Digital Filtering

A digital filter is an operation that associates an input time series x[n] into an output one, y[n]. Methods developed in the LTPDA Toolbox deal with linear digital filters, i.e. those which fulfill that a linear combination of inputs results in a linear combination of outputs with the same coefficients (provided that these are not time dependent). In these conditions, the filter can be expressed as

described in these terms, the filter is completely described by the impulse response h[k], and can then be subdivided into the following classes:

Digital filters classification

Digital filters can be described as difference equations. If we consider an input time series x and an output y, three specific cases can then be distinguished: