discrete time system

The response of a discrete time system y[n] obeys the following relation: y[n] = (5/6)y[n-1] - (1/6)y[n – 2] + x[n]. The input to the system is x[n] = δ[n] – (1/3)δ[n – 1]. Which o...

Consider the discrete time system (S) with input x[n] and output y[n] as shown in the Figure. The two sub-systems represented by their impulse responses $h_1[n]$ and $h_2[n]$ are l...

Consider the discrete-time system below with input x[n] and output y[n]. In the figure, h₁[n] and h₂[n] denote the impulse responses of LTI Subsystems 1 and 2, respectively. Also,...

The output $y[n]$ of a discrete - time system for an input $x[n]$ is $$ y[n]=\max\limits_{-\infty \leq k \leq n}|x[k]| $$ The unit impulse response of the system is

Consider a single input single output discrete-time system with $$h\left[ n \right]\,$$ as input and $$y\left[ n \right]\,$$ as output, where the two are related as $$y\left[ n \ri...

A system is defined by its impulse response $$h\left( n \right) = {2^n}\,u\left( {n - 2} \right).$$ The system is

The transfer function of a discrete time LTI system is given by $$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$ Cons...

A system with input $$x\left( n \right)$$ and output $$y\left( n \right)$$ is given as $$y\left( n \right)$$ $$ = \left( {\sin {5 \over 6}\,\pi \,n} \right)x\left( n \right).$$ The...

Let P be linearity, Q be time-invariance, R be causality and S be stability. A discrete time system has the input-output relationship, $$y\left( n \right) = \left\{ {\matrix{ {x\le...

If the impulse response of a discrete-time system is $$h\left[ n \right]\, = \, - {5^n}\,\,u\left[ { - n\, - 1} \right],$$ then the system function $$H\left( z \right)\,\,\,$$ is e...

The output of a system is given in difference equation form as $$y\left( k \right) = \,a\,\,y\left( {k - 1} \right) + x\left( k \right),$$ where $$x\left( k \right)$$ is the input....