Signals and Sys...

The Fourier transform of x(t) = A cos (2π f₀ t) is X(jω) = 10[δ(ω – 4π) + δ (ω + 4π)].  The value f₀ is _______  (in Hz).

The signal x(t) is described by

\(x\left( t \right) = \left\{ {\begin{array}{*{20}{c}} {1\;for}&{ - 1 \le t \le 1}\\ 0&{otherwise} \end{array}} \right.\)

The DTFT of a signal f(n) = {a, b, c, d} is F(ω). The inverse DTFT of F(ω - π) is:

The impulse response of the causal LTI system that is characterised by the difference equation \(y\left[ n \right] - \frac{3}{4}y\left[ {n - 1} \right] + \frac{1}{8}y\left[ {n - 2} \right] = 2x\left[ n \right]\) is

Consider the given convolution y₁(t) = x₁(t) * x₂(t) and y₂(t) = x₁(3t) * x₂(3t), then \(\frac{{{y_2}\left( t \right)}}{{{y_1}\left( {3t} \right)}} = \) _________.(up to two decimal places)

The impulse response h(t) of linear time invariant continuous time system is given by h(t) = exp (-2t) u(t), where u(t) denotes the unit step function.

The value of the following summation \(\underset{n=0}{\overset{\infty }{\mathop \sum }}\,n{{\left( \frac{1}{3} \right)}^{n}}\) is _______.(up to two decimal places)