List of top Signals and Systems Questions on Convolution of Signals asked in GATE EC

For a unit step input \( u[n] \), a discrete-time LTI system produces an output signal \( \left( 2\delta[n + 1] + \delta[n] + \delta[n - 1] \right) \). Let \( y[n] \) be the output of the system for an input \( \left(\frac{1}{2}\right)^n u[n] \). The value of \( y[0] \) is _________.
Consider two 16-point sequences \(x[n]\) and \(h[n]\). Let the linear convolution of \(x[n]\) and \(h[n]\) be denoted by \(y[n]\), while \(z[n]\) denotes the 16-point inverse discrete Fourier transform (IDFT) of the product of the 16-point DFTs of \(x[n]\) and \(h[n]\). The value(s) of \(k\) for which \(z[k] = y[k]\) is/are