An Experimental Study of Roundoff Effects in a Tenth-Order Recursive Digital Filter

This paper reports experimental measurements of limitcycle amplitude and period in digital recursive filters. The results that were obtained on two cascaded forms of a tenth-order filter show good agreement with existing theoretical bounds. (The bounds only apply to single second-order sections because analysis of cascaded sections is difficult.) Roundoff noise of the filter was measured and it agreed both in spectral shape and total power with that predicted by computer simulation. Some preliminary observations on relative magnitude of limit cycle and roundoff noise were made. In addition, the gradual buildup of a signal through a limit cycle was observed and 1 bit of noise in the least significant bit (LSB) in the filter was seen to break up limit cycles.