Sampling and Digital Filters - Signals and Systems - Biomedical Engineering Previous Year Questions

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

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 (Δf) in FFT is ______ kHz.

x(t) is a real continuous-time signal whose magnitude frequency response (|X(jω)|) is shown below. After sampling x(t) at 100 rad.s⁻¹, the spectral point P is down-converted to ______ rad.s⁻¹ in the spectrum of the sampled signal.

A continuous time, band limited signal \(x(t)\) has its Fourier transform described by:
\(X(f) = \begin{cases} 1 - \frac{|f|}{200}, & |f| \leq 200 \text{ Hz} \\ 0, & |f| > 200 \text{ Hz} \end{cases}\)
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 \(\frac{X_s(600)}{X_s(500)}\)? (Round off the answer to one decimal place.)

A time domain signal is given by \( x(t) = 20 \sin(100\pi t) + 36 \sin(150\pi t) - 2\sin (300\pi t) \), where time \( t \) is in seconds. Among the following options, what is the frequency (in Hz) at which \( x(t) \) should be sampled for accurate signal reconstruction?