Filtering employing a new transform

The increasingly stringent demands of signal and information processing applied to problems arising in underwater communications and elsewhere point to the need for filters that are free from internally generated noise arising from rounding effects in the calculations. The use of finite number systems in digital signal processing provides a means of overcoming or reducing this problem. A new transform employing the Mersenne numbers (Boussakta and Holt, 1992) is used to implement filter designs without rounding errors. Convolutions based upon this transform are presented to show both the responses of a range of filters and also the effects of different transform parameters. Attention is concentrated upon filters defined by multiple poles sets. The time responses of these filters are shown. The ease with which calculations exceeding the modulus may be detected with the new transform is demonstrated. Error-free filter implementations will be a valuable contribution to signal processing for many applications in underwater communications and sonar