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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

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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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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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Q6.The output of a linear time invariant system can be obtained from its unit impulse response function and the input function by
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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
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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:
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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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Q1.The Fourier Transform of an real and even function results in:
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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 : 
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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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