signals and systems

The Laplace Transform of the signal $x(t) = u(t - 2) * (tu(t))$ is given by which of the following expressions? [" * " represents convolution operator]

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...

The continuous time signal x(t) is real, periodic with period T and satisfies the Dirichlet conditions. The Fourier series representation of x(t) = $\sum_{-\infty}^{\infty} a_n e^{...

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 a continuous-time, real-valued signal f(t) whose Fourier transform F(ω) = ∫_(-∞)^∞ f(t) exp(-j ωt) dt exists. Which one of the following statements is always TRUE?

A continuous time signal x(t) = 2 cos(8πt + π/3) is sampled at a rate of 15 Hz. The sampled signal x_s(t) when passed through an LTI system with impulse response h(t) = (sin 2πt /...

The relationship between any N-length sequence $x[n]$ and its corresponding N-point discrete Fourier transform $X[k]$ is defined as $X[k] = \mathcal{F}\{x[n]\}$. Another sequence $...

Consider a system with input x(t) and output y(t) = x(eᵗ). The system is

In the table shown below, match the signal type with its spectral characteristics. Signal type (i) Continuous, aperiodic (ii) Continuous, periodic (iii) Discrete, aperiodic (iv) Di...

For a real signal, which of the following is/are valid power spectral density/densities?

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 unilateral Laplace transform of $$f(t)$$ is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of $$g\left( t \right) = t.f\left( t \...

The unilateral Laplace transform of F(t) is $${1 \over {{s^2} + s + 1}}$$. Which one of the following is the unilateral Laplace transform of g(t) = $$t \cdot f\left( t \right)$$

Given that $$F(s)$$ is the one-sided Laplace transform of $$f(t),$$ the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)} d\tau $$ is

Given that F(s) is the one-sided Laplace transform of f(t), the Laplace transform of $$\int\limits_0^t {f\left( \tau \right)\,d\tau } $$ is

Given that $$L\left[ {f\left( t \right)} \right]\, = \,$$ $${{s + 2} \over {{s^2} + 1}},$$ $$$L\left[ {g\left( t \right)} \right] = {{{s^2} + 1} \over {\left( {s + 3} \right)\left(...

If $$\,\,\,$$ $$L\left\{ {f\left( t \right)} \right\} = {{s + 2} \over {{s^2} + 1}},\,\,L\left\{ {g\left( t \right)} \right\} = {{{s^2} + 1} \over {\left( {s + 3} \right)\left( {s...

The z-transform F(z) of the function f(nT) = $${a^{nT}}$$ is

Flat top sampling of low pass signals

The Fourier transform of a voltage of a voltage signal x(t) is X(f). The unit of |X(f)| is

The function f(t) has the Fourier Transform g($$\omega $$). The Fourier Transform of $$$g(t) = \left( {\int\limits_{ - \infty }^\infty {g(t){e^{ - j\omega t}}} } \right)\,is$$$

The Laplace transform of a function f(t)u(t), where f(t) is periodic with period T, is A(s) times the Laplace transform of its first period. Then