11. If X(z) is $$\frac{1}{{1 - {z^{ - 1}}}}$$ with |z| > 1, then what is the corresponding x(n)?
12. A causal LTI system is described by the difference equation 2y[n] = αy[n - 2] - 2x[n] + βx[n - 1]
The system is stable only if
The system is stable only if
13. The spectral density of a random signal is given by π[δ(ω - ω0) + δ(ω + ω0)]. The auto-correlation function of the signals is
14. In a discrete-time Low Pass Filter, the frequency response is
15. A discrete time system y(n) is the resultant convolution of f(n) and h(n) having length 3 and 5 respectively. The maximum possible sample value of f(n) and h(n) are 10 and 20 respectively. Find the maximum possible value for sum of all sample value of y(n).
16. The autocorrelation function Rx(τ) of the signal x(τ) = V sin ωt is given by
17. The impulse response of a linear time invariant system is a rectangular pulse of duration T. It is excited by an input of a pulse of duration T. What is the filter output waveform?
18. Consider a cascade system with unit step u(t) as input and h1(t) = e-2tu(t) and h2(t) = e-tu(t) respectively as impulse responses of two systems, find out the overall output.
19. A system has impulse response h[n] = cos(n)u[n]. The system is:
20. Consider the following system
h(n) is a filter with frequency response, then
h(n) is a filter with frequency response, then

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