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Elementary recirculating filter

The elementary recirculating filter is the recirculating comb filter of Figure 7.7 with a complex-valued feedback gain as shown in Figure 8.11 (part a). By the same analysis as before, feeding this network a sinusoid whose th sample is gives an output of:

so the transfer function is

The recirculating filter is stable when ; when, instead, the output grows exponentially as the delayed sample recirculates.

Figure 8.11: The elementary recirculating filter: (a) block diagram; (b) frequency response.

The transfer function is thus just the inverse of that of the non-recirculating filter (first form). If you put the two in series with , the output theoretically equals the input. (This analysis only demonstrates it for sinusoidal inputs; that it follows for other signals as well can be verified by working out the impulse response of the combined network).

Next: Compound filters Up: Elementary filters Previous: Non-recirculating filter, second form Contents Index