Additional Information About Filtering
Gérard Blanchet, Maurice Charbit · 2015
This chapter deals with the technical aspects of filtering. It studies the implementation of the filtering function, in other words its programming. The system theory demonstrates that the possibility of reconstruction is related to the concept of observability. The chapter presents some results concerning filter banks that can be encountered when dealing with processing architectures. The Fast Fourier Transform (FFT) calculation implies the use of array pointers, which cause a considerable increase in the calculation time. A commonly used approach in sub-band decomposition techniques uses the FFT calculation structure. The Remez algorithm, and its subsequent application to the synthesis of finite impulse response (FIR) filters by Parks and McClellan, is based on the alternance theorems and an optimal error control at each step of an iterative calculation.