Question

How do the results differ between performing an N-point FFT and per- forming an N-point discrete Fourier transform (DFT) on the same set of time samples?

Answer 1

Performing an N-point FFT and performing an N-point DFT on the same set of time samples can result in different results, with the FFT algorithm being computationally more efficient.

Step-by-step explanation:

Performing an N-point FFT (Fast Fourier Transform) and performing an N-point DFT (Discrete Fourier Transform) on the same set of time samples can result in different results.

The main difference between the two is the computational efficiency. The FFT algorithm is a faster version of the DFT and can provide the same exact results as the DFT, but in a shorter amount of time.

For example, let's say you have 1024 time samples and you want to compute the Fourier transform. If you use the FFT algorithm, it will take significantly less time compared to using the DFT algorithm, while still producing the same frequency components.