List of top Signals and Systems Questions asked in GATE BM

\(x[n]\) is a real and odd signal. Which one of the following statements is true about its Discrete Time Fourier Transform (DTFT) \(X(e^{j\omega})\)?

The output \(y[n]\) of a digital moving average filter for an input \(x[n]\) is given by
\[ y[n] = \frac{1}{4}\big(x[n] + 2x[n-1] + x[n-2]\big) \]
Which one of the following options is a correct statement about the transfer function of this filter?

The figure below shows the impulse response of a linear time-invariant (LTI) system, \(h[n] = [0, 0.6, 0.8, 0.5, 0.3, 0]\) for \(n = 0\) to \(5\). For an input \(x[n] = [1, 0.6, 0, 0, 0, 0]\) for \(n = 0\) to \(5\), the maximum value of its output \(y[n]\) is . (Round off to one decimal place)