PYQs Based test 7: Signals & Systems

Consider the difference equation $y\left[n\right]-\frac{1}{3}y\left[n-1\right]=x\left[n\right]$ and suppose that $x\left[n\right]={\left(\frac{1}{2}\right)}^{n}u\left[n\right]$. Assuming the condition of initial rest, the solution for y[n], n ≥ 0 is

The magnitude of Fourier transform X(ω) of a function x(t) is shown below in figure (a). The magnitude of Fourier transform Y(ω) of another function y(t) is shown in figure (b). The phases of X(ω) and Y(ω) are zero for all ω. The magnitude and frequency units are identical in both the figures. The function y(t) can expressed in terms of x(t) as

The z-transform of x[n] = a${}^{|n|}$, 0 < |a|< 1, is X(z). The region of convergence of X(z) is

A continuous time signal x(t) = 4 cos(200πt) + 8 cos(400πt), where t is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response

h≤ft( t ) = ≤ft\{ {*20c {{{2≤ft( 300π t )}}π t}&t ≠ 0\\ 600,&t = 0 } .

Let y(t) be the output of this filter. The maximum value of |y(t)| is ________.

A LTI system described by the following differential equation, where x(t) is the input to system and y(t) is output of system

y${}^{{}^{\prime }}$ (t) + 3y(t) = x(t)

When y (0) = 2, the output y (t) for an unit step input is