Band filter for filtering a discrete time series signal

1. A band filter ( 100 , 200 ) for filtering a discrete time series signal ( 110 , 210 ), the band filter ( 100 , 200 ) comprising:

an input frequency shifter ( 120 , 220 ) configured to frequency down shift the discrete time series signal ( 110 , 210 ) to provide a frequency down shifted discrete time series signal ( 120 a , 220 a );

a high-pass higher order polynomial regression based zero frequency centered band filter ( 130 , 230 ) communicatively coupled to the input frequency shifter ( 120 , 220 ), the high-pass higher order polynomial regression based zero frequency centered band filter ( 130 , 230 ) being configured to:

operate on an entire length of the frequency down shifted discrete time series signal ( 120 a , 220 a ); and

filter the frequency down shifted discrete time series signal ( 120 a , 220 a ) to provide a filtered and frequency down shifted discrete time series signal ( 130 a , 230 a ); and

an output frequency shifter ( 140 , 240 ) communicatively coupled to the high-pass higher order polynomial regression based zero frequency centered band filter ( 130 , 230 ), the output frequency shifter ( 140 , 240 ) being configured to frequency up shift the filtered and frequency down shifted discrete time series signal ( 130 a , 230 a ).

2. The band filter ( 100 , 200 ) of claim 1 , wherein:

the input frequency shifter ( 120 , 220 ) being configured to frequency down shift the discrete time series signal ( 110 , 210 ) comprises the input frequency shifter ( 120 , 220 ) being configured to multiply the discrete time series signal ( 110 , 210 ) by an exponent of a negatived frequency shift term k 0 .

3. The band filter ( 100 , 200 ) of claim 1 , wherein:

the output frequency shifter ( 140 , 240 ) being configured to frequency up shift the filtered and frequency down shifted discrete time series signal ( 130 a , 230 a ) comprises the output frequency shifter ( 140 , 240 ) being configured to multiply the filtered and frequency down shifted discrete time series signal ( 130 a , 230 a ) by an exponent of the frequency shift term k 0 .

4. The band filter ( 100 ) of claim 1 , wherein the high-pass higher order polynomial regression based zero frequency centered band filter ( 130 ) comprises a polynomial regression smoothing filter.

5. The band filter ( 200 ) of claim 1 , wherein the high-pass higher order polynomial regression based zero frequency centered band filter ( 230 ) comprises:

a polynomial regression filter ( 232 ) communicatively coupled to the input frequency shifter ( 220 ), the polynomial regression filter ( 232 ) being configured to:

receive the frequency down shifted discrete time series signal ( 220 a ) provided by the input frequency shifter ( 220 ); and

smooth the frequency down shifted discrete time series signal ( 220 a ) to provide a smoothed frequency down shifted discrete time series signal ( 232 a ).

6. The band filter ( 200 ) of claim 5 , wherein the high-pass higher order polynomial regression based zero frequency centered band filter ( 230 ) further comprises:

a feed forward loop ( 234 ) communicatively coupled to the input frequency shifter ( 220 ), the feed forward loop ( 234 ) being configured to receive the frequency down shifted discrete time series signal ( 220 a ) provided by the input frequency shifter ( 220 ); and

a summation ( 236 ) communicatively coupled to the polynomial regression filter ( 232 ) and the feed forward loop ( 234 ), the summation ( 236 ) being configured to:

receive the smoothed frequency down shifted time series signal ( 232 a ) from the polynomial regression filter ( 232 );

receive the frequency down shifted time series signal ( 220 a ) from the feed forward loop ( 234 ); and

sum the smoothed frequency down shifted discrete time series signal ( 232 a ) and the frequency down shifted discrete time series signal ( 220 a ) to provide a filtered and frequency down shifted discrete time series signal ( 230 a ).

7. The band filter ( 100 , 200 ) of claim 1 , wherein:

the input frequency shifter ( 120 , 220 ) is further configured to receive the discrete time series signal ( 110 , 210 );

the high-pass higher order polynomial regression based zero frequency centered band filter ( 130 , 230 ) is further configured to receive the frequency down shifted discrete time series signal ( 120 a , 220 a ); and

the output frequency shifter ( 140 , 240 ) is further configured to receive the filtered and frequency down shifted discrete time series signal ( 130 a , 230 a ).

8. A method of filtering a discrete time series signal with a band filter, the method comprising:

frequency down shifting the discrete time series signal to provide a frequency down shifted discrete time series signal;

using a high-pass higher order polynomial regression based zero frequency centered band filter to operate on an entire length of the frequency down shifted discrete time series signal and filter the frequency down shifted discrete time series signal to provide a filtered and frequency down shifted discrete time series signal; and

frequency up shifting the filtered and frequency down shifted discrete time series signal.

9. The method of claim 8 , wherein frequency down shifting the discrete time series signal comprises multiplying the discrete time series signal by an exponent of a negatived frequency shift term k 0 .

10. The method of claim 8 , wherein frequency up shifting the filtered and frequency down shifted discrete time series signal comprises multiplying the filtered and frequency down shifted discrete time series signal by an exponent of the frequency shift term k 0 .

11. The method of claim 8 , wherein the high-pass higher order polynomial regression based zero frequency centered band filter comprises a polynomial regression smoothing filter.

12. The method of claim 8 , wherein using the high-pass higher order polynomial regression based zero frequency centered band filter to filter the frequency down shifted discrete time series signal to provide a filtered and frequency down shifted discrete time series signal comprises using a polynomial regression filter to smooth the frequency down shifted discrete time series signal.

13. The method of claim 12 , wherein using the high-pass higher order polynomial regression based zero frequency centered band filter to filter the frequency down shifted discrete time series signal to provide a filtered and frequency down shifted discrete time series signal further comprises using a summation to sum the smoothed and frequency down shifted discrete time series signal and the frequency down shifted discrete time series signal.

14. The method of claim 12 , further comprising:

receiving with a feed forward loop receive the frequency down shifted discrete time series signal;

receiving with a summation the smoothed frequency down shifted time series signal from the polynomial regression filter;

receiving with the summation the frequency down shifted time series signal from the feed forward loop; and

summing with the summation the smoothed frequency down shifted discrete time series signal and the frequency down shifted discrete time series signal to provide a filtered and frequency down shifted discrete time series signal.

15. The method of claim 8 , further comprising:

receiving the discrete time series signal with the input frequency shifter;

receiving the frequency down shifted discrete time series signal with the high-pass higher order polynomial regression based zero frequency centered band filter; and

receiving the filtered and frequency down shifted discrete time series signal with the output frequency shifter.