What is spectral analysis of a function?

Question

Discrete Math

The task is given: to perform a spectral analysis and synthesis of a function using the fast Fourier transform (FFT).
With spectral analysis, everything is still clear, but with the spectral synthesis of a function - no. Tell me, what is this synthesis, and what is its result? Also in the condition of the problem it is indicated that when performing the inverse FFT, it is necessary to take into account 1, 2, 4, 8, 16 and 128 values ​​obtained using the direct FFT. What does it mean to consider these values?

Answer 1

Read in the MATLAB documentation:
Spectral analysis: https://docs.exponenta.ru/signal/ug/spectral-analy...
FFT for spectral analysis: https://docs.exponenta.ru/matlab/math/fft- for-spec...