Z-transform

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...

The bilateral z-transform of a discrete-time signal x[n] is X(z) = (1-a^2) / ((z-a)(z^-1 - a)) with 0 < a < 1, and the region of convergence a < |z| < 1/a. Let u[n] be the discrete...

If the Z-transform of a finite-duration discrete-time signal x[n] is X(z), then the Z-transform of the signal y[n] = x[2n] is

If the Z-transform of a finite-duration discrete-time signal $x[n]$ is $X(z)$, then the Z-transform of the signal $y[n] = x[2n]$ is

The Z-transform of a discrete signal x[n] is $X(z) = \frac{4z}{(z-\frac{1}{2})(z-\frac{2}{3})(z-3)}$ with ROC = R. Which one of the following statements is true?

The Z-transform of a discrete signal $$x[n]$$ is $$X(z) = {{4z} \over {(z - {1 \over 5})(z - {2 \over 3})(z - 3)}}$$ with $$ROC = R$$. Which one of the following statements is true...

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

The z-Transform of a sequence x[n] is given as X(z) = 2z+4−4/z+3/z 2 . If y[n] is the first difference of x[n], then Y(Z) is given by

Consider a discrete time signal given by x[n]=(-0.25) n u[n]+(0.5) n u[-n-1] The region of convergence of its Z-transform would be

An input signal x(t) = 2 + 5sin(100$$\mathrm\pi$$t) is sampled with a sampling frequency of 400 Hz and applied to the system whose transfer function is represented by $$$\frac{Y\le...

Let $$X\left(z\right)=\frac1{1-z^{-3}}$$ be the Z–transform of a causal signal x[n]. Then, the values of x[2] and x[3] are

If $$x\left[ N \right] = {\left( {1/3} \right)^{\left| n \right|}} - {\left( {1/2} \right)^n}\,u\left[ n \right],$$ then the region of convergence $$(ROC)$$ of its $$Z$$-transform...

The $$z$$$$-$$ transform of a signal $$x\left[ n \right]$$ is given by $$4{z^{ - 3}} + 3{z^{ - 1}} + 2 - 6{z^2} + 2{z^3}.$$ It is applied to a system, with a transfer function $$H\...

Given $$X(z) = {z \over {{{(z - a)}^2}}}$$ with |z| > a, the residue of $$X(z){z^{n - 1}}$$ at z = a for $$n \ge 0$$ will be

Given X(z)=$$\frac z{\left(z-a\right)^2}$$ with $$\left|z\right|$$ > a, the residue of X(z)z n-1 at z = a for n $$\geq$$ 0 will be

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

A signal is processed by a causal filter with transfer function $$G(s).$$ For a distortion free output signal waveform, $$G(s)$$ must. $$G\left( z \right) = a{z^{ - 1}} + \beta \,\...

The discrete-time signal $$$x\left[n\right]\leftrightarrow X\left(z\right)={\textstyle\sum_{n=0}^\infty}\frac{3^n}{2+n}z^{2n}$$$ where $$\leftrightarrow$$ denote a transform-pair r...

A discrete real all pass system has a pole at $$z = 2\angle {30^ \circ };\,$$ it, therefore,

$$y\left[ n \right]$$ 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...