List of top Signals and Systems Questions on Digital Signal Processing asked in GATE BM

The time delay between the peaks of the voltage signals \( v_1(t) = 2\cos(6t + 60^\circ) \) and \( v_2(t) = -3\sin(6t) \) is ____ s.

An input $x(t)$ is applied to a system with a frequency transfer function given by $H(j\omega)$ as shown. The magnitude and phase response are shown. If $y(t_d)=0$ for $x(t)=u(t)$, the time $t_d (>0)$ is _________ µs.
The block diagram of a two-tap high-pass FIR filter is shown below. The filter transfer function is given by \( H(z) = \frac{Y(z)}{X(z)} \).
If ratio of the maximum to minimum value of \( H(z) \) is 2 and \( |H(z)|_{\max} = 1 \), the coefficients \( \beta_0 \) and \( \beta_1 \) are _________ and _________, respectively.
Discrete signals \( x[n] \) and \( y[n] \) are shown below. The cross-correlation \( r_{xy}[0] \) is _________