Computational Toolsmiths Software Tools for Computational Science, Engineering, and Medicine

### FirWav Real Orthogonal Filters

• Examples of Individual Filters
• Daubechies Real Orthogonal Least Asymmetric (DROLA)
• Daubechies Real Orthogonal Most Asymmetric (DROMA)
• Daubechies Real Orthogonal Least Uncertain (DROLU)
• Daubechies Real Orthogonal Most Regular (DROMR)
• Examples of Filter Families
• Daubechies Real Orthogonal Least Disjoint (DROLD)
• Daubechies Real Orthogonal Most Disjoint (DROMD)
• Daubechies Real Orthogonal Least Asymmetric (DROLA)
• Daubechies Real Orthogonal Most Asymmetric (DROMA)
• Daubechies Real Orthogonal Least Regular (DROLR)
• Daubechies Real Orthogonal Most Regular (DROMR)
• Daubechies Real Orthogonal Least Uncertain (DROLU)
• Daubechies Real Orthogonal Most Uncertain (DROMU)

### Examples of Individual Filters

In the following examples of filters, each figure contains a matrix of subplots with rows corresponding to product, analysis, and synthesis filters, and with columns corresponding to characteristics of the filters in the complex z domain, the frequency domain, and the time domain.

• f(t) = filter in time t domain;
• F(z) = filter in complex z domain;
• F(w) = filter in frequency w domain;
• mag(F) = magnitude of F(w);
• db(F) = magnitude of F(w) in decibels;
• ang(F) = phase angle of F(w);
• up(F) = unwrapped phase angle of F(w);
• pd(F) = phase delay of F(w);
• gd(F) = group delay of F(w);
• P(z) = Product filter;
• A(z) = Analysis filter, primary spectral factor of P(z);
• S(z) = Synthesis filter, complementary spectral factor of P(z);
• tfu = Time-Frequency Uncertainty;
• tdr = Time-Domain Regularity;
• fds = Frequency-Domain Selectivity; and
• pnl = total Phase NonLinearity.

Scalets (lowpass filters) are in green; wavelets (highpass filters) are in red. In the z domain plots, the number near the zero at z = -1 indicates the multiplicity of that zero. This number determines the theoretical number of vanishing moments of the corresponding wavelet filter.