Signals and Sys...

If δ(t) is a unit impulse function, then the value of integral \(\mathop \smallint \nolimits_{ - \infty }^\infty {e^{ - t}}\delta \left( {2t - 2} \right)\;dt\) equals to _______. (Correct up to two decimal places)

If the signal cos (15 t) is sampled at a sampling interval of T_s and the resulting discrete time signal is periodic with period 4. Then the sampling interval T_s may be:

The raised cosine pulse x(t) is defined as

\(x\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{1}{2}(\cos \omega t + 1),\;\;\;}\\ {0,} \end{array}\begin{array}{*{20}{c}} { - \frac{\pi }{\omega } \le t \le \frac{\pi }{\omega }}\\ {otherwise} \end{array}} \right.\)

Let x[n] = x[-n] Let X(z) be the Z-transform of x[n]. if 1 + j2 is a zero of X(z). Which one of the following must also be a zero of X(z)

Given that H(z) is a causal and stable IIR filter, if z in H(z) is replaced by \(\frac{1}{z}\), the resulting filter will be

DFT of a real valued signal is defined as:

F(k) = {1, A, 1 + j, B, -1, -1 - j, C, -1 + j}

A function is given by f(t) = cos²t + cos 2t. Which of the following is true?

If an all pass causal LTI system is described by the expression

y[n] – ay[n - 1] = bx[n] + x[n - 1]

The time-domain signal corresponding to the following z-transform is:

\(X\left( z \right) = \mathop \sum \limits_{k = 5}^{10} \frac{1}{k}{z^{ - k}},\left| {\rm{z}} \right| > 0\)

Let X(e^jΩ) denote the Fourier transform of the signal x[n], where:

\(x\left( n \right) = \left\{ { - 1,0,1,\begin{array}{*{20}{c}} 2\\ \uparrow \end{array},1,0,1,2,1,0, - 1} \right\}\)

A three point filter with impulse response \(h\left[ n \right] = \begin{array}{*{20}{c}}{\left\{ {p,q,p} \right\}}\\ \uparrow \end{array}\) that completely blocks \(f = \frac{1}{4}\;Hz\) and passes \(f = \frac{1}{8}\;Hz\) with unity gain. The value of p +q is _____.