List of top Biomedical Engineering Questions on Signals and Systems

The Laplace transform of \( u(t) \) and its ROC is given as
The input \( x(t) \) is related to its output \( y(t) \) as: \( \frac{dy(t)}{dt} + y(t) = 3x(t - 3)u(t - 3) \). Here \( u(t) \) represents a step function. The transfer function of this system is

The overall impulse response of the system shown in figure is given by (Block diagram provided: Input $X(n)$ splits. One path goes to $h_1[n]$, another to $h_2[n]$. The outputs of $h_1[n]$ and $h_2[n]$ are subtracted. This result is convolved with $h_3[n]$. Separately, $X(n)$ also goes to $h_5[n]$. The output of $h_3[n]$ and $h_5[n]$ are subtracted. This result is convolved with $h_4[n]$ to produce $y(n)$.)

Consider two signals $x(n)=\{0,1,1,2\}$ and $h(n)=\{a,b,c\}$. The signal $y(n)=x(n)\otimes h(n)$. The DFT of $y(n)$ is given as $Y(e^{j\omega})$. If $Y(e^{j0})$ is 36, then which of the following relation is correct?
A band-limited signal with a maximum frequency of 5 kHz is to be sampled. According to the sampling theorem, the sampling frequency which is not valid is
Consider a system output \( y(t) \) is related to its input \( x(t) \) as, \( y(t) = x(t) + \cos (x(t)) \). This system is
A continuous system is described by \( y(t) = x(t) \cos(200 \pi t) \). If \( x(t) \) is a two-tone signal with frequencies 25 Hz and 50 Hz, then the frequency components present in \( y(t) \) will be
Let a discrete time signal \( x(n) \) has Z-transform \( X(z) = \frac{1}{1+2 z^{-1}}, |z|>2 \). If its Fourier transform is denoted as \( X(e^{j\omega}) \), then
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 __________________.