Representation of Wavelet Transform using a Matrix Form and Its Implementation

Three representations are known to implement the discrete wavelet transform (DWT) ; i.e., direct, lifting and matrix forms. In these representations, direct and lifting forms are well known so far. This paper derives the matrix form of the DWT from the direct form. Then, we implement these three representations on a programmable digital signal processor (in the following, DSP processor) and compare them in terms of the number of calculations and instruction cycles. As a result, we confirm that the lifting form has the lowest number of calculations and cycles, and the matrix form has an effective decrease in the number of cycles than other representations on the DSP processor.