NEW METHOD OF SYNTHETISING LINEAR DIGITAL FILTERS BASED ON CONVOLUTION INTEGRAL

A new procedure for realizing 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 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 also to highpass and bandstop filters. The gain at zero frequency is completely independent of the sampling rate. The tpme and frequency-domaincharacteristics of several Butterworth filters are studied. It is also shown that the so-called impulse- invariant technique of synthetizing digital filters can be derived by approximating to the convolution integral in a special manner. Paper 6141 E.