Wavelet transform
（重定向自Wavelet compression）
![An example of the 2D discrete wavelet transform that is used in JPEG2000.](/Images/godic/202502/20/Jpeg2000_2-level_wavelet_transform-lichtenstein3506.png")
![](/Images/godic/202502/20/Basis_function_with_compression_factor3506.jpg")
![](/Images/godic/202502/20/STFT_and_WT3506.jpg")
![](/Images/godic/202502/20/Analysis_of_three_superposed_sinusoidal_signals3506.jpg")
In mathematics, a wavelet series is a representation of a square-integrable (real- or complex-valued) function by a certain orthonormal series generated by a wavelet. Nowadays, wavelet transformation is one of the most popular of the time-frequency-transformations. This article provides a formal, mathematical definition of an orthonormal wavelet and of the integral wavelet transform.