Signal Representations and Transforms - Signals and Systems - Biomedical Engineering Previous Year Questions

1

2020 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2020

\(X(s)\) is the Laplace transform of a signal \(x(t)\).
The Laplace transform of \(\frac{dx(t)}{dt}\), assuming \(x(0) = 0\), is

A

\(sX(s)\)

B

\(X(s)/s\)

C

\(\frac{dX(s)}{ds}\)

D

\(\frac{1}{s} \frac{dX(s)}{ds}\)

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2

2021 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2021

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 \(\frac{1}{2\pi} \int_{-\infty}^{\infty} X(j\omega) \, d\omega = ____\). (where \(\omega = 2\pi f\))

A

\(10\pi\)

B

100

C

10

D

\(20\pi\)

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3

2021 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2021

In the block diagram shown below, an infinite tap FIR filter with transfer function \(H(z) = Y(z)/X(z)\) is realized. If \(H(z) = \frac{1}{1 - 0.5z^{-1}}\) the value of α is ______.

A

2

B

1/√2

C

1/2

D

√2

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4

2022 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2022

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.

A

300π/360

B

10π/360

C

50π/360

D

200π/360

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5

2022 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2022

If \( g(t) = \frac{df(t)}{dt} \), and \( F(s) = \frac{1+s}{s^2+12s+32} \), where \( F(s) \) is the Laplace transform of the function \( f(t) \), then the value of \( g(t) \) at \( t=0 \) is ________.

A

-11

B

-5

C

-17

D

\(\infty\)

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6

2023 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2023

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 ________.

A

\(2 |\cos(\omega)| \)

B

\(2 |\sin(\omega)| \)

C

\(2 |\cos(\omega/2)| \)

D

\(2 |\sin(\omega/2)| \)

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7

2023 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2023

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?

A

The region of convergence of \(X_1(s)\) is \(Re(s) > 0\).

B

The region of convergence of \(X_2(s)\) is confined to the left half-plane of \(s\).

C

The region of convergence of \(X_1(s)\) is confined to the right half-plane of \(s\).

D

The imaginary axis in the \(s\)-plane is included in both the region of convergence of \(X_1(s)\) and the region of convergence of \(X_2(s)\).

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8

2024 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2024

The Fourier transform of \(e^{-|2t|}\) is ________.

A

\(\frac{4}{4 - \omega^2}\)

B

\(\frac{4}{4 + \omega^2}\)

C

\(\frac{2}{2 + \omega}\)

D

\(\frac{2}{2 - \omega}\)

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9

2024 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2024

The trigonometric Fourier series expansion of the periodic function in the figure has coefficients \(\{a_n\}\) and \(\{b_n\}\) for cosine and sine terms, respectively. The value of \(a_1/a_3\) is ________. Give your answer rounded off to 1 decimal place.

Check answer

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10

2026 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2026

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^{jω})?

A

X(e^{jω}) is real and even

B

X(e^{jω}) is imaginary and even

C

X(e^{jω}) is real and odd

D

X(e^{jω}) is imaginary and odd

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11

2026 · Biomedical Engineering · Signals and Systems · Signal Representations and Transforms

Biomedical Engineering (BM) 2026

The table below shows the average values of the power spectral density (PSD) of an EEG signal in different frequency bands.

Frequency bands (Hertz)	Average PSD (microvolts²/Hertz)
0.4 – 4.0	3
4.0 – 8.0	4
8.0 – 13.0	8
13.0 – 30.0	5
30.0 – 100.0	3

The PSD of the EEG signal has a noise floor of 2 microvolts²/Hertz. The signal to noise ratio for the alpha-band, expressed in decibels, is ______

A

1.76

B

3.01

C

6.02

D

3.98

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