PYQs Based Test - 03 : Signals and Systems

The z-transform of x[n] = a${}^{|n|}$, 0 < |a|< 1, is X(z). The region of convergence of X(z) is

Three DFT coefficients, out of five DFT coefficients of a five-point real sequence are given as: X(0) = 4, X(1) = 1 – j1 and X(3) = 2 + j2. The zero-th value of the sequence x(n), x(0), is

Consider two discrete-time signals:

x₁(n) = {1, 1} and x₂(n) = {1, 2}, for n = 0, 1.

The Z-transform of the convoluted sequence x(n) = x₁(n) * x₂(n) is

For the sequence x[n] = {1, -1, 1, -1}, with n = 0, 1, 2, 3, the DFT is computed as $X\left(k\right)=\sum _{n=0}^{3}x\left[n\right]e^{-j\frac{2\pi }{4}nk}$, for k = 0, 1, 2, 3. The value of k for which X(k) is not zero is

The frequency response of a digital filter H(ω) has the following characteristics

Passband: 0.95 < |H (ω)|< 1.05 for 0 < ω < 0.3π and

Stopband: 0 <|H (ω)|< 0.005 for 0.4π < ω < π,

where ω is the normalized angular frequency in rad/sample. If the analog upper cut off frequency for the passband of the above digital filter is to be 1.2 kHz, then the sampling frequency should be ________ kHz.