GATE ECE 2000 | GATE ECE Year Wise Previous Years Questions

GATE ECE 2000

MCQ (Single Correct Answer)

-0.6

A system has a phase response given by $$\phi \,(\omega )$$ where $$\omega $$ is the angular frequency. The phase delay and group delay at $$\omega $$ = $${\omega _0}$$ are respectively given by

$$ - {{\phi ({\omega _0})} \over {{\omega _0}}}, - {{d\phi (\omega )} \over {d\omega }}\left| {\omega = {\omega _0}} \right.$$

$$\phi ({\omega _0}), - {{{d^2}\phi (\omega )} \over {d{\omega ^2}}}\left| {\omega = {\omega _0}} \right.$$

$${{{\omega _0}} \over {\phi ({\omega _0})}}, - {{d\phi (\omega )} \over {d\omega }}\left| {\omega = {\omega _0}} \right.$$

$${\omega _0}\,\phi \,({\omega _0})\,,\,\int_{ - \infty }^{{\omega _0}} \phi (\lambda )\,d\,\lambda $$

GATE ECE 2000

Subjective

-0

A band limited signal x(t) with a spectrum X(f) as shown in Fig. a is processed as shown in Fig.b. p(t) is a periodic train of impulses as in Fig. c. The ideal band pass filter has a pass band from 26 KHz to 34 KHz.
(a) Calculate the Fourier series coefficients $${c_n}$$ in the Fourier expansion of p(t) in form $$p(t) = \sum\limits_{n = - \infty }^{ + \infty } {{c_n}} \,\exp \,\,(j\,n\,2\pi \,t/T)$$.
(b) Find the Fourier Transform of p(t).
(c) Obtain and sketch the spectrum of $${x_s}(t)$$.
(d) Obtain and sketch the spectrum of y(t). GATE ECE 2000 Signals and Systems - Sampling Question 8 English 1

GATE ECE 2000 Signals and Systems - Sampling Question 8 English 1

GATE ECE 2000 Signals and Systems - Sampling Question 8 English 2

GATE ECE 2000 Signals and Systems - Sampling Question 8 English 3

GATE ECE Papers

2023