List of top Signals and Systems Questions asked in GATE BM

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)

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?

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

Which of the following statement(s) about pulse oximetry is/are TRUE?

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.

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.

$x(t)$ 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 _________

In the block diagram shown below, an infinite tap FIR filter with transfer function $ H(z) = \frac{Y(z)}{X(z)} $ is realized. If \[ H(z) = \frac{1}{1 - 0.5z^{-1}}, \] the value of $ \alpha $ is $\underline{\hspace{2cm}}$

$x[n]$ is convolved with $h[n]$ to give $y[n]$. If $y[2] = 1$ and $y[3] = 0$, then $h[0] = \underline{\hspace{1cm}}.$ (Graphs are not uniformly scaled)

A unit step input is applied to a system with impulse response $ H(s) = \dfrac{1-s/\omega_z}{1+s/\omega_p} $ at $ t = 0 $. The output of the system $ y(t) $ at $ t = 0^+ $ is

A continuous time transfer function $ H(s) = \dfrac{1 + s/10^6}{s} $ is converted to a discrete time transfer function $ H(z) $ using a bilinear transform at a sampling rate of 100 MHz. The pole of $ H(z) $ is located at $ z = $ $\underline{\hspace{2cm}}$.

Let $X(j\omega)$ denote the Fourier transform of $x(t)$. If $X(j\omega) = 10 e^{-j\pi f} \left( \frac{\sin(\pi f)}{\pi f} \right)$, then $ \frac{1}{2\pi} \int_{-\infty}^{\infty} X(j\omega) d\omega = \underline{\hspace{1cm}}. $ (where $\omega = 2\pi f$)

An analog signal is sampled at 100 MHz to generate 1024 samples. Only these samples are used to evaluate 1024-point FFT. The separation between adjacent frequency points ($ \Delta F $) in FFT is $\underline{\hspace{2cm}}$ kHz.