A specification language for the optimal design of exotic FIR filters with second-order cone programs

Application-tailored individual and joint FIR-filter designs of remarkable complexity are elegantly coded using our MATLAB toolbox Opt, a research tool providing a DSP-oriented modeling language for driving ultra-efficient off-the-shelf numerical solvers of (linear and) second-order cone programs. Opt data types symbolically capture affine or (nonnegative definite) quadratic dependencies on optimization variables, which gain numeric values only later, when optimized. On those basic types it builds affine vector and complex-time-sequence types for specifying impulse response structures in 1D or multi-D, with sample spacing either uniform or not. Dependencies can be manipulated symbolically with arithmetic and DSP operations including convolution, filter match, and Fourier transform. Linear and MS errors in frequency and time domains can be constructed, constrained and optimized. MSE constructions include output powers of filter systems driven by symbolic random-process drive signals having user-specified PSDs.