Signals and Sys...

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

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

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

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)

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

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