List of top Signals and Systems Questions asked in GATE BM

In a catheter-sensor system to measure blood pressure (P) as shown in the below figure, the liquid resistance (R_L) of the catheter is due to friction between shearing molecules flowing through the catheter. Which of the following is TRUE for R_L if only the radius of the catheter is doubled. Assume that the pressure difference across the catheter segment is fixed.

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.

$x(t)$ is a real continuous-time signal whose magnitude frequency response ($|X(j\omega)|$) is shown below. After sampling $x(t)$ at $100\ \text{rad s}^{-1}$, the spectral point P is down-converted to _________ rad·s$^{-1}$ in the spectrum of the sampled signal.

Discrete signals \( x[n] \) and \( y[n] \) are shown below. The cross-correlation \( r_{xy}[0] \) is _________