Virtual Labs

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

1. 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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2. 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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3. 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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4. 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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5. 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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6. What happens when you double the frequency of a sinusoidal signal in the time domain?

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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7. What is the consequence of sampling a signal below its Nyquist rate?

a: The signal becomes periodic. Explanation

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b: The signal's frequency increases. Explanation

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c: Aliasing occurs, causing frequency overlap. Explanation

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d: The amplitude of the signal increases. Explanation

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8. What does the sampling theorem guarantee?

a: Signals can be reconstructed exactly from samples if sampled below Nyquist rate. Explanation

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b: Signals must be periodic to be sampled correctly. Explanation

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c: Exact reconstruction is possible if sampling rate is greater than twice the highest frequency. Explanation

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d: Aliasing is unavoidable. Explanation

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9. 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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10. How does aliasing appear in the frequency domain?

a: As increased amplitude of the spectral components. Explanation

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b: As copies of the spectrum overlapping due to undersampling. Explanation

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c: As a single narrow spike. Explanation

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d: As a shift of the whole spectrum to zero frequency. Explanation

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