Virtual Labs

Understand various signal processing tools like Fourier series, Fourier transform, Power spectral density etc. for analyzing the signal

What is the Fourier Transform of the Dirac delta function?

a: A sinc function. Explanation

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b: A Gaussian function. Explanation

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c: A constant function. Explanation

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d: An impulse in the frequency domain. Explanation

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What is the significance of the duality property in the Fourier Transform?

a: It simplifies convolution calculations. Explanation

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b: It allows the Fourier Transform of a signal to be obtained from its inverse. Explanation

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c: It relates time-domain multiplication to frequency-domain convolution. Explanation

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d: It explains how energy is conserved in the transform. Explanation

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What type of signal corresponds to a sinc function in the frequency domain?

a: A Gaussian signal. Explanation

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b: A unit step signal. Explanation

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c: A rectangular pulse. Explanation

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d: A cosine wave. Explanation

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Which of the following best describes the Fourier Transform of a time-limited signal?

a: A time-limited signal has a band-limited Fourier Transform. Explanation

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b: The Fourier Transform is always infinite in duration. Explanation

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c: The Fourier Transform has the same duration as the signal. Explanation

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d: The Fourier Transform is finite only for periodic signals. Explanation

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What is the effect of multiplying a signal by a cosine wave in the time domain?

a: It results in a band-pass filter effect. Explanation

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b: It shifts the signal's spectrum to a higher frequency. Explanation

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c: It convolves the signal with a sinc function in frequency. Explanation

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d: It reduces the signal's bandwidth. Explanation

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What happens in the frequency domain when you double the frequency of a sinusoidal signal?

a: Its Fourier Transform shifts to the left. Explanation

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b: Its Fourier Transform shifts to higher frequencies. Explanation

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c: The signal's duration increases. Explanation

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d: The signal becomes band-limited. Explanation

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If x1(t) and x2(t) have Fourier Transforms X1(ω) and X2(ω), what is the Fourier Transform of a*x1(t) + b*x2(t)?

a: X1(ω) + X2(ω) Explanation

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b: a*X1(ω) + b*X2(ω) Explanation

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c: a*X2(ω) + b*X1(ω) Explanation

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d: a*b*X1(ω)*X2(ω) Explanation

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What happens to the Fourier Transform of x(t) if the signal is multiplied by e^{jω0t} in time domain?

a: The transform shifts by ω0 in frequency Explanation

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b: The transform scales by ω0 Explanation

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c: The transform is inverted in frequency Explanation

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d: The transform remains unchanged Explanation

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What happens in the frequency domain when two signals overlap in time?

a: Their spectra multiply. Explanation

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b: Their spectra add. Explanation

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c: Their bandwidths compress. Explanation

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d: They cancel out each other. Explanation

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What is the Fourier Transform of a unit step signal u(t) in angular frequency ω?

a: 1 Explanation

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b: πδ(ω) + 1/(jω) Explanation

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c: sinc(ω) Explanation

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d: Another unit step function Explanation

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