Multi-rate implementation without high-pass filter
A filtering method approximates a target Finite Impulse Response (FIR) (or transversal) filter and reduces computational requirements by eliminating high pass filtering required by known multi-rate filters. An input signal is copied into two identical signals and processed in parallel by a full-rate path, and by a reduced-rate path. Parallel filters are computed and applied in each path, the reduced-rate signal is up-sampled, and the two signals summed. The high pass filter required by known multi-rate filters is eliminated and the low pass filter in the prior art is implicit in a down sampling. Linear phase FIR filters are used for down and up sampling, resulting in constant group delay. Added benefits include the option of zero added latency through the filtering and the constant group delay added to the target FIR. The user may choose criteria such as minimum resolution in each band.
1. An improved multi-rate digital filter comprising:
a first path including a full-rate Finite Impulse Response (FIR) filter FIR F , the full-rate filter FIR F receiving and filtering an input signal to produce a filtered full-rate signal;
a second path in parallel to the first path and also receiving the input signal, the second path sequentially comprising:
a down sampler processing the input signal to produce a reduced-rate signal;
a reduced-rate FIR filter FIR R in signal communication with the down sampler to receive and processing the reduced-rate signal to produce a filtered reduced-rate signal; and
an up sampler in signal communication with the reduced-rate filter FIR R to receive and process the filtered reduced-rate signal and to provide an up sampled filtered signal; and
a summer in signal communication with the full-rate filter FIR F to receive the filtered full-rate signal and in signal communication with the reduced-rate filter FIR R to receive the up sampled filtered signal, the summer summing the filtered full-rate signal and the up sampled filtered signal to provide a filtered signal.
2. The improved multi-rate digital filter of claim 1 , wherein the full-rate filter FIR F receives a wideband input signal.
3. The improved multi-rate digital filter of claim 1 , wherein the full-rate filter FIR F receives an unfiltered version of the input signal.
4. The improved multi-rate digital filter of claim 1 , wherein the full-rate filter FIR F is computed by windowing a target FIR filter with a window W.
5. The improved multi-rate digital filter of claim 4 , wherein the window W comprises:
a first leading region of ones; and
a second trailing region of a second trailing half of a known window function.
6. The improved multi-rate digital filter of claim 5 , wherein the known window function is selected from the group consisting of a Hann window, a Gausian window, and Kaiser window.
7. The improved multi-rate digital filter of claim 5 , wherein:
the target FIR filter has a length N; and
the window W has a length of approximately N/4.
8. The improved multi-rate digital filter of claim 5 , wherein the reduced-rate filter FIR R is computed by subtracting the full-rate filter FIR F from the target FIR filter to obtain a residual filter R and convolving the residual filter R with an anti-aliasing filter A.
9. The improved multi-rate digital filter of claim 8 , wherein the reduced-rate filter FIR R is computed by subtracting the full-rate filter FIR F from the target FIR filter to obtain the residual filter R, removing leading zeros from the residual filter R to obtain a second residual filter, and convolving the second residual filter with the anti-aliasing filter A.
10. The improved multi-rate digital filter of claim 9 , wherein the result of the convolution is decimated to reduce the number of elements in the reduced-rate filter FIR R .
11. A method for filtering a signal, the method comprising:
providing an input signal to a full-rate a Finite Impulse Response (FIR) filter FIR F ;
filtering the input signal in the full-rate filter FIR F to produce a filtered full-rate signal;
providing the input signal to a down sampler;
processing the input signal in the down sampler to produce a reduced-rate signal;
providing the reduced-rate signal to a reduced-rate FIR filter FIR R ;
processing the reduced-rate signal in the reduced-rate filter FIR R to produce a filtered reduced-rate signal;
providing the filtered reduced-rate signal to an up-sampler;
processing the filtered reduced-rate signal in the up-sampler to provide a up-sampled filtered signal;
providing the filtered full-rate signal and the up-sampled filtered signal to a summer; and
summing the filtered full-rate signal and the up sampled filtered signal in the summer to provide a filtered signal.
12. The method of claim 11 , further including designing the full-rate filter FIR F using the steps of:
choosing a target FIR filter of length N to be modeled;
designing a window W of length M used to create the full-rate filter FIR F ; and
term by term multiplying the window W times the first M terms of the target FIR filter to create the full-rate filter FIR F of length M.
13. The method of claim 12 , further including designing the reduced-rate filter FIR R using the steps of:
choosing a decimation factor and design an appropriate anti-aliasing filter A;
subtracting the windowed full-rate FIR F from the target FIR filter to obtain a residual FIR filter R of length N;
removing the leading zeros from the residual FIR filter R to obtain a shortened residual FIR filter;
convolving the shortened residual FIR filter with the anti-aliasing filter A; and
decimating the result of the convolution to create the reduced-rate filter FIR R .
14. The method of claim 13 , further including the anti-aliasing filter A in the down-sampler.
15. The method of claim 11 , further including delaying the signal in the reduced-rate path before summing with the signal in the full-rate path.
16. The method of claim 15 , further including delaying the signal in the reduced-rate path before up-sampling.
17. The method of claim 15 , further including delaying the signal in the reduced-rate path after up-sampling.
18. The method of claim 11 , further including delaying the signal in the full-rate path before summing with the signal in the reduced-rate path.
19. A method for filtering a signal, the method comprising:
designing a full-rate filter using the steps of:
choosing a target Finite Impulse Response (FIR) filter of length N to be modeled;
designing a window W of length M used to create a full-rate filter FIR F ; and
term by term multiplying the window W times the first M terms of the target FIR filter to create the full-rate filter FIR F of length M;
providing an input signal to the full-rate filter FIR F ;
filtering the input signal in the full-rate filter FIR F to produce a filtered full-rate signal;
designing a reduced-rate filter using the steps of:
selecting a down sampling rate;
designing an anti-aliasing filter A to control aliasing due to the down-sampling;
subtracting the windowed full-rate filter FIR F from the target FIR filter to obtain a residual filter R of length N;
removing the leading zeros from the residual filter R to obtain a shortened residual filter;
convolving the shortened residual filter with the anti-aliasing filter A; and
decimating the result of the convolution to create a reduced-rate filter FIR R ;
providing the input signal to a down sampler;
processing the input signal in the down sampler to produce a reduced-rate signal;
providing the reduced-rate signal to a reduced-rate filter FIR R ;
processing the reduced-rate signal in the reduced-rate filter FIR R to produce a filtered reduced-rate signal;
providing the filtered reduced-rate signal to an up-sampler;
processing the filtered reduced-rate signal in the up-sampler to provide an up-sampled filtered signal;
providing the filtered full-rate signal and the up-sampled filtered signal to a summer; and
summing the filtered full-rate signal and the up sampled filtered signal in the summer to provide a filtered signal.