New method of synthetising linear digital filters based on convolution integral

A new procedure for realising the cascade and parallel forms of digital filters is presented. The method is based on using a Taylor expansion of the input signal over each sampling interval. The results reported in the paper are largely concerned with the simplest expansion, namely that the input remains constant during the sampling period. The method is shown to be applicable to lowpass and bandpass filters and, with a certain modification (which involves both delay equalisation and frequency doubling), to highpass and bandstop filters too. Another important feature of the method is that the gain at zero frequency is completely independent of the sampling rate. The time-and frequency-domain characteristics of several Butter-worth filters are studied. It is also shown that the so-called impulse-invariant technique of synthetising digital filters can be derived by approximating to the convolution integral in a special manner.