Virtual Labs

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

1. Which mathematical property of the Fourier Transform explains why time-domain convolution corresponds to frequency-domain multiplication?

a: Linearity Explanation

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b: Duality Explanation

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c: Convolution Theorem Explanation

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d: Time-shifting Explanation

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2. What effect does time reversal have on the Fourier Transform of a signal x(t)?

a: It results in a phase shift. Explanation

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b: It produces the complex conjugate of the Fourier Transform. Explanation

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c: It reflects the Fourier Transform about the origin. Explanation

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d: It shifts the Fourier Transform by a constant frequency. Explanation

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3. If x(t) is real and even, what is the nature of its Fourier Transform X(f)?

a: Imaginary and odd Explanation

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b: Real and even Explanation

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c: Complex and odd Explanation

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d: Real and odd Explanation

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4. Why does a rectangular window in the time domain lead to spectral leakage in the frequency domain?

a: Because the Fourier Transform of a rectangular function is a Gaussian. Explanation

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b: Because the time-domain window is not smooth, causing sinc-like ripples in frequency. Explanation

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c: Because the rectangular window causes frequency-domain aliasing. Explanation

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d: Because it increases the resolution in the frequency domain. Explanation

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5. Which of the following is a necessary condition for a signal to have a Fourier Transform?

a: The signal must be periodic. Explanation

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b: The signal must be real-valued. Explanation

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c: The signal must be absolutely integrable. Explanation

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d: The signal must have finite bandwidth. Explanation

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6. What is the relationship between the bandwidth of a signal and the width of its Fourier Transform?

a: The bandwidth is inversely proportional to the width of the Fourier Transform. Explanation

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b: The bandwidth is directly proportional to the width of the Fourier Transform. Explanation

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c: The bandwidth is unaffected by the Fourier Transform. Explanation

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d: The bandwidth is related to the phase spectrum of the Fourier Transform. Explanation

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7. What is the Fourier Transform of a triangular pulse?

a: A sinc function. Explanation

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b: A Gaussian function. Explanation

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c: A triangular function. Explanation

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d: A sinc function squared. Explanation

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8. What is the effect of frequency scaling on the Fourier Transform of a signal?

a: The Fourier Transform is scaled by the same factor. Explanation

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b: The Fourier Transform is scaled by the reciprocal of the scaling factor. Explanation

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c: The Fourier Transform is shifted in frequency by the scaling factor. Explanation

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d: The Fourier Transform is unchanged. Explanation

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9. What is the Fourier Transform of a signal x(t) sampled at a rate fs?

a: The Fourier Transform is periodic with period fs. Explanation

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b: The Fourier Transform is continuous with no periodicity. Explanation

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c: The Fourier Transform has a frequency shift by fs. Explanation

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d: The Fourier Transform is a sinc function. Explanation

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10. What happens to the Fourier Transform of a signal when the signal is convolved with a filter in the time domain?

a: The Fourier Transform of the signal is multiplied by the Fourier Transform of the filter. Explanation

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b: The Fourier Transform of the signal is shifted in frequency. Explanation

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c: The Fourier Transform is unaffected by convolution. Explanation

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d: The Fourier Transform of the signal is convolved with the Fourier Transform of the filter. Explanation

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