discrete-time

Consider the infinite-length, discrete-time sequence x[n] = 0.9|n|, where n is an integer. The region of convergence of its Z-transform X(Z) is given by: (Note: z is a complex vari...

Consider a discrete-time linear time-invariant (LTI) system S, where y[n] = S{x[n]} Let S{δ[n]} = {1, n ∈ {0, 1, 2} {0, otherwise where δ[n] is the discrete-time unit impulse funct...

Consider a discrete-time linear time-invariant (LTI) system, $\boldsymbol{S}$, where $$ y[n]=S\{x(\mathrm{n})\} $$ $$Let\,\,\,\, S\{\delta[n]\}=\left\{\begin{array}{lc} 1, & n \in\...

Consider the discrete-time systems $T_1$ and $T_2$ defined as follows: { $T_1 x[ n ] = x[ 0 ] + x[ 1 ] + \cdots + x[ n ] $} { $T_2 x[ n ] = x[ 0 ] + \frac{1}{2} x[ 1 ] + \cdots + \...

Which of the following statement(s) is/are true?

The period of the discrete-time signal $$x[n]$$ described by the equation below is $$N=$$ __________ (Round off to the nearest integer). $$x[n] = 1 + 3\sin \left( {{{15\pi } \over...

The causal signal with $z$-transform $z^2(z-a)^{-2}$ is ( $u[n]$ is the unit step signal)

Two discrete-time linear time-invariant systems with impulse responses $h_1\lfloor n\rfloor=\delta\lfloor n-1\rfloor+\delta\lfloor n+1\rfloor$ and $h_2[n]=\delta[n]+\delta[n-1]$ ar...

A cascade system having the impulse responses h₁(n) = {1, -1} and h₂(n) = {1, 1} is shown in the figure below, where symbol ↑ denotes the time origin. The input sequence x(n) for w...

Consider the system with following input-output relation $$y\left[n\right]=\left(1+\left(-1\right)^n\right)x\left[n\right]$$ where, x[n] is the input and y[n] is the output. The sy...

L et y[n] denote the convolution of h[n] and g[n], where $$h\left[n\right]=\left(1/2\right)^nu\left[n\right]$$ and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1]...

$$X\left( z \right) = 1 - 3\,\,{z^{ - 1}},\,\,Y\left( z \right) = 1 + 2\,\,{z^{ - 2}}$$ are $$Z$$-transforms of two signals $$x\left[ n \right],\,\,y\left[ n \right]$$ respectively...

$$y\left[ n \right]$$ denotes the output and $$x\left[ n \right]$$ denotes the input of a discrete-time system given by the difference equation $$y\left[ n \right] - 0.8y\left[ {n...

$$x\left[ n \right] = 0;\,n < - 1,\,n > 0,\,x\left[ { - 1} \right] = - 1,\,x\left[ 0 \right]$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2$$ is the input...