Signal Processing - Study Mode
[#351] The transfer function of a linear system is the
Correct Answer
(C) ratio of the Laplace transform of the output and that of the input with all initial conditions zeros
[#352] Match List-I with List-II and select the correct answer using the options given below: List-I (Function) List-II (Fourier Transforms) a. $$exp left( { - alpha t}
ight)uleft( t
ight),,alpha > 0$$ 1. $$frac{1}{{{{left( {alpha + j2pi f}
ight)}^2}}}$$ b. $$exp left( { - alpha left| t
ight|}
ight),,alpha > 0$$ 2. $$frac{1}{{alpha + j2pi f}}$$ c. $${ ext{texp}}left( { - alpha t}
ight)uleft( t
ight),,alpha > 0$$ 3. $$delta left( {f - frac{alpha }{{{t_0}}}}
ight)$$ d. $$exp left( {j2pi alpha t/{t_0}}
ight)$$ 4. $$frac{{2alpha }}{{{alpha ^2} + {{left( {2pi f}
ight)}^2}}}$$
Correct Answer
(B) a-2, b-4, c-1, d-3
[#353] The Fourier Transform of a function x(t) is X(f). The Fourier transform of $$frac{{dxleft( t
ight)}}{{dt}}$$ xa0will be
Correct Answer
(B) $$j2pi fXleft( f
ight)$$
[#354] A finite duration discrete-time signal x(n) is obtained by sampling the continuous-time signal x(t) = cos(200πt) at sampling instant t = n/400, n = 0, 1, . . . , 7. The 8-point discrete Fourier transform (DFT) of x(n) is defined as $$Xleft[ k
ight] = sumlimits_{n = 0}^7 {xleft[ n
ight]{e^{frac{{ - jpi kn}}{4}}},,k = 0,,1,,.....,,7} $$ Which one of the following statements is true?
Correct Answer
(A) Only X(2) and X(6) are non-zero
[#355] In inverse DTFT, the . . . . . . . . is defined between -π to π because of the property.
Correct Answer
(B) Periodicity