Fig. 5.

Block diagram of Mallat algorithm for discrete wavelet transformation (DWT) and reconstruction with an additional denoising step. The input signal (C) is passed through two complementary filters, a high-pass filter (g) and a low-pass filter (h). The filtered signals are subsequently decimated by a factor of 2 to maintain the same number of data points as the input signal. Two sets of DWT coefficients, the low frequency approximation coefficients (a) and high-frequency detail coefficients (d) are the result of these processes. These steps can then be repeated using the approximation coefficients as the input, resulting in another set of approximation and detail coefficients. The original signal can then be reconstructed by reversing the process. Applying a thresholding step prior to reconstruction allows for significant noise reduction.