Virtual Labs

Fourier transforms with procedures such as Discrete Fourier Transforms and Fast Fourier Transforms

What is the primary purpose of the Fourier Transform?

a: To convert a time-domain signal into a frequency-domain representation Explanation

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b: To compress data Explanation

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c: To remove noise from a signal Explanation

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d: To convert analog signals into digital signals Explanation

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What does the Discrete Fourier Transform (DFT) operate on?

a: Continuous signals Explanation

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b: Only analog waveforms Explanation

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c: Discrete-time sampled data Explanation

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d: Random noise sequences exclusively Explanation

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What is the computational complexity of the DFT?

a: O(N) Explanation

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b: O(N log N) Explanation

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c: O(N^2) Explanation

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d: O(log N) Explanation

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Which algorithm is widely used to compute the DFT efficiently?

a: Laplace Transform Algorithm Explanation

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b: Fast Fourier Transform (FFT) Explanation

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c: Wavelet Packet Transform Explanation

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d: Kalman Filtering Explanation

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Which property of DFT states that both input and output sequences repeat every N samples?

a: Linearity Explanation

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b: Circular Convolution Explanation

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c: Periodicity Explanation

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d: Symmetry Explanation

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The FFT algorithm reduces computation using which strategy?

a: Divide and combine Explanation

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b: Trial and error Explanation

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c: Random sampling Explanation

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d: Neural optimization Explanation

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The complex exponential used in DFT, e^{-j(2π/N)kn}, is known as a:

a: Kernel Explanation

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b: Twiddle Factor Explanation

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c: Impulse response Explanation

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d: Wavelet function Explanation

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The Cooley–Tukey algorithm is associated with:

a: Continuous Fourier Transform Explanation

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b: Wavelet Transform Explanation

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c: Fast Fourier Transform Explanation

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d: Z-transform computation Explanation

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Which of the following is a key advantage of FFT over DFT?

a: FFT produces more accurate results than DFT Explanation

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b: FFT requires significantly fewer computations Explanation

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c: FFT eliminates spectral leakage Explanation

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d: FFT only works for real-valued signals Explanation

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In practical DSP applications, the DFT is mainly used for:

a: Frequency analysis of discrete-time signals Explanation

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b: Converting digital signals to analog signals Explanation

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c: Generating random numbers Explanation

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d: Performing time-domain smoothing only Explanation

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