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The output of a linear time invariant system can be obtained from its unit impulse response function and the input function by

This question was previously asked in
VSSC ISRO Technical Assistant Electronics 14 July 2021 Official Paper
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  1. Convolution
  2. Addition
  3. Multiplication
  4. Autocorrelation

Answer (Detailed Solution Below)

Option 1 : Convolution
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Detailed Solution

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Discrete-Time System:

The convolution of two a signal with a system with impulse response h(n) is represented as:

y[n] = x[n] ∗ h[n]

Continuous Time System:

The convolution of two a signal with a system with impulse response h(t) is represented as:

y(t) = x(t) ∗ h(t)

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More Properties of Z Transform Questions

Q1.The 𝑍-transform of a discrete signal 𝑥[𝑛] is \(\rm X(z)=\frac{4z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}\) with ROC = R. Which one of the following statements is true?
Q2.Which one of the following statements not correct for convolution?
Q3.Two systems with impulse responses h1(t) and h2 (t) are connected in cascade. Then the overall impulse response of the cascaded system is given by
Q4.Which of the following is not a step in the evaluation of convolution?
Q5.The ROC of the Z-Transform of the signal 2nu(n) - 3nu(-n - 1):
Q6.If ROC1 is the region of convergence of x(n) and ROC2 is the region of convergence of y(n), then x(n) * y(n) is _______. (Where '*' represents the convolution opetation)
Q7.The output of a linear time invariant system can be obtained from its unit impulse response function and the input function by
Q8.Frequency scaling [relationship between discrete time frequency (Ω) and continuous time frequency (ω)] is defined as 
Q9.Convolution of two sequences X1[n] and X2[n] is represented as
Q10.If Z transform of x(n) is X(z) then the Z transform of x(n - k) is _______

More Z Transform Questions

Q1.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q2.What is the formula of finding the final value of any time varying function f(t)?
Q3.The z-transform of the impulse response of a causal LTI system is H(z) = \(\frac{1}{2}\frac{z^{-1}}{z^{-2} - 4.5z^{-1 }+5}\) .What is an input x(n) that would produce the output y(n) = u(-n) + (0.5)n u(n)? \(\frac{1}{2}\frac{z^-1}{z^-2 - 4.5z^-1 +5}\)12z−1z−2−4⋅5z−1+512z−1z−2−4⋅5z−1+512z−1z−2−4⋅5z−1+512z−1z−2−4⋅5z−1+12z−1z−2−4⋅5z−1+12z−1z−2−4⋅5z−1+ 12z−1z−2−4⋅5z−1+ 12z−1z−2−4⋅5z−1+ 12z−1z−2−4⋅5z−1+5 12z−1z−2−4⋅5z−1+5
Q4.The 𝑍-transform of a discrete signal 𝑥[𝑛] is \(\rm X(z)=\frac{4z}{\left(z-\frac{1}{5}\right)\left(z-\frac{2}{3}\right)(z-3)}\) with ROC = R. Which one of the following statements is true?
Q5.The z transform of e−t sampled at 10 Hz will be:
Q6.Consider the transfer function \(\rm H_c(s)=\frac{1}{(s+1)(s+3)}\) Bilinear transformation with a sampling period of 0.1 s is employed to obtain the discrete-time transfer function  Hd(z). Then Hd(z) is _______
Q7.Consider a signal x[n] = 2n u [n] having Z Transform as X (z) with ROC R. The Inverse Z Transform for X(2z) will be:
Q8.For an LTI system, the transfer function is \(H(z) = \frac{z}{{\left( {z - 0.2} \right)\left( {z - 0.5} \right)}};|z| > 0.5\), the system is ______ and _______.
Q9.If an LTI system with the transfer function H(z) = 1 + 2z-1 is excited with input x (n) = {3, 4}, compute the output of the system.
Q10.For a casual LTI system the impulse response is \(h(n)= \left\{ {\mathop 1\limits_ \uparrow ,2,1,3} \right\}\). What will be the system difference equation?
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More Signals and Systems Questions

Q1.The Fourier Transform of an real and even function results in:
Q2.Sinc pulse shaping is derived from the Fourier Transform of a _______ function.
Q3.What type of distortion occurs if a signal that contains frequency components up to 15 kHz is sampled using 20 kHz?
Q4.Which one of the following systems described by the following input-output relations is time invariant ? 
Q5.The equation for voltage waveform v(t) shown below is (where u(t) is unit step input) :
Q6.A continuous-time signal x(t) is defined as : \(x(\mathrm{t})=\left\{\begin{array}{cc} 5 & -2 \leq \mathrm{t} \leq 2 \\ 0 & \text { otherwise } \end{array}\right.\) The energy of signal x(t) is : 
Q7.If Z(un) = f(z), then Z(a − nun) (where Z denotes z-transform) equals to :
Q8.The Laplace transform of x(t) is \(\sqrt{\frac{2}{s-3}}\).  Then Laplace transform of e−6tx(t) is :
Q9.Which one of the following is the correct relation ? (a > 0) 
Q10.What is the formula of finding the final value of any time varying function f(t)?
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