Re s> -3
Find the inverse LT of X (s) = 10se-2s +5e-4s +6 (s + 13s +40) ROC: Re s> -5
Find the initial and final value of \(y(t)\) if its \(\mathrm{LT} Y(s)\) is given by Y(s) = (s + 2s + 5) s (s + 4s + 6)
Using convolution property of LT find \(y(t)=x_{1}(t) * x_{2}(t)\)\[\begin{aligned}& x_{1}(t)=u(t) \\& x_{2}(t)=e^{-2 t} u(t)\end{aligned}\]
Consider an LTIC system described by the following differential equation\[\frac{d^{2} y(t)}{d t^{2}}+\frac{d y(t)}{d t}-6 y(t)=X(s)\]Determine(a) the system transfer function.(b) impulse response of
Determine the LT of the periodic signal shown in Fig. 4.53. 3 X(t) 2 1 1 I 4 6 8 10 t
Consider the electrical circuit shown in Fig. 4.54. Initially the switch \(S\) is closed. Derive an expression for the current through the inductor as soon as the switch is open. \(i(t)=\left[3 e^{-3
Find the Laplace inverse of the following \(\boldsymbol{X}(\boldsymbol{s})\) (Fig. 4.55): -2 jw 2 (a) ROC: Res > 2 Causal and unstable system -2 jw 0 2 (c) Non-causal and stable system -2 a jw (b)
Solve the following differential equation:\[\frac{d^{2} y(t)}{d t^{2}}+\frac{d y(t)}{d t}-2 y(t)=\frac{d x(t)}{d t}+x(t)\]The initial conditions are \(y\left(0^{-}ight)=2 ; \frac{d
The unit step response of a certain LTIC system \(y(t)=10 e^{-5 t}\). Find (a) The impulse response? (b) The response due to the exponential decay \(x(t)=e^{-3 t} u(t)\)?
The impulse response of a certain system is \(h_{1}(t)=e^{-3 t} u(t)\) and the impulse response of another system is \(h_{2}(t)=e^{-5 t} u(t)\). These two systems are connected in cascade. Find (a)
The impulse response of a certain system is given by \(h(t)=e^{-5 t}\). The system is excited by \(x(t)=e^{-3 t} u(t)+e^{-2 t} u(-t)\). Determine(a) The system transfer function(b) Output of the
A certain LTIC system is described by the following differential equation\[\frac{d^{2} y(t)}{d t^{2}}-\frac{d y(t)}{d t}-30 y(t)=\frac{d x(t)}{d t}+4 x(t)\]The system is subjected to the following
A certain LTIC system is described by the following differential equation:\[\frac{d^{2} y(t)}{d t^{2}}+3 \frac{d y(t)}{d t}+2 y(t)=\frac{d x(t)}{d t}+4 x(t)\]where \(x(t)=e^{-3 t} u(t)\). The initial
An LTIC system has the following T.F\[H(s)=\frac{(s+10)}{s^{3}+5 s^{2}+3 s+4}\]Determine the differential equation.
An LTIC system is described by the following differential equation\[\frac{d^{2} y(t)}{d t^{2}}+4 \frac{d y(t)}{d t}+3 y(t)=\frac{d x(t)}{d t}+4 x(t)\]The system is in the initial state of
The impulse response of an LTIC system is given by \(x(t)=e^{-2 t} u(t)\). Is the system causal?
The impulse response of an LTIC system is given by \(h(t)=\boldsymbol{e}^{-2|t|}\). Is the system causal.
Consider the following transfer function.\[X(s)=\frac{1}{(s+2)(s-2)}\]Identify all possible ROCs and in each case find the impulse response, stability, and causality. Also sketch the ROC. (1) ROC:
Find the bilateral LT of _a= (1) x -10|t|
Find the bilateral LT of x (t) = eu(t) e (1-)n,
Find the bilateral LT of X (s) = (s - 5) (s + 2)(s + 5) ROC: 5 < Res < -2
Find the inverse bilateral LT of X (s): = (s + 2) (s 2)(s - 5) - ROC: 2 Res
Find the inverse bilateral LT of X (s) = (s - 2s - 3) (s + 2) (s + 4) (s 6) - ROC: 2 < Res < 6 -
Define the \(z\)-transform.
Define \(z\)-transform pair.
What do you understand by ROC of \(z\)-transform?
Mention the properties of ROC.
What is the scaling property of \(z\)-transform?
What is the convolution property of \(z\)-transform?
What is difference property in the \(z\)-transform?
What are initial and final value theorems?
What do you understand by the time reversal property of \(z\)-transform?
What do you understand by the causality of an LTID system?
What do you understand by stability of an LTID system?
When the system is said to be both causal and stable?
Define system function.
What is the \(z\)-transform of \(\delta[n-2]\) ?
What is the \(z\)-transform of \(u[n]\) and \(\delta[n]\) ?
Find the \(z\)-transform of \(x[n]=u[n]-u[n-5]\).
Write the relationship between \(z\)-transform and Fourier transform.
Write the relationship between \(z\)-transform and Laplace transform.

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