One Shot Marathon Series Test - Signals and Systems

The system described by following differential equation is

Two signals x(t) and h(t) are defined as follows

x(t) = 0 |t| > T₁

h(t) = 0 |t| > T₂

x(t)*h(t) =0 |t| > T₃

T₃ will be

What is the convolution of x₁(t) = sin 3t u(t), x₂(t) = cos2t u(t)

Find the time signal corresponding to  .

If x_e(t) represents even part of signal x(t) and x_o(t) represents odd part of signal x(t) then choose the correct expression for x(t).

An input signal x(t) = 4 + cos (4πt) – sin(8πt) is is applied to an LTI system with impulse response Then the response is _______.

Consider the interconnection of three LTI systems as shown in below figure.

Assume, h₁[n] = u[n + 2], h₂[n] = δ[n – 2]

h₃[n] = u[n] – u[n – 2]

Then the impulse response of overall system at n = 2 is_______.

A periodic signal f(t) is shown in the figure below.

The frequency of the 3^rd harmonic of its spectrum is ________kHz.

Consider two signals

and

If then is

Which of the following operations are true with respect to signals?

Here E = Even signal

O = odd signal

+ = Additional of signals

× = Multiplication of signals
[Multi Select Question]

The relationship between the input x(t) and output y(t) of a system is described by the differential equation

The impulse response of the system is

X(f) is signal that has a rational Laplace transform with exactly two poles located at s = — 1 and s = — 3. If g(t) = e^2t x(t) and Fourier transform of g(t) i.e. G(jω) converges, then x(t) is

The frequency response of a system for impulse sequence response

Find inverse L.T. of

The value of integral

If δ[n] is a discrete time unit impulse function, then find the value of summation.

Consider a discrete time signal x[n] as

the energy of conjugate symmetric part of signal x[n] is_____J.

Consider a discrete time signal shown in figure below.

If y[n] = n x[n] then

will be_____

Let x[n] be the periodic extension of the sequence δ[n] – δ[n – 2] with period 4. The DTFS coefficients of x[n] is such that A is

Let, .

The LT of x(t) is X(s). Then value of x(1) is____?

If and y[n] is defined as

What is value of y[2]

The DTFT of is where the constant is

Consider the following system

The system is ____

Which of the following is/are correct.

Given the z-transform X(Z)

=, the value of x [∞] is _________.