Convolution invariance and corrected impulse invariance

The impulse invariant method of digital implementation of analog filters is re-interpreted as a convolution invariance. This leads automatically to the corrected impulse invariant method that was recently introduced by Mecklenbräuker [Remarks on and correction to the impulse invariant method for the design of IIR digital filters. Signal Processing 80 (2000) 1687–1690] and Jackson [A correction to impulse invariance. IEEE Signal Processing Lett. 7 (10) (2000) 273–275] and extends its application to a larger class of transfer functions.