On the design and use of digital filters in certain experimental situations
Michael R. Smith, Sorin Cohn-Sfetcu · Journal of Physics E Scientific Instruments · 1975
The difficulty of defining a digital filter whose frequency characteristics match those of a desired continuous filter is discussed theoretically. The 'impulse invariant' filter design is used to derive a formula for calculating the digital filter parameters. Important aspects of the actual use of digital filters are analysed with special reference to the single section RC, three pole Butterworth and three pole Bessel filters. It is shown that reverse time filtering of signals which start discontinuously but decay slowly to zero enables output signal discontinuities to be avoided. Such filtering enhances the slow decay components of multicomponent exponential decays but leaves the exponential nature of the data unchanged. The optimum reverse time filter for exponential signals is an RC filter whose time constant equals that of the decay. The use of digital filters whose bandwidth echoes changes in the signal information bandwidth are examined with special reference to multicomponent exponential decays.