Fast FIR filtering technique for multirate filters
Data samples are filtered by using a digital filter where the length of an impulse response of the digital filter is finite, an impulse response of the digital filter is symmetric and the operation of the digital filter is multi-rate. The method uses a polyphase decomposition to break down the input data stream into N parallel substreams and the multi-rate digital filter is separated by a polyphase decomposition into multiple lower-rate sub-filters where each of the sub-filters is separated into a set of simpler sub-sub-filters which operate upon the same set of input samples and which have impulse responses which are jointly centro-symmetric, a set of pre-filtering arithmetic structures, and a set of post-filtering arithmetic structures and performing each such pair of sub-sub-filtering operations using a single shared filter structure, a set of pre-filtering combining adders, and a set of post-filtering separating adders.
1. A method for filtering data samples comprising:
using a digital filter to act upon a input data stream in order to transform it into an output data stream, wherein:
the length of an impulse response of the digital filter is finite;
an impulse response of the digital filter is symmetric;
the operation of the digital filter is multi-rate;
using a polyphase decomposition to break down the input data stream into N parallel substreams;
the multi-rate digital filter being separated by a polyphase decomposition into multiple lower-rate sub-filters;
each of the sub-filters being separated one or more times into a set of simpler sub-sub-filters, a set of pre-filtering arithmetic structures, and a set of post-filtering arithmetic structures, according to a fast FIR filtering decomposition algorithm;
the set of sub-sub-filters comprising one or more pairs of sub-sub-filters which operate upon the same set of input samples and which have impulse responses which are jointly centro-symmetric;
and performing each such pair of sub-sub-filtering operations using a single shared filter structure, a set of pre-filtering combining adders, and a set of post-filtering separating adders.
2. The method according to claim 1 , wherein the multi-rate digital filter is
a digital interpolator and wherein a single pre-filtering arithmetic structure is used to generate the set of input data samples required by multiple sets of sub-sub-filters.
3. The method according to claim 2 , wherein the order of the pre-filtering and post-filtering arithmetic structures is interchanged through a circuit transposition operation.
4. The method according to claim 1 , wherein the filter is a digital decimator and a single post-filtering arithmetic structure is used to process the output samples from Multiple sets of sub-sub-filters.
5. The method according to claim 4 , wherein the order of the pre-filtering and post-filtering arithmetic structures is interchanged through a circuit transposition operation.
6. The method according to claim 1 , wherein the fast FIR decomposition algorithm is a 2×2 decomposition as described in equation 6.
7. The method according to claim 1 , wherein the fast FIR decomposition algorithm is a 3×3 decomposition as described in equation 8.
8. A method for filtering data samples comprising:
using a digital filter to act upon a input data stream in order to transform it into an output data stream, wherein:
the length of an impulse response of the digital filter is finite;
an impulse response of the digital filter is symmetric;
the operation of the digital filter is multi-rate;
using a polyphase decomposition to break down the input data stream into N parallel substreams;
the multi-rate digital filter being separated by a polyphase decomposition into multiple lower-rate sub-filters;
each of the sub-filters being separated one or more times into a set of simpler sub-sub-filters, a set of pre-filtering arithmetic structures, and a set of post-filtering arithmetic structures, according to a fast FIR filtering decomposition algorithm;
wherein the multi-rate digital filter is a digital interpolator and wherein a single pre-filtering arithmetic structure is used to generate the set of input data samples required by multiple sets of sub-sub-filters.
9. The method according to claim 8 , wherein the order of the pre-filtering and post-filtering arithmetic structures is interchanged through a circuit transposition operation.
10. The method according to claim 8 , wherein the fast FIR decomposition algorithm is a 2×2 decomposition as described in equation 6.
11. The method according to claim 8 , wherein the fast FIR decomposition algorithm is a 3×3 decomposition as described in equation 8.
12. A method for filtering data samples comprising:
using a digital filter to act upon a input data stream in order to transform it into an output data stream, wherein:
the length of an impulse response of the digital filter is finite;
an impulse response of the digital filter is symmetric;
the operation of the digital filter is multi-rate;
using a polyphase decomposition to break down the input data stream into N parallel substreams;
the multi-rate digital filter being separated by a polyphase decomposition into multiple lower-rate sub-filters;
each of the sub-filters being separated one or more times into a set of simpler sub-sub-filters, a set of pre-filtering arithmetic structures, and a set of post-filtering arithmetic structures, according to a fast FIR filtering decomposition algorithm;
wherein the filter is a digital decimator and a single post-filtering arithmetic structure is used to process the output samples from multiple sets of sub-sub-filters.
13. The method according to claim 12 , wherein the order of the pre-filtering and post-filtering arithmetic structures is interchanged through a circuit transposition operation.
14. The method according to claim 12 , wherein the fast FIR decomposition algorithm is a 2×2 decomposition as described in equation 6.
15. The method according to claim 12 , wherein the fast FIR decomposition algorithm is a 3×3 decomposition as described in equation 8.