Recent questions in Discrete-time Signals

Consider the sequence $x[n]=\left[\begin{array}{lll}-4- \uparrow{j} 5 & 1+j 2 & 4\end{array}\right]$The conjugate anti-symmetric part of the sequence is$[-4-j 2.5 \quad j...

A causal $\text{LTI}$ system is described by the difference equation\[2 y[n]=\alpha y[n-2]-2 x[n]+\beta x[n-1]\]The system is stable only if$|\alpha|=2, \quad|\beta|<2$$|...

The impulse response $h|n|$ of a linear time invariant system is given as\[h[n]=\left\{\begin{array}{cc}-2 \sqrt{2} & n=1,-1 \\4 \sqrt{2} & n=2,-2 \\0, & \text { otherwis...

The region of convergence of $Z$-transform of the sequence$\left(\frac{5}{6}\right)^{n} u(n)-\left(\frac{6}{5}\right)^{n} u(-n-1)$ must be$|z|<\frac{5}{6}$$|z|>\frac{6}{5...

Let $x(n)=\left(\frac{1}{2}\right)^{n} u(n), y(n)=x^{2}(n)$ and $\mathrm{Y}\left(e^{j i e}\right)$ be the Fourier transform of $y(n)$. Then $Y\left(e^{j i e}\right)$ is$\...

A signal $x(n)=\sin \left(\omega_{0} n+\phi\right)$ is the input to a linear time-invariant system having a frequency response $\text{H}(e^{j \omega})$. If the output of ...

Statement of Linked Answer Questions 85a and 85bA sequence $x(n)$ has non-zero values as shown in the figureThe sequence $y(n)=\left\{x\left(\frac{n}{2}-1\right)\right.$ ...

If the region of convergence of $x_1[n]+x_2[n]$ is $\frac{1}{3}<|z|<\frac{2}{3}$, then the region of convergence of $x_1[n]-x_2[n]$ includes $\frac{1}{3}<|z|<3$$\frac{2}{...

A system with input $x[n]$ and output $y[n]$ is given as $y[n]=\left(\sin \frac{5}{6} \pi n\right) x(n)$.The system islinear, stable and invertiblenon-linear, stable and ...

In the following figure the minimum value of the constant ' $C$ ', which is to be added to $y_{1}(t)$ such that $y_{1}(t)$ and $y_{2}(t)$ are different, is$\Delta$$\frac{...

A Hilbert transformer is anon-linear systemnon-causal systemtime-varying systemlow-pass system

A $5$-point sequence $x[n]$ is given as\[ x[-3]=1, \quad x[-2]=1, \quad x[-1]=0, \quad x[0]=5, \quad x =1 .\]Let $X\left(e^{j \omega}\right)$ denote the discrete-time Fou...

The $z$-transform $X[z]$ of a sequence $x[n]$ is given by $X[z]=\dfrac{0.5}{1-2 z^{-1}}$. It is given that the region of convergence of $X[z]$ includes the unit circle. T...

A discrete time linear shift-invariant system has an impulse response $h[n]$ with $h[0]=1, h =-1$, $h =2$, and zero otherwise. The system is given an input sequence $x[n]...

$\{x(n)\}$ is a real-valued periodic sequence with a period N. $x(n)$ and $X(k)$ form $\mathrm{N}$-point Discrete Fourier Transform (DFT) pairs. The DFT $Y(k)$ of the seq...

In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.The samples $x(n) \quad(n=0,1,2,...

In the following network, the switch is closed at $t=0$ - and the sampling starts from $t=0$. The sampling frequency is $10 \mathrm{~Hz}$.The expression and the region of...

The $\text{ROC}$ of $\text{Z}$-transform of the discrete time sequence $\quad x(n)=\left(\dfrac{1}{3}\right)^{n} u(n)-\left(\dfrac{1}{2}\right)^{n} u(-n-1) \quad$ is$\fra...

A system with transfer function $H(z)$ has impulse response $h(\cdot)$ defined as $h(2)=1, h(3)=-1$ and $h(k)=0$ otherwise. Consider the following statements.$\qquad \qqu...

The $4$-point Discrete Fourier Transform (DFT) of a discrete time sequence $\{1,0,2,3\}$ is$[0,-2+2 j, 2,-2-2 j]$$[2,2+2 \mathrm{j}, 6,2-2 \mathrm{j}]$$[6,1-3 \mathrm{j},...