Harmonic wavelet analysis 论文

详细信息

发表期刊/会议

Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences

发表日期

1993-10-08

发表年份

1993

摘要

Abstract A new harmonic wavelet is suggested. Unlike wavelets generated by discrete dilation equations, whose shape cannot be expressed in functional form, harmonic wavelets have the simple structure ω(x) = {exp(i4πx) - exp(i2πx)}/i2πx. This function ω(x) is concentrated locally around x = 0, and is orthogonal to its own unit translations and octave dilations. Its frequency spectrum is confined exactly to an octave band so that it is compact in the frequency domain (rather than in the x domain). An efficient implementation of a discrete transform using this wavelet is based on the fast Fourier transform (FFT). Fourier coefficients are processed in octave bands to generate wavelet coefficients by an orthogonal transformation which is implemented by the FFT. The same process works backwards for the inverse transform.