We investigate the relation between discrete wavelet shrinkage and integrodifferential equations in the context of
simplification and denoising of one-dimensional signals. In the continuous setting, strong connections between
these two approaches were discovered in 6 (see references). The key observation is that the wavelet transform can be understood
as derivative operator after the convolution with a smoothing kernel. In this paper, we extend these ideas to the
practically relevant discrete setting with both orthogonal and biorthogonal wavelets. In the discrete case, the
behaviour of the smoothing kernels for different scales requires additional investigation. The results of discrete
multiscale wavelet shrinkage and related discrete versions of integrodifferential equations are compared with
respect to their denoising quality by numerical experiments.