Desensitized filters with droop correction
A method and system for the design and implementation of desensitized digital filters with droop correction. The desensitized digital filter includes a first filter configured to receive an input signal, a decimator or upsampler, and a modified desensitized half-band filter. The first filter introduces droop into the passband of the desensitized digital filter. The desensitized half-band filter has a transfer function F(z)=K(1+z −1 )G(z) wherein K≠0 is a scale factor, that is modified to omit a (1+z −1 ) factor block. The modified desensitized half-band filter compensates for the passband droop introduced by the first filter. The first filter may be a sinc filter, CIC filter, or filter having similar properties.
1. A desensitized digital filter with droop correction, comprising:
a first filter configured to receive an input signal;
a decimator; and
a second filter implemented in hardware and coupled to the decimator and the first filter, wherein G(z) is a discrete-time transfer function of the second filter and has a degree greater than one, such that a desensitized half-band filter has a transfer function F(z)=K·(1+z −1 )·G(z) wherein K≠0 is a scale factor,
wherein the second filter compensates for passband droop introduced by the first filter.
2. The digital filter of claim 1 , wherein the second filter is an FIR filter.
3. The digital filter of claim 1 , wherein the decimator is placed before components of the second filter.
4. The digital filter of claim 1 , wherein the decimator is placed after components of the second filter.
5. The digital filter of claim 1 , wherein the first filter is a sinc filter.
6. The digital filter of claim 1 , wherein the first filter is a CIC filter.
7. The digital filter of claim 1 , wherein the transfer function of the desensitized half-band filter includes an additional (1+z −1 ) block.
8. A desensitized digital filter with droop correction, comprising:
a first filter configured to receive an input signal;
an upsampler; and
a second filter implemented in hardware and coupled to the upsampler and the first filter, wherein G(z) is a discrete-time transfer function of the second filter and has a degree greater than one, such that a desensitized half-band filter has a transfer function F(z)=K·(1+z −1 )·G(z) wherein K≠0 is a scale factor,
wherein the second filter compensates for passband droop introduced by the first filter.
9. The digital filter of claim 8 , wherein the second filter is an FIR filter.
10. The digital filter of claim 8 , wherein the upsampler is placed before components of the second filter.
11. The digital filter of claim 8 , wherein the upsampler is placed after components of the second filter.
12. The digital filter of claim 8 , wherein the first filter is a sinc filter.
13. The digital filter of claim 8 , wherein the first filter is a CIC filter.
14. A method for filtering an input signal in a digital filter having a first filter, implemented in hardware, and a second filter, implemented in hardware, coupled in cascade, comprising:
filtering the input signal in the first filter to produce a first filter output signal, wherein the first filter introduces droop into a passband of the digital filter;
modifying a sampling rate within the digital filter; and
filtering the first filter output signal in the second filter to produce an output signal of the digital filter, wherein G(z) is a discrete-time transfer function of the second filter and has a degree greater than one, such that a half-band filter has a transfer function F(z)=K·( 1+z −1 )·G(z) wherein K≠0 is a scale factor,
wherein the second filter compensates for passband droop introduced by the first filter.
15. The method of claim 14 , wherein modifying the sampling rate within the digital filter comprises:
downsampling the sampling rate within the second filter.
16. The method of claim 14 , wherein modifying the sampling rate within the digital filter comprises:
upsampling the sampling rate within the second filter.
17. The method of claim 14 , wherein filtering the input signal in the first filter includes filtering using a sinc filter.
18. The method of claim 14 , wherein filtering the input signal in the first filter includes filtering using a CIC filter.
19. The method of claim 14 , wherein filtering the first filter output signal in the second filter includes filtering the first filter output in an FIR filter.