Скачать или смотреть Wavelets vs Fourier transform

The wavelet transform is a mathematical tool that breaks signals into different frequency components, analyzing each with a resolution matched to its scale. Unlike the Fourier transform, which uses infinite sine and cosine waves, wavelets are small, localized waves that can stretch or compress, making them better for analyzing signals with sharp changes or discontinuities.
Comparison with Fourier Transform
Time-Frequency Localization:
Fourier gives frequency info but loses time details (good for stationary signals).
Wavelet provides both time and frequency info (ideal for non-stationary signals like audio, images).
Basis Functions:
Fourier uses sine/cosine waves (fixed frequency, infinite in time).
Wavelets use short-duration waves (variable size, localized in time).
Resolution:
Fourier has uniform resolution.
Wavelet adapts resolution (high freq = fine detail, low freq = broad overview).
Best for:
Fourier: Smooth, periodic signals (e.g., sound analysis).
Wavelet: Transient signals (e.g., ECG, image compression, denoising).
Wavelets are like a "microscope" for signals, zooming in/out where needed!