A method for designing Wavelets for communications and radar which combines requirements for Wavelets and finite impulse response FIR filters including no excess bandwidth, linear performance metrics for passband, stopband, quadrature mirror filter QMF properties, intersymbol interference, and adjacent channel interference, polystatic filter design requirements, and non-linear metrics for bandwidth efficient modulation BEM and synthetic aperture radar SAR. Demonstrated linear design methodology finds the best design coordinates to minimize the weighted sum of the contributing least-squares LS error metrics for the respective performance requirements. Design coordinates are mapped into the optimum FIR symbol time response. Harmonic design coordinates provide multi-resolution properties and enable a single design to generate Wavelets for arbitrary parameters which include dilation, down-sampling, up-sampling, time translation, frequency translation, sample rate, symbol rate, symbol length, and set of design harmonics. Non-linear applications introduce additional constraints. Performance examples are linear communications, BEM, and SAR.