Test on The Fast Fourier Transform (FFT)

The Fast Fourier Transform (FFT) Explained for Students

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Question 1 of 50%

For a Discrete Fourier Transform (DFT) with N points, each spectrum coefficient calculation inherently demands N unique exponential function calculations in the complex domain, even when utilizing computational re-orderings and simplifications.

Test: Fast Fourier Transform (FFT)

20 questions

Question 1: For a Discrete Fourier Transform (DFT) with N points, each spectrum coefficient calculation inherently demands N unique exponential function calculations in the complex domain, even when utilizing computational re-orderings and simplifications.

A. Ano

B. Ne

Explanation: The study materials state that 'Repeating the same power of the same DFT phasor is a potential for saving a lot of computations' and that 'Using some simplifications and computation re-orderings, we can significantly reduce the computational demands.' This implies that not all N exponential function calculations for each spectrum coefficient will be unique or need to be recomputed if simplifications are applied.

Question 2: When applying FFT for N=8, a bit-reversal permutation is used to reorder the resulting coefficients from their initial non-natural order.

A. Ano

B. Ne

Explanation: The study materials state that when FFT is applied, the resulting coefficients are not in the natural order, and a bit-reversal permutation should be applied to reorder them, with an example provided for N=8.

Question 3: The default 'norm' option for numpy.fft.fft in Python is 'forward'.

A. Ano

B. Ne

Explanation: The study materials indicate that when using 'norm' in numpy.fft.fft, 'ortho' is the default option.

Question 4: The expression W_N = e^(-j2π/N) is defined as the DFT phasor of order N.

A. Ano

B. Ne

Explanation: The study materials explicitly state that the DFT formula contains powers of the expression e^(-j2π/N), and this expression is called the DFT phasor of order N.

Question 5: For a Discrete Fourier Transform (DFT) with N=4, the DFT matrix W4 contains more than 4 unique complex exponential expressions.

A. Ano

B. Ne

Explanation: The study materials state that 'Thanks to the complex exponential periodicity, the matrix W4 contains only 4 (generally N) different expressions'. This means for N=4, there are exactly 4 unique expressions.