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2005•Journal of Nanjing Institute of TechnologyRequires access

A Fast Wavelet Transform Algorithm Based on Discrete Fourier Transform

Hui Zong

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Abstract

The Multi-resolution analysis and Mallat algorithm of wavelet theory have been widely used in digital signal processing recently. However, if the signal decomposition and reconstruction are calculated in terms of the above-mentioned algorithm, the computational complexity will be very huge. Based on the analysis of the Discrete Fourier Transform and Mallat algorithm principle, a fast algorithm for Discrete Wavelet Transform is proposed, and has been proven valid in theory. Compared with the direct method, it can reduce the computational complexity effectively.

About this research paper

What this paper is about

The Multi-resolution analysis and Mallat algorithm of wavelet theory have been widely used in digital signal processing recently. However, if the signal decomposition and reconstruction are calculated in terms of the above-mentioned algorithm, the computational complexity will be very huge. Based on the analysis of the Discrete Fourier Transform and Mallat algorithm principle, a fast algorithm for Discrete Wavelet Transform is proposed, and has been proven valid in theory. Compared with the direct method, it can reduce the computational complexity effectively.

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Available abstract

The Multi-resolution analysis and Mallat algorithm of wavelet theory have been widely used in digital signal processing recently. However, if the signal decomposition and reconstruction are calculated in terms of the above-mentioned algorithm, the computational complexity will be very huge. Based on the analysis of the Discrete Fourier Transform and Mallat algorithm principle, a fast algorithm for Discrete Wavelet Transform is proposed, and has been proven valid in theory. Compared with the direct method, it can reduce the computational complexity effectively.

Key concepts: Algorithm, Harmonic wavelet transform, Discrete Fourier transform (general), Second-generation wavelet transform, Discrete wavelet transform, Computational complexity theory, Stationary wavelet transform, Wavelet transform

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