ABSTRACT
In discrete-time signal processing, filter design is the art of turning a set of requirements into a well-defined numerical algorithm. The requirements, or specifications, are usually formulated in terms of the filter’s frequency response; the design problem is solved by finding the appropriate coefficients for a suitable difference equation which implements the filter and by specifying the filter’s architecture. Since realizable filters are described by rational transfer functions, filter design can usually be cast in terms of a polynomial optimization procedure for a given error measure. Additional design choices include the computational cost of the designed filters, i.e. the number ofmathematical operations and storage necessary to compute each output sample. Finally, the structure of the difference equation defines an explicit operational procedure for computing the filter’s output values; by arranging the terms of the equation in different ways, we can arrive at different algorithmic structures for the implementation of digital filters.
