Signals and Sys...

Two systems H₁(z) and H₂(z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one-unit delay. The transfer function of the second system H₂(z) is

A function f(t) is an even function, if for all values of (t)

(T is the time-period of the function)

A control system transfer function is H(s) = 1/s³. Express its impulse response in terms of unit step signal

The unit impulse response of a linear time invariant system is the unit step function u(t) for t > 0, the response of the system to an excitation e^-at u(t), a > 0 will be

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

If F(ω) is the Fourier transform of f(t), then which of the following is/are true?

What is the signal corresponding to the following z-transform? (Where u[n] is the unit-step signal)

\(X\left( z \right) = \frac{{6{z^2}}}{{\left( {2z - 1} \right)\left( {3z - 1} \right)}},\frac{1}{3} < \left| z \right| < \frac{1}{2}\)

Let \(X\left( {{e^{j\omega }}} \right) = 10 - 4{e^{ - j2\omega }}\). If y(t) = x(t - 2) then what is value of Y(e^jω) at ω = π is ________

If a 100 Hz sinusoidal signal is sampled at the rates of 140 Hz, 90 Hz, and 30 Hz, then the aliased frequencies correspond to each sampling rate will be respectively

If a function f(t) u(t) is shifted to the right side by t0, then the function can be expressed as

The DTFT of x[n] = 0.5ⁿ u[n] using geometric series is:

A discrete time signal x[n] and its discrete Fourier transform X(k) related by \(x\left[ n \right]\mathop \leftrightarrow \limits^{DFS\;12} X\left( k \right)\). Another discrete series with Fourier coefficients Y(k) given as Y(k) = X(k - 4) + X(k + 4) then the corresponding sequence y[n] will be

The impulse response of a causal, linear, time- invariant, continuous time system is h(t). The output y(t) of the same system to an input x(t). Where x(t) = 0 for t < -2 is

The unit step response of a system is given by (1 - e^-αt) u(t), the impulse response is given by

Figure I and Figure II, shows the input x(t) to a linear time invariant system and the impulse response h(t) of the system

the output of the system is zero everywhere except for the time interval.

Consider a signal y(t) = x₁(t) * x₂(t). If x₁(t) = 2 cos 4t u(t) and x₂(t) = sin 2t u(t). The value of y(t) at t = π / 2 is _______

The total area under the function \(x\left( t \right) = 10\;sinc\;\left( {\frac{{t + 4}}{7}} \right)\) is

A signal f(t) = cos8πt + 0.5cos4πt is instantaneously sampled. The maximum allowable value of sampling interval T_s in sec is

The unilateral z-transform of signal x[n] = u[ n + 4 ] is

The sequence x[n] is (0.7)ⁿ u(n) and y (n) is x (n)*x (n). Then which of the following statement(s) is/are true?

Consider a system with frequency response of \(H\left( {j\omega } \right) = \frac{{j\omega + 2}}{{\left( {j\omega + 1} \right)\left( {j\omega + 3} \right)}}\) and suppose that the input to the system is x(t) = e^-t u(t). If the output response is y(t), the value of y(1) is _______ (answer up to two decimal places)

X(z) = ln(1 + z^-1), |z| > 0

Let X(e^jΩ) denote the Fourier transform of the signal x[n], where:

\(x\left( n \right) = \left\{ { - 1,0,1,\begin{array}{*{20}{c}} 2\\ \uparrow \end{array},1,0,1,2,1,0, - 1} \right\}\)

If z-transform is given by

X(z) = cos(z^-3), |z| > 0

The value of x[12] is