Desensitized filters
A method and system for the design and implementation of filters is presented in which the filter's transfer function can be provided with a significant insensitivity to the filter's tap coefficient values. A desensitized digital filter includes a first halfband filter and a second filter coupled in cascade between an input of the digital filter and the output of the digital filter. In embodiments, the first filter has the transfer function F(z)=K(1+z −1 )(1+z −1 ) wherein K≠0 is a scale factor. The digital filter may also interact with an up-sampler or a down-sampler. A desensitized Hilbert transformer includes an FIR filter having filter-tap coefficients whose absolute values equal the absolute values of the coefficients of an FIR filter F(z) for which the product (1+z −1 )F(z) is a halfband filter coupled in cascade with a second filter.
1. A digital filter comprising: a first filter including a delay loop coupled to a plurality of multipliers and having a transfer function G(z) of degree greater than one; and a second filter implemented in hardware and having a transfer function F(z)=K·(1+z −1 ) where K≠0, wherein the first filter and the second filter are coupled in cascade to make a filter having a transfer function H(z)=F(z)·G(z), with H(z) being a transfer function of a halfband filter.
2. The digital filter of claim 1 , wherein the first filter is a finite impulse response (FIR) filter.
3. The digital filter of claim 1 , wherein the second filter includes an additional (1+z −1 ) block.
4. The digital filter of claim 1 , wherein the digital filter interacts with an up-sampler.
5. The digital filter of claim 4 , wherein the up-sampler is a sample-and-hold up-sampler.
6. The digital filter of claim 1 , wherein the digital filter interacts with a down-sampler.
7. The digital filter of claim 1 , wherein the first filter includes:
a multiplier block coupled to the delay loop; and
a plurality of adders coupled between the delay loop and the multiplier block.
8. The digital filter of claim 7 , wherein the multiplier block includes a plurality of filter multipliers, each having a corresponding multiplier coefficient.
9. The digital filter of claim 8 , wherein each of the multiplier coefficients is calculated using at least one coefficient in a transfer function of the digital filter.
10. The digital filter of claim 7 , wherein the multiplier block includes:
a plurality of adders; and
a plurality of shift elements.
11. The digital filter of claim 10 , wherein the multiplier block is configured to generate a plurality of output values.
12. The digital filter of claim 1 , wherein the digital filter is a finite impulse response (FIR) filter.
13. The digital filter of claim 1 , wherein the digital filter is an infinite impulse response (IIR) filter.
14. The digital filter of claim 1 , wherein the digital filter is a halfband-like filter.
15. A Hilbert transformer, comprising: a first FIR filter including a delay loop coupled to a plurality of multipliers and having a transfer function G(z) of degree greater than one whose filter-tap coefficients have absolute values equal to sums of one or more filter-tap coefficients of said Hilbert transformer, and a second filter implemented in hardware and having a transfer function F(z)=K·(1+z −1 ) where K≠0, wherein the first filter and the second filter are coupled in cascade to make a filter having a transfer function H(z)=F(z)·G(z), with H(z) being a transfer function of the Hilbert transformer.
16. A digital filter comprising: a first filter configured to provide a coarse approximation of a desired transfer function for the digital filter, the first filter including a delay loop coupled to a plurality of multipliers and having a transfer function G(z) of degree greater than one; and a second filter coupled to the first filter in cascade, wherein the second filter has a transfer function F(z)=K·(1+z −1 ) where K≠0 and is configured to compensate for the coarse approximation of the first filter, wherein H(z)=G(z)·F(z), with H(z) being a transfer function of a halfband filter.
17. The digital filter of claim 16 wherein the first filter is an FIR filter.
18. The digital filter of claim 16 , wherein the second filter includes an additional (1+z −1 ) block.
19. The digital filter of claim 16 , wherein the digital filter interacts with an up-sampler.
20. The digital filter of claim 19 , wherein the up-sampler is a sample-and-hold up-sampler.
21. The digital filter of claim 16 , wherein the digital filter interacts with a down-sampler.
22. 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 includes a delay loop coupled to a plurality of multipliers and has a transfer function G(z) of degree greater than one; and filtering the first filter output signal in the second filter having a transfer function F(z)=K·(1+z −1 ) where K≠0 to produce an output signal of the digital filter, wherein the digital filter has a transfer function H(z)=F(z)·G(z), with H(z) being a halfband filter.
23. The method of claim 22 , wherein filtering the input signal in the first filter includes filtering using an FIR filter.
24. The method of claim 22 , wherein filtering the first filter output signal includes filtering using the second filter having an additional (1+z −1 ) block.
25. The method of claim 22 , further comprising: receiving said input signal of a digital filter from an up-sampler.
26. The method of claim 25 , wherein the up-sampler is a sample-and-hold up-sampler.
27. The method of claim 22 , further comprising: down-sampling said digital filter output.
28. The method of claim 22 , wherein filtering the input signal in the first filter includes producing a coarse approximation of a set of characteristics of a desired output signal for the digital filter.
29. A method for filtering an input signal in a Hilbert transformer, comprising:
filtering the input signal in a first FIR filter including a delay loop coupled to a plurality of multipliers. and having a transfer function G(z) of degree greater than one with filter-tap coefficients whose absolute values equal sums of one or more filter-tap coefficients of said Hilbert transformer; and filtering the first filter output signal in a second filter implemented in hardware and having transfer function F(z)=K·(1+z −1 ) where K≠0, such that G(z)·F(z) is the transfer function of a Hilbert transformer.
30. A method for filtering an input signal in a Hilbert transformer, comprising:
filtering the input signal in a first filter implemented in hardware and having a transfer function F(z)=K·(1+z −1 ) where K≠0, to produce a first filter output signal; and filtering the first filter output signal in an FIR implemented in hardware and including a delay loop coupled to a plurality of multipliers, and having a transfer function G(z) of degree greater than one with filter-tap coefficients whose absolute values equal sums of one or more filter-tap coefficients of said Hilbert transformer, such that F(z)·G(z) is the transfer function of a Hilbert transformer.