Interval algebras are introduced as media in which to simulate digital filters for the purpose of analyzing quantization effects due to finite wordlength. The theory presented forms the basis of a computer-aided analysis scheme which generates confidence interval error bounds on the time domain response of a digital filter. The techniques are applicable to filters of arbitrary order and configuration implemented in either fixed or floating-point arithmetic. Experimental data is presented for a fourth-order low-pass Butterworth filter realized with fixed-point arithmetic in the direct, canonical direct, parallel, cascade, and ladder configurations. An example of Parker and Hess is used to illustrate the bounding limit cycles with interval techniques.
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