A modified FFT-based algorithm for real-time computation of discrete wavelet transform

In this paper, an efficient FFT-based algorithm is proposed for fast computation of discrete wavelet transform (DWT). By virtue of the Fourier-space operations, significant saving in computational complexity is achieved. The Fourier-domain subsampling results in single IFFT operation at the intermediate level thus reducing the computational burden. The Fourier-domain subsampling and the Hermitian symmetry property of the Fourier-transform of a real function provides significant reduction in overall computations. The comparison of the computational complexity of an FFT-based fast wavelet transform (FWT) algorithm with the proposed algorithm for various cases of decomposition levels and wavelet kernel size is done. We found that the proposed algorithm reduces the number of multiplications per point by 22% and by 35% in the case of additions for ´db8´ wavelet at a of five. This gain is of practical interest in computationally intensive applications.