Constrained digital matched filter method for optimum filter synthesis

We present a new method to directly calculate the optimum filter in presence of any additive stationary noise, with arbitrary time and domain constraints (flat-top, zero-area, etc.). A more concise re-deduction of digital penalized LMS method (DPLMS) is given. This method is fully developed, and synthesis results of a typical situation are given and compared with the DPLMS method. Optimum filter can be synthesized without a prior knowledge of the noise power spectral density, which makes it suitable to be used in adaptive, self-calibrating digital spectroscopy.