Multi-rate filter and filtering method for digital pre-distorters

1. A pre-distorter memory modeling apparatus, comprising:

a plurality of branches, each branch receiving a different output basis function signal, at least one branch including:

a down-sampler, the down-sampler down-sampling the received output basis function signal received at the branch by a down-sampling factor of 1/M k , M k being different for each of the at least one branch and being based on an evaluation period associated with the corresponding each of the at least one branch; and

a memory structure, the memory structure receiving and filtering an output of the down-sampler, the memory structure including:

at least one delay element, at least one of the at least one delay element delaying the output of the down-sampler according to a corresponding pre-determined delay; and

a memory structure output based on an output of the at least one delay element; and

an up-sampler, the up-sampler up-sampling the memory structure output by an up-sampling factor equal to M k .

2. The apparatus of claim 1 , wherein the down-sampler includes an accumulator and a register, the accumulator and register cooperatively configured to low-pass filter and down-sample the received output basis function signal.

3. The apparatus of claim 1 , wherein the up-sampler includes an interpolator configured to interpolate over M k −1 zeros between non-zero samples.

4. The apparatus of claim 1 , wherein the pre-determined delay is different for each branch.

5. The apparatus of claim 1 , wherein an evaluation period associated with a first branch of the plurality of branches is on an order of nanoseconds and an evaluation period associated with a second branch of the plurality of branches is on an order of microseconds.

6. The apparatus of claim 1 , wherein an evaluation period associated with a first branch of the plurality of branches is on an order of microseconds and an evaluation period associated with a second branch of the plurality of branches is on and order of milliseconds.

7. The apparatus of claim 1 , wherein the factor M k is related to a number of delay elements in the memory structure of a corresponding branch of the plurality of branches.

8. The apparatus of claim 7 , wherein an increase in a number of delay elements of the memory structure of a branch of the plurality of branches is associated with a decrease in the corresponding factor M k of the branch of the plurality of branches.

9. The apparatus of claim 1 , wherein the factor M k is based on an exponential power associated with the output basis function signal received at the corresponding branch of the plurality of branches.

10. The apparatus of claim 9 , wherein an increase in the exponential power associated with the output basis function is associated with a decrease in the factor M k of the corresponding branch of the plurality of branches.

11. A method of calculating a distortion signal, d(n), the method comprising:

receiving an input signal, x(n);

supplying the input signal, x(n), to each of K branches, where K is an integer not less than 1;

in each of the K branches, operating on the input signal, x(n), by a different basis function, to produce in each branch an output signal, u k (n), where k=0 to K−1; and

in each of the K branches, applying one of the K output signals, u k (n), to a different one of K memory models, each of the K memory models:

down-sampling the signal u k (n) by a factor 1/M k , to produce a down-sampled signal, v k (n) the factor M k of a branch of the K branches corresponding to an order of the basis function associated with the branch;

filtering the down-sampled signal v k (n) by a filter including at least one delay element to produce a filtered output;

up-sampling the filtered output by the factor, M k , to produce a distortion component d k (n); and

adding the outputs d k (n) of each branch to produce the distortion signal d(n).

12. The method of claim 11 , wherein operating on the input signal by a basis function includes raising the input signal x(n) by an integer power, the integer denoting the order of the basis function.

13. The method of claim 11 , wherein an amount of delay of a delay element is associated with an order of the basis function.

14. The method of claim 11 , wherein the factor M k of a branch of the K branches is based on an evaluation period associated with the branch.

15. The method of claim 14 , wherein an amount of delay provided by the filter is related to the factor M k of the corresponding branch.

16. A pre-distorter memory module, comprising:

a combination of a register and an accumulator, the combination arranged to low-pass filter and down-sample an input signal;

a filter comprising at least one delay element, the filter producing a filtered output;

an interpolator, comprising:

a first delay element receiving the filtered output and producing a first delay element output;

a first multiplier, the first multiplier multiplying the first delay element output by a first factor, the first factor depending upon an up-sampling factor, M k , M k being based on an evaluation period associated with the pre-distorter memory module;

a second delay element receiving the first delay element output and producing a second delay element output;

a second multiplier, the second multiplier multiplying the second delay element output by a second factor; and

an adder, the adder adding the output of the first multiplier and the second multiplier.

17. The pre-distorter of claim 16 , wherein the second factor is one minus the first factor.

18. The pre-distorter of claim 16 , wherein the first and second delay elements operate at a down-sampled rate of an output of the register.