Training a recursive filter by use of derivative function

Abstract

A method of training a recursive filter comprises updating recursive parameters of the filter with delta values computed from sampling of an error signal and obtaining derivative terms of the output signal with respect to the parameters. Adaptation using derivatives for FIR filters is known, but this technique was not available for IIR filters because of the unavailability of the derivative values. However, when it is realized that the derivative itself is recursive, a parameter derivative function is obtained which will produce derivative terms for updating the filter parameters with acceptable filter performance.

I claim:  
     
       1. A method of adapting a filter having a plurality of recursive filter parameters, said recursive filter effective for producing an output signal in response to receiving an input signal, the method comprising: 
       subtracting said output signal from a desired signal to produce an error signal;  
       producing a plurality of derivative functions, each of whose level is representative of a derivative of said output signal with respect to a particular recursive filter parameter; and  
       updating each of said recursive filter parameters based on said derivative functions and said error signal.  
     
     
       2. The method of  claim 1  further including: 
       delaying for a period of time subsequent to said step of updating, in order to allow transient signals arising from said step of updating to subside; and  
       repeating above said steps;  
       whereby said recursive filter remains stable during the adapting thereof.  
     
     
       3. The method of  claim 2  wherein said period of time is determined by: 
       providing a test circuit which duplicates said filter, applying a constant input to said test circuit;  
       monitoring an output of said test circuit; and  
       measuring the time required for said test circuit output to remain stable within a user-defined window.  
     
     
       4. The method of  claim 1  wherein for each recursive filter parameter, said step of updating includes computing a change of value of said filter parameter, said change of value being proportional to a level of its corresponding derivative function and said error signal. 
     
     
       5. The method of  claim 1  further including updating non-recursive filter parameters of said filter. 
     
     
       6. A method of adapting a filter having a plurality of recursive and non-recursive parameters, said filter effective for producing an output signal in response to receiving an input signal, the method comprising: 
       subtracting said output signal from a desired signal to produce an error signal;  
       producing a plurality of derivative functions, each of whose level is representative of a derivative of said output signal with respect to a particular recursive parameter; and  
       producing a plurality of derivative functions, each of whose level is representative of a derivative of said output signal with respect to a particular non-recursive parameter; and  
       updating each said recursive and non-recursive parameter based upon its corresponding derivative function and said error signal.  
     
     
       7. The method of  claim 6  further including: 
       delaying for a period of time subsequent to said step of updating, in order to allow transient signals arising from said step of updating to subside; and  
       repeating above said steps;  
       whereby said filter remains stable during the adapting thereof.  
     
     
       8. The method of  claim 6  wherein said derivatives are computed and  said error signal is sampled over N periods of time to produce a plurality of error samples are taken for each of said N periods of time . 
     
     
       9. The method of  claim 8  wherein said substep of computing a delta-value of step (c)  updating includes evaluating the equation:          Δ                   P   i       =       ∑   n                         error   n            D   n          (     P   i     )         K                       
       where ΔP i  is said delta-value for a  an update value for one of said recursive and non- recursive  parameters P i ; 
       error n  is an error sample taken at a time t n ;  
       D n (P i ) is a derivative function of said output signal y with respect to parameter P i ; and  
       K is an adjustment factor.  
     
     
       10. The method of  claim 9  further including a substep of computing said adjustment factor K for each of said error samples by evaluating the equation:          K   n     =       ∑   i                       (       D   n          (     P   i     )       )     2                       
       where K n  is an adjustment factor corresponding to time t n . 
     
     
       11. An adaptive recursive filter comprising: 
       input means for obtaining an input signal;  
       computing means, coupled to said input means, for producing an output signal, said computing means characterized by a plurality of recursive parameters; and  
       error means, coupled to said computing means, for comparing said output signal with a desired output signal;  
       derivative function means for producing a plurality of signals, each signal representative of a derivative of said output signal with respect to one of said recursive filter parameters;  
       update means, coupled to said error means and said derivative function means, for updating said plurality of recursive parameters.  
     
     
       12. The adaptive filter of  claim 11  wherein said update means includes delay means for delaying for a period of time between updates of said plurality of recursive parameters. 
     
     
       13. The adaptive circuit of  claim 12  wherein delay means is a test circuit having the same parameters as said recursive circuit, said test circuit having a constant-valued input signal, whereby a delay period is established as the time required for an output signal of said test circuit to remain stable within a user-defined window. 
     
     
       14. The adaptive filter of  claim 11  wherein said recursive filter further includes a plurality of non-recursive elements and means for updating said non-recursive elements.