Signal Processing - Study Mode

[#321] Let δ(t) denote the delta function. The value of the integral $$intlimits_{ - infty }^infty {delta left( t
ight)} cos left( {{{3t} over 2}}
ight)dt$$ xa0 xa0 is
Correct Answer

(A) 1

[#322] If a signal f(t) has energy E, the energy of the signal f(2t) is equal to
Correct Answer

(B) $${E over 2}$$
(F) $$frac{{ ext{E}}}{2}$$

[#323] The input-output relationship of a causal stable LTI system is given as y[n] = αy[n - 1] + βx[n]. If the impulse response h[n] of this system satisfies the condition $$sumlimits_{n = 0}^infty {hleft[ n
ight] = 2,} $$ xa0 the relationship between α and β is
Correct Answer

(A) $$alpha = 1 - {x08eta over 2}$$

[#324] The bilateral Laplace transform of a function $$fleft( t
ight) = left{ {matrix{
{1,} & {{
m{if}},a le t le b} cr
0 & {{
m{otherwise}}} cr

} }
ight.$$ xa0 xa0 is
Correct Answer

(C) $${{{e^{ - as}} - {e^{ - bs}}} over s}$$

[#325] {a(n)} is a real-valued periodic sequence with a period N. x(n) and X(k) form N-point Discrete Fourier Transform (DFT) pairs. The DFT Y(k) of the sequence $$yleft( n
ight) = frac{1}{N}sumlimits_{r = 0}^{N - 1} {xleft( r
ight)} xleft( {n + r}
ight)$$ xa0 xa0xa0 is
Correct Answer

(A) $${left| {Xleft( k ight)} ight|^2}$$