21. Two discrete time systems with impulse responses h1[n] = δ[n - 1] and h2[n] = δ[n - 2] are connected in cascade. The overall impulse response of the cascaded system is
22. The ACF of a rectangular pulse of duration T is
23. Assuming zero initial condition, the response y(t) of the system given below to a unit step input u(t) is
\[\xrightarrow{{U\left( s \right)}}\boxed{\frac{1}{s}}\xrightarrow{{Y\left( s \right)}}\]
\[\xrightarrow{{U\left( s \right)}}\boxed{\frac{1}{s}}\xrightarrow{{Y\left( s \right)}}\]
24. Let x(t) ↔ X(jω) be Fourier Transform pair. The Fourier Transform of the signal x(5t - 3) in terms of X(jω) is given as
25. A 1.0 kHz signal is flat-top sampled at the rate of 1800 samples/sec and the samples are applied to an ideal rectangular LPF with cut-off frequency of 1100 Hz, then the output of the filter contains
26. The input and output of a continuous time system are respectively denoted by x(t) and y(t). Which of the following descriptions corresponds to a casual system?
27. The impulse response of a continuous time system is given by h(t) = δ(t - 1) + δ(t - 3). The value of the step response at t = 2 is
28. Choose the function f(t), -∞ < t < ∞, for which a Fourier series cannot be defined?
29. The Laplace transform of a function f(t) u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform of its first period. Then
30. The DFT of a vector [a b c d] is the vector [α β γ δ]. Consider the product
\[\left[ {p\,q\,r\,s} \right] = \left[ {a\,b\,c\,d} \right]\left[ {\begin{array}{*{20}{c}}
a&b&c&d \\
d&a&b&c \\
c&d&a&b \\
b&c&d&a
\end{array}} \right]\]
The DFT of the vector [p q r s] is a scaled version of
\[\left[ {p\,q\,r\,s} \right] = \left[ {a\,b\,c\,d} \right]\left[ {\begin{array}{*{20}{c}} a&b&c&d \\ d&a&b&c \\ c&d&a&b \\ b&c&d&a \end{array}} \right]\]
The DFT of the vector [p q r s] is a scaled version of
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