# Questions & Answers of Representation of Continuous and Discrete-Time Signals

## Weightage of Representation of Continuous and Discrete-Time Signals

Total 13 Questions have been asked from Representation of Continuous and Discrete-Time Signals topic of Signals and Systems subject in previous GATE papers. Average marks 1.77.

Consider the two continuous-time signals defined below:

$x_1(t)=\left\{\begin{array}{l}\left|t\right|,-1\leq t\leq1\\0,\;\;otherwise\end{array},\;\;\;\;\;\;x_2\left(t\right)=\left\{\begin{array}{l}1-\left|t\right|,\;\;-1\leq t\leq1\\0,\;\;\;\;\;\;\;\;\;\;otherwise\;\end{array}\right.\right.$

These signals are sampled with a sampling period of $T=0.25$ seconds to obtain discrete time signals $x_1\left[n\right]$ and $x_2\left[n\right]$ , respectively. Which one of the following statements is true?

The signal energy of the continuous-time signal

$x(t)=\lbrack(t-1)u(t-1)\rbrack-\lbrack(t-2)u(t-2)\rbrack-\lbrack(t-3)u(t-3)\rbrack+\lbrack(t-4)u(t-4)\rbrack$ is

The mean square value of the given periodic waveform f(t) is____________

The value of $\int\limits_{-\infty}^{+\infty}\mathrm e^{-\mathrm t}\mathrm\delta\left(2\mathrm t-2\right)\mathrm{dt}$ where $\delta \left(t\right)$ is the Dirac delta function, is

The function shown in the figure can be represented as

A discrete system is represented by the difference equation

It has initial conditions X1(0) = 1; X2(0) = 0. The pole locations of the system for a = 1, are

An input signal x(t) 2 +  5sin(100πt) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by

$\frac{\mathrm{Y}\left(\mathrm{z}\right)}{\mathrm{X}\left(\mathrm{z}\right)}=\frac{1}{\mathrm{N}}\left(\frac{1-{\mathrm{Z}}^{-\mathrm{N}}}{1-{\mathrm{Z}}^{-1}}\right)$

where, N represents the number of samples per cycle. The output y(n) of the system under steady state is

A sinusoid x(t) of unknown frequency is sampled by an impulse train of period 20 ms. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at 25 Hz. The filter output is seen to be a sinusoid of frequency 20 Hz. This means that x(t) has a frequency of

A zero mean random signal is uniformly distributed between limits −a and +a and its mean square value is equal to its variance. Then the r.m.s value of the signal is

Given a sequence x[n], to generate the sequence y[n] = x[3 − 4n], which one of the following procedures would be correct ?

The frequency spectrum of a signal is shown in the figure. If this signal is ideally sampled at intervals of 1 ms, then the frequency spectrum of the sampled signal will be

 (A) (B) (C) (D)

$G\left(s\right)=\alpha {z}^{-1}+\beta {z}^{-3}$ is a low pass digital filter with a phase characteristics same as that of the above question if