linearity

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,...

Let the input be u and the output be y of a system, and the other parameters are real constants. Identify which among the following systems is not a linear system:

The input x(t) and the output y(t) of a continuous time system are related as $$y\left( t \right) = \int\limits_{t - T}^t {x\left( u \right)du.} $$. The system is

The state equation of a second-order linear system is given by $$\mathop x\limits^ \bullet \left( t \right) = Ax\left( t \right),x\left( 0 \right) = {x_0}.$$ For $${x_0} = \left[ {...

Let x(t) be the input and y(t) be the output of a continuous time system. Match the system properties P1, P2 and P3 with system relations R1, R2, R3, R4. Properties P1 : Linear but...

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

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...

A system with an input x(t) and an output y(t) is described by the relation: y(t) = t x(t). This system is

The emitter coupled pair of BJT’s gives a linear transfer relation between the differential output voltage and the differential input voltage V id only. When the magnitude of V id...

Match each of the items A, B and C with an appropriate item from 1, 2, 3, 4 and 5. List - 1 (A) $${a_1}{{{d^{2y}}} \over {d{x^2}}} + {a_2}y{{dy} \over {dx}} + {a_3}y = {a_4}$$ (B)...