Cascaded integrator comb filter with arbitrary integer decimation value and scaling for unity gain
We disclose a CIC digital filter having an arbitrary-integer decimation rate. The filter has a shifter connected to its input. The shifter receives a shift control input, where the shift control input is pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter. There is a multiplier connected between the input and the shifter. In other embodiments, the multiplier could be connected between the input and the shifter. Sequentially-connected integrator functions are connected to the shifter (or multiplier); a decimation function receives input from the integrator functions; and sequentially-connected differentiator functions receive input from the decimation function. The decimation function has a selectable rate equal to any integer between 1 and a number equal to the predetermined maximum decimation value. The multiplier is configured to compute the product of each input data sample by a correction factor; the correction factor being pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter, so as to correct the gain of the CIC filter for decimation values not a power of 2.
1. A CIC digital filter for filtering input data samples, comprising:
at least one integrator function;
a decimation function receiving input from the integrator function;
at least one differentiator function receiving input from the decimation function;
a multiplier connected between the input and the integrator function;
a shifter connected to output of the multiplier; and,
the multiplier configured to compute the product of each input data sample by a correction factor, so as to correct the gain of the CIC filter for decimation values not a power of 2.
2. The CIC filter of claim 1 , where the correction factor is pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter.
3. The CIC filter of claim 1 , further comprising the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter.
4. The CIC filter of claim 1 , comprising four sequentially-connected integrator functions and four sequentially-connected differentiator functions.
5. The CIC filter of claim 1 , where the decimation function operates at any decimation rate from 1 to 131,072.
6. A CIC digital filter for filtering input data samples; the filter having an input for data samples; the filter comprising:
a shifter connected to the input; the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter;
a multiplier connected between the input and the shifter;
at least four sequentially-connected integrator functions connected to the shifter;
a decimation function receiving input from the integrator functions;
at least four sequentially-connected differentiator functions receiving input from the decimation function; the decimation function having a selectable rate equal to any integer between 1 and a number equal to the predetermined maximum decimation value; and,
the multiplier configured to compute the product of each input data sample by a correction factor; the correction factor being pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter, so as to correct the gain of the CIC filter for decimation values not a power of 2.
7. A method of implementing a CIC filter having an input, an output, a shifter, a shift control, a multiplier, one or more integrator functions, a decimation function, and one or more differentiator functions, the method comprising:
receiving an input stream of data samples;
shifting each data sample by a left shift equal to the integer portion of the base-2 logarithm of the CIC filter gain;
multiplying each so shifted data sample by the fractional portion of the base-2 logarithm of the CIC filter gain;
integrating the shifted and multiplied data sample at least once;
decimating the data sample by a pre-determined decimation rate;
differentiating the decimated data sample at least once; and,
rounding the differentiated data sample to a pre-determined number of bits before outputting the data sample.
8. The method of claim 7 where the data sample is integrated a plurality of times.
9. The method of claim 7 where the data sample is differentiated a plurality of times.
10. The method of claim 7 where the decimation rate is an arbitrary integer between 1 and a number equal to a predetermined maximum decimation value.
11. An integrated circuit for performing a CIC digital filter function; the integrated circuit comprising:
at least one integrator;
a decimator; the decimator receiving input from the integrator;
at least one differentiator receiving input from the decimator;
a multiplier connected to the input;
a shifter connected between the output of the multiplier and to the integrator; and,
the multiplier configured to compute the product of each input data sample by a correction factor, so as to correct the gain of the CIC filter for decimation values not a power of 2.
12. The integrated circuit of claim 11 , where the correction factor is pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter.
13. The integrated circuit of claim 11 , further comprising the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter.
14. The integrated circuit of claim 11 , comprising four sequentially-connected integrators and four sequentially-connected differentiators.
15. The integrated circuit of claim 11 , where the decimator operates at any decimation rate from 1 to a predetermined maximum decimation value.
16. An integrated circuit for performing a CIC digital filter function for filtering input data samples, comprising:
a shifter; the shifter connected to the input; the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter;
a multiplier connected to the shifter;
at least four sequentially-connected integrators connected to the multiplier;
a decimator receiving input from the integrators;
at least four sequentially-connected differentiators receiving input from the decimator; the decimator having a selectable rate equal to any integer between 1 and a number equal to a predetermined maximum decimation value; and,
the multiplier configured to compute the product of each input data sample by a correction factor; the correction factor being pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter, so as to correct the gain of the CIC filter for decimation values not a power of 2.
17. A multi-channel CIC digital filter for filtering input data samples from a multiplexed data stream, comprising:
a multiplier connected to the input;
a shifter connected to the multiplier;
a demultiplexer connected to the shifter for demultiplexing the multiplexed data stream into two or more data streams;
where each demultiplexed data stream is input to:
at least one integrator function;
a decimation function receiving input from the integrator function;
at least one differentiator function receiving input from the decimation function;
the multiplier and shifter configured to compute the product of the input data samples by a correction factor, so as to correct the gain of the multi-channel CIC filter for decimation values not a power of two.
18. The multi-channel CIC filter of claim 17 , where the correction factor is pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter.
19. The multi-channel CIC filter of claim 17 , further comprising the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter.
20. The multi-channel CIC filter of claim 17 , where each channel comprises four sequentially-connected integrator functions and four sequentially-connected differentiator functions.
21. The CIC filter of claim 17 , where the decimator operates at any decimation rate from 1 to 131,072.
22. A method of implementing a multi-channel CIC filter for filtering input data samples from a multiple data stream; the multi-channel CIC filter having an input, an output, a shifter, a shift control, a multiplier, a demultiplexer, and a plurality of channels; each channel having one or more integrator functions, a decimation function, and one or more differentiator functions, the method comprising:
receiving an input stream of multiplexed data samples;
shifting each data sample by a left shift equal to the integer portion of the base-2 logarithm of the CIC filter gain;
multiplying each so shifted data sample by the fractional portion of the base-2 logarithm of the CIC filter gain;
demultiplexing the multiplexed data stream into two or more data streams;
for each data stream:
integrating the shifted and multiplied data sample at least once;
decimating the data sample by a pre-determined decimation rate;
differentiating the decimated data sample at least once; and,
rounding the differentiated data sample to a pre-determined number of bits before outputting the data sample.
23. The method of claim 22 where each data sample is integrated a plurality of times.
24. The method of claim 22 where each data sample is differentiated a plurality of times.
25. The method of claim 22 where the decimation rate is an arbitrary integer between 1 and a number equal to a predetermined maximum decimation value.
26. An integrated circuit for performing a multi-channel CIC digital filter function on a multiplexed stream of data samples; the integrated circuit comprising:
a multiplier connected to the input;
a shifter connected to the multiplier;
a demultiplexer connected to the shifter for demultiplexing the multiplexed data stream into two or more channels, each channel comprising a demultiplexed data stream;
where each channel further comprises:
at least one integrator;
a decimator; the decimator receiving input from the integrator;
at least one differentiator receiving input from the decimator; and, the multiplier and shifter configured to compute the product of each input data sample by a correction factor, so as to correct the gain of the CIC filter for decimation values not a power of 2.
27. The integrated circuit of claim 26 , where the correction factor is pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the multi-channel CIC filter.
28. The integrated circuit of claim 26 , further comprising the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the multi-channel CIC filter.
29. The integrated circuit of claim 26 , where each channel comprises four sequentially-connected integrators and four sequentially-connected differentiators.
30. The integrated circuit of claim 26 , where each decimator operates at any decimation rate from 1 to a predetermined maximum decimation value.
31. An integrated circuit for performing a multi-channel CIC digital filter function on a multiplexed stream of data samples, comprising:
a multiplier connected to the input; the multiplier configured to compute the product of each input data sample by a correction factor; the correction factor being pre-computed as equal to the fractional portion of 2 raised to the base-2 logarithm of the gain of the CIC filter, so as to correct the gain of the CIC filter for decimation values not a power of 2; and,
a shifter connected to the multiplier; the shifter receiving a shift control input; the shift control input being pre-computed as equal to the integer portion of 2 raised to the base-2 logarithm of the gain of the CIC filter;
a demultiplexer connected to the shifter for demultiplexing the multiplexed data stream into two or more channels; where each channel comprises a demultiplexed data stream;
where each channel further comprises:
at least four sequentially-connected integrators;
a decimator receiving input from the integrators;
at least four sequentially-connected differentiators receiving input from the decimator; the decimator having a selectable rate equal to any integer between 1 and a number equal to a predetermined maximum decimation value.