Problem For The Day! 15 - Oct - 2014

A few samples of $11-$point DFT $X[k]$ of a $11-$length signal are given by

$X[0] = 4$, $X[2] = -1+j3$, $X[4] = 2+j5$ and $X[6] = 9-j6$.

The value of $X[5]$ is $\underline{\hspace{1cm}}$.

Problem For The Day! 14 - Oct - 2014

Let a discrete random process be defined as $Y[n] = 2X[n]-4X[n-1]$, where $X[n]$ is a zero mean WSS process with auto-correlation function $R_X[k] = \left\{ \ldots,0,\frac{1}{2},{\underset{\uparrow}{1}},\frac{1}{2},0,\ldots \right\}$. The average power of the process $Y[n]$ would be $\underline{\hspace{1cm} }$.

Problem For The Day! 13 - Oct - 2014

Let $x(t)$ be a time limited signal from $t = -1$ to $t = 3$. The signal given by $$y(t) = x(1-t)+x(2t-1)u(1-t)$$ is time limited from

(A)  -1 to 1. $\quad$ (B)  -2 to 2. $\quad$ (C)  -2 to 1.$\quad$ (D)  -1 to 2.

Problem For The Day! 12 - Oct - 2014

Sunday is a holiday! See you tomorrow! Happy Weekend!

Problem For The Day! - 11 - Oct - 2014

Let $X_1,X_2$ and $X_3$ be three i.i.d. exponential distributed random variables with parameter $\lambda = 1$. Let $Y_1 = X_1 + X_2$, $Y_2 = X_1+X_3$ and $Y_3 = X_2 + X_3$. The probability that $\left\{ Y_1 > Y_2>Y_3\right\}$ is

(A) $\frac{1}{2} \quad$ (B) $\frac{1}{3}\quad$ (C) $\frac{1}{6}\quad$ (D) $\frac{5}{6}$

Problem For The Day! - 10 - Oct - 2014

Let $x[n] = \left\{\underset\uparrow{6},5,4,3,2,1 \right\}$ and $h[n] = \left\{\underset\uparrow{1},0,0,0,1,0 \right\}$. Let $y_1[n]$ and $y_2[n]$ be $6-$point and $10-$point circular convolutions of $x[n]$ and $h[n]$. The values of $y_1[2]$ and $y_2[2]$ respectively are

(A) $6,4 \quad$ (B) $4,6 \quad$ (C) $6,6 \quad$ (D) $4,4$.

Problem For The Day! - 09 - Oct - 2014

The integral $$\displaystyle \int_{-\infty}^{\infty}x(-2t+1)\delta(-2t+1)dt$$ is same as

(A) $x(-2t+1) \quad$  (B) $x(2t-1) \quad$ (C) $\frac{1}{2}x(0) \quad$ (D) $x(t)$