PYQs Based Test - 04 : Signals & Systems

A discrete time signal,

x[n] = 2 sin(π²n), n being an integer, is

The energy of the signal $x(t)=\frac{\sin \left(4\pi \mathrm{t}\right)}{4\pi \mathrm{t}}$ is______

Consider two 16-point sequences x[n] and h[n]. Let the linear convolution of x[n] and h[n] be denoted by y[n], while z[n] denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of x[n] and h[n]. The value(s) of k for which z[k] = y[k] is/are

For a vector x̅ = [x[0], x[1],......x[7]] the 8-point discrete Fourier transform (DFT) is denoted by X̅ = DFT (x̅) = X[0], X[1], ...., X[7]], where

$\mathrm{X}[\mathrm{k}]={\sum }_{\mathrm{n}=0}^7\mathrm{x}[\mathrm{n}]\exp \left(-\mathrm{j}\frac{2\pi }{8}\mathrm{nk}\right)$

Here j = √-1, if X̅ = [1, 0, 0, 0, 2, 0, 0, 0] and y̅ = (DFT (x̅)), then the value of y[0] is ________ (rounded off to one decimal place).

Consider a single input single output discrete-time system with x[n] as input and y[n] as output. Where the two are related as

y≤ft[ n ] = ≤ft\{ {*20c n≤ft| x≤ft[ n ] |, \\ x≤ft[ n ] - x≤ft[ n - 1 ], } .*20c for 0 ≤ n ≤ 10\\ otherwise.

Which one of the following statements is true about the system?