Analogue-to-digital transform to preserve the frequency-magnitude characteristics of all-pole filters

When the bilinear transform is applied to an all-pole analogue filter, zeros are obtained in the derived digital transfer function. The corresponding digital-filter structure must provide feedforward terms. A new transform is described which enables implementation without feedforward terms. The frequency-magnitude characteristic is preserved, though not the phase, and the frequency warping differs from that of the bilinear transform. In addition a technique to compensate for a zero-order hold is described.