List of top Biomedical Engineering Questions on Signals and Systems asked in GATE BM

A continuous time, band limited signal \(x(t)\) has its Fourier transform described by \( X(f)= \begin{cases} 1-\dfrac{|f|}{200}, & |f|\le 200\text{ Hz}\\[4pt] 0, & |f|>200\text{ Hz} \end{cases} \). The signal is uniformly sampled at a sampling rate of \(600\) Hz. The Fourier transform of the sampled signal is \(X_s(f)\). What is the value of \(\dfrac{X_s(600)}{X_s(500)}\)? (Round off the answer to one decimal place.)
The Laplace transform of \(x_{1}(t)=e^{-t}u(t)\) is \(X_{1}(s)\), where \(u(t)\) is the unit step function. The Laplace transform of \(x_{2}(t)=e^{t}u(-t)\) is \(X_{2}(s)\). Which one of the following statements is TRUE?
The continuous time signal \(x(t)\) is described by \[ x(t) = \begin{cases} 1, & 0 \leq t \leq 1 \\ 0, & \text{elsewhere} \end{cases} \] If \(y(t)\) represents \(x(t)\) convolved with itself, which of the following statements is/are TRUE?
A system is described by the following differential equation \[ 0.01 \frac{d^2y(t)}{dt^2} + 0.2 \frac{dy(t)}{dt} + y(t) = 6x(t), \] where time \((t)\) is in seconds. If \(x(t)\) is the unit step input applied at \(t=0\) s to this system, the magnitude of the output at \(t=1\) s is ________. (Round off the answer to two decimal places.)
Two sequences \(x_1[n]\) and \(x_2[n]\) are described as follows: \[ x_1[0] = x_2[0] = 1, x_1[1] = x_2[2] = 2, x_1[2] = x_2[1] = 1 \] \[ x_1[n] = x_2[n] = 0 \text{for all } n<0 \text{ and } n>2 \] If \(x[n]\) is obtained by convolving \(x_1[n]\) with \(x_2[n]\), which of the following equations is/are TRUE?
A causal, discrete time system is described by the difference equation \[ y[n] = 0.5 \, y[n-1] + x[n], \text{for all n, \] where \(y[n]\) denotes the output sequence and \(x[n]\) denotes the input sequence. Which of the following statements is/are TRUE?}
A finite impulse response (FIR) filter has only two non-zero samples in its impulse response \(h[n]\), namely \(h[0]=h[1]=1\). The Discrete Time Fourier Transform (DTFT) of \(h[n]\) equals \(H(e^{j\omega})\), as a function of the normalized angular frequency \(\omega\). For the range \(|\omega|\leq \pi\), \(|H(e^{j\omega})|\) is equal to __________________.