Asynchronous digital sample rate converter

• US 5,475,628 A
• Filed: 09/30/1992
• Issued: 12/12/1995
• Est. Priority Date: 09/30/1992
• Status: Expired due to Term

• Current Assignee: Analog Devices, Inc.
• Original Assignee: Analog Devices, Inc.
• Inventors: Coln, Michael, Kwan, Tom W., Adams, Robert W.
• Primary Examiner(s): Envall, Jr., Roy N.
• Assistant Examiner(s): Ngo, Chuong D.
• Application Number:
  US07/954,149
• Time in Patent Office: 1,168 Days
• Field of Search: 364/701, 364/724.01, 364/724.1, 364/718
• US Class Current: 708/313
• CPC Class Codes: H03H 17/0628 the input and output signals being derived from two separate clocks, i.e. asynchronous sample rate conversion

Abstract

An asynchronous digital sample rate converter includes a random access memory for storing input data values and a read only memory for storing a reduced set of interpolation filter coefficients. Input data is written to the random access memory at the input sample rate. Output samples are provided from a multiply/accumulate engine which given a stream of input data and filter coefficients produces an output sample upon request at the output frequency. The initial address for reading input data from the random access memory, and the addresses for coefficients from the read only memory are provided by an auto-centering scheme which is a first order closed loop system with a digital integrator fed by an approximation of the input to output sample rate ratio. This auto-centering scheme may include a feed forward low pass filter to cancel steady state error, and an interpolated write address to reduce noise. A circuit determining the output to input sample rate ratios can also be provided to scale coefficient addresses and resulting output samples to allow for decimation. This circuit includes a form of digital hysteresis to eliminate noise. The ROM coefficients are reduced by relying on the symmetry of the impulse response of the interpolation filter and by utilizing a variable step size forward and backward linear interpolation.

Claims

1. A system for converting a sequence of input samples at a first sampling rate to a sequence of output samples at a second sampling rate, the system comprising:

means for producing a periodically overflowing ramp signal at the second sampling rate having an average slope proportional to the first sampling rate, an integer part and a fractional part; and

a first memory element for storing the input samples received at the first sampling rate;

a second memory element for storing coefficients;

means for selecting and accessing input samples from the first memory element according to the integer part of the ramp signal and an increment value related to the first and second sampling rates;

means for selecting and accessing coefficients from the second memory element according to the fractional part of the ramp signal and an increment value related to the first and second sampling rates;

means for computing filter coefficients according to both the fractional part of the ramp signal and the selected coefficients; and

means for producing, at the second sampling rate, an output sample as a sum of products of the selected input samples and computed filter coefficients.

2. The system of claim 1, wherein the means for producing the periodically overflowing ramp signal comprises:

means for producing a coarse periodically overflowing ramp signal at the second sampling rate, having an average slope proportional to the first sampling rate; and

a filter having an input which receives the coarse periodically overflowing ramp signal and an output providing the periodically overflowing ramp signal at the second sampling rate.

3. The system of claim 2, wherein the filter comprises:

a modulo integrator having an output signal which is the output of the filter and an input;

a subtractor circuit having a first input connected to the output of the modulo integrator, a second input connected to receive the coarse periodically overflowing ramp signal and an output providing a signal indicative of a difference between the first and second input;

a gain element having an input connected to the output of the subtractor circuit, a gain, and an output; and

means for connecting the output of the gain element to the input of the modulo integrator.

4. The system of claim 3, wherein both said inputs of the subtractor circuit are adapted to receive positive N-bit signals, and the output of the subtractor circuit is a twos complement N+1 bit output signal and wherein the input to the gain element is the N least significant bits of the output of the subtractor circuit.

5. The system of claim 4, wherein the means for connecting comprises an adder having an input connected to the output of the gain element and which adds a constant thereto to provide an output to the input of the modulo integrator.

6. The system of claim 5, wherein the means for producing the coarse periodically overflowing ramp signal comprises:

a counter clocked at the first sampling rate to provide an output which increments at a rate proportional to the first sampling rate, and

a latch having an input connected to the output of the counter that stores the output of the counter at the second sampling rate, to produce as an output the coarse periodically overflowing ramp signal.

7. The system of claim 6, wherein the means for producing the coarse periodically overflowing ramp signal further comprises:

means for receiving a high frequency clock signal having pulses occurring at a frequency independent of and substantially higher than the first and second sampling rates;

a fractional count circuit including

(i) a first number of pulses of the high frequency clock signal that occur between an arrival of an input sample and an arrival of an immediately subsequent output sample request and

(ii) means for counting and for providing as a second output a second number of pulses of the high frequency clock signal that occur between arrivals of two consecutive input samples;

a dividing circuit having a first and second inputs connected to receive the first and second numbers from the fractional count circuit and an output which provides a signal indicative of a ratio of the first number to the second number; and

means for combining the output of the latch with the output of the divider circuit, wherein the output of the divider circuit forms a fractional part and the output of the latch forms an integer part, to provide the coarse periodically overflowing ramp signal.

8. The system of claim 2, wherein the means for producing the coarse periodically overflowing ramp signal comprises:

a counter clocked at the first sampling rate to provide an output which increments at a rate proportional to the first sampling rate, and

a latch having an input connected to the output of the counter that stores the output of the counter, at the second sampling rate, to produce as an output the coarse periodically overflowing ramp signal.

9. The system of claim 8, wherein the means for producing the coarse periodically overflowing ramp signal further comprises:

means for receiving a high frequency clock signal having pulses occurring at a frequency independent of and substantially higher than the first and second sampling rates;

a fractional count circuit including

(i) means for counting and for providing as a first output a first number of pulses of the high frequency clock signal that occur between an arrival of an input sample and an arrival of an immediately subsequent sample request and

(ii) means for counting and for providing as a second output a second number of pulses of the high frequency clock signal that occur between arrivals of two consecutive input samples;

a dividing circuit having a first and second inputs connected to receive the first and second numbers from the fractional count circuit and an output which provides a signal indicative of a ratio of the first number to the second number; and

means for combining the output of the latch with the output of the divider circuit, wherein the output of the divider circuit forms a fractional part and the output of the latch forms an integer part, to provide the coarse periodically overflowing ramp signal.

10. The system of claim 2, wherein the filter comprises:

a subtractor circuit having a first input, a second input connected to receive the coarse periodically overflowing ramp signal and an output providing a signal indicative of the difference between the first and second input;

a first low-pass filter having an input connected to receive the output of the subtractor circuit and an output providing a first output signal connected to the first input of the subtractor circuit;

a second low-pass filter having an input connected to receive the output of the subtractor circuit and an output providing an second output signal; and

an adder having inputs which receive the first and second output signals and an output which provides a summation signal indicative of the sum of the first and second output signals, wherein the summation signal is the output of the filter.

11. The system of claim 10, wherein the first low-pass filter comprises:

a modulo integrator having an input and an output which is the output of the first low-pass filter;

a gain element having an input connected to the output of the subtractor circuit, a gain, and an output; and

means for connecting the output of the gain element to the input of the modulo integrator.

12. The system of claim 11, wherein both said inputs of the subtractor circuit are adapted to receive as two positive N-bit signals, and the output of the subtractor circuit is a twos complement N+1 bit output signal and wherein the input to the gain element is the N least significant bits of the output of the subtractor circuit.

13. The system of claim 12, wherein the first low-pass means for connecting comprises an adder having an input connected to the output of the gain element and which adds a constant thereto to provide an output to the input of the modulo integrator.

14. The system of claim 13, wherein the means for producing the coarse periodically overflowing ramp signal comprises:

a counter clocked at the first sampling rate to provide an output which increments at a rate proportional to the first sampling rate, and

a latch having an input connected to the output of the counter that stores the output of the counter at the second sampling rate, to produce as an output the coarse periodically overflowing ramp signal.

15. The system of claim 14, wherein the means for producing the coarse periodically overflowing ramp signal further comprises:

means for receiving a high frequency clock signal having pulses occurring at a frequency independent of and substantially higher than either of the first and second sampling rates;

a fractional count circuit including

(i) means for counting and for providing as a first output a first number of pulses of the high frequency clock signal that occur between an arrival of an input sample and an arrival of an immediately subsequent output sample request and

(ii) means for counting and for providing as a second output a second number of pulses of the high frequency clock signal that occur between arrivals of two consecutive input samples;

a dividing circuit having a first and second inputs connected to receive the first and second numbers from the fractional count circuit and an output which provides a signal indicative of a ratio of the first number to the second number; and

means for combining the output of the latch with the output of the divider circuit, wherein the output of the divider circuit forms a fractional part and the output of the latch forms an integer part, to provide the coarse periodically overflowing ramp signal.

16. The system of claim 10, wherein the means for producing the coarse periodically overflowing ramp signal comprises:

a counter clocked at the first sampling rate to provide an output which increments at a rate proportional to the first sampling rate, and

a latch having an input connected to the output of the counter that stores the output of the counter at the second sampling rate, to produce as an output the coarse periodically overflowing ramp signal.

17. The system of claim 16, wherein the means for producing the coarse periodically overflowing ramp signal comprises:

means for receiving a high frequency clock signal having pulses occurring at a frequency independent of and substantially higher than either of the first and second sampling rates;

a fractional count circuit including

(i) means for counting and for providing as a first output a first number of pulses of the high frequency clock signal that occur between an arrival of an input sample and an arrival of an immediately subsequent output sample request and

(ii) means for counting and for providing as a second output a second number of pulses of the high frequency clock signal that occur between arrivals of two consecutive input samples;

a dividing circuit having a first and second inputs connected to receive the first and second numbers from the fractional count circuit and an output which provides a signal indicative of a ratio of the first number to the second number; and

means for combining the output of the latch with the output of the divider circuit, wherein the output of the divider circuit forms a fractional part and the output of the latch forms an integer part, to provide the coarse periodically overflowing ramp signal.

18. The system of claim 2, further comprising:

means for determining a scaling value for each output sample request according to a ratio of the second sampling rate to the first sampling rate; and

wherein the means for selecting and accessing coefficients includes means for scaling the fractional part of the ramp signal by the scaling value to obtain an address for accessing a first coefficient from the second memory element.

19. The system of claim 1, wherein the means for selecting and accessing input samples comprises an adder having an input connected to the means for producing the periodically overflowing ramp signal, for determining a sum of the increment value and the integer part of the periodically overflowing ramp signal and means for using the sum to select the input samples.

20. The system of claim 1, further comprising:

means for determining a scaling value for each output sample request according to a ratio of the second sampling rate to the first sampling rate; and

where in the means for selecting and accessing coefficients includes means for scaling the fractional part of the ramp signal by the scaling value to obtain an address for accessing a first coefficient from the second memory element.

21. A system for converting a sequence of input samples at a first sampling rate defining an input period to a sequence of output samples at a second sampling rate, comprising:

a coefficient memory in which a set of filter coefficients is stored;

means for measuring a time period between an arrival of an input sample and an immediately subsequent output sample request, comprising means for receiving a clock signal providing pulses occurring at a rate independent of and substantially higher than the first and second sampling rates, and means for counting a number of pulses of the received clock signal occurring between the arrival of the input sample and the arrival of the immediately subsequent output sample request; and

means for selecting, at the second sampling rate, a plurality of filter coefficients from the coefficient memory according to a first coefficient address, defined by a ratio of the measured time period to the input period, and an increment value related to the first and second sampling rates; and

means for computing an output sample as a sum of products of the sequence of input samples and the selected filter coefficients.

22. The system of claim 21, wherein the means for selecting comprises:

means for determining a scaling value for each output sample request according to a ratio of the second sampling rate to the first sampling rate;

means for scaling the first coefficient address by the scaling value; and

means for accessing the coefficient memory using the scaled first coefficient address and the increment value.

23. A system for convening a first sequence of input samples at a first sampling rate to a second sequence of output samples m a second sampling rate, comprising:

means for generating a first coefficient address related to the first and second sampling rates and a phase difference between the first sequence and the second sequence;

means for storing a predetermined set of filter coefficients,

means, responsive to the input and output sample rates, for determining a scaling value according to a ratio of the second sampling rate to the first sampling rate; and

means for determining a sum of products of the first sequence input samples and selected filter coefficients, including means for scaling the first coefficient address by the scaling value, and means for accessing and selecting the filter coefficients according to the scaled first coefficient address and the scaling value.

24. The system of claim 23, wherein the scaling value is unity when the second sampling rate is faster than the first sampling rate and wherein the scaling value is approximately the ratio of the second sampling rate to the first sampling rate when the second sampling rate is slower than the first sampling rate.

25. The system of claim 24, further comprising means for scaling the sum of products by the scaling value determined by the means for determining the scaling value.

26. The system of claim 23, wherein the means for determining a scaling value comprises:

a first counter having an output which increments at the first sampling rate, and a terminal count output which indicates overflow of the output of the first counter;

a second counter having an output which increments at the second sampling rate and which resets after overflow of the first counter;

means for latching the output of the second counter to provide a latch output;

a low-pass filter having an input connected to receive the latch output and having a filtered output; and

a limiter which limits the filtered output of the low-pass filter to be less than or equal to unity to provide an output which is the scaling value.

27. The system of claim 26, wherein the means for latching includes:

a first latch having an input connected to the second counter and an output;

a subtractor having a first input for receiving the output of the first latch and a second input for receiving the output of the second counter and having an output indicative of a difference between the first and second inputs;

a threshold circuit having an input connected to the output of the subtractor and an output which indicates whether the output of the subtractor is above or below a predetermined threshold;

means for causing the first latch to latch the output of the second counter when the first counter overflows and the output of the subtractor is higher than the predetermined threshold; and

a second latch having an input connected to the output of the first latch and an output connected to the input of the low-pass filter and latched at the second sampling rate.

28. A digital integrated circuit for convening a sequence of input samples arriving at a first sampling rate defining an input period to a sequence of output samples at a second sampling rate and having an input for receiving a master clock signal from an external signal source, the master clock signal having a frequency independent of and substantially higher than the first and second sampling rates, and comprising:

means, clocked by the master clock signal, for determining a measure of a time period between an arrival of an input sample and an arrival of an immediately subsequent request for an output sample;

means for storing a set of predetermined filter coefficients;

means for selecting some of the predetermined filter coefficients according to a ratio of the measure of the time period to the input period and a ratio between the first and second sampling rates; and

means for computing an output sample from the sequence of input samples and the selected filter coefficients.

29. A method for converting a sequence of input samples at a first sampling rate to a sequence of output samples at a second sampling rate, comprising the steps of:

storing input samples in a first memory element at the first sampling rate;

generating a periodically overflowing ramp signal at the second sampling rate with an average slope proportional to the first sampling rate and having an integer part and a fractional part and an increment value related to the first and second sampling rates;

selecting, in response to an output sample request, input samples stored in the first memory element according to the integer part of the ramp signal and an increment value related to the first and second sampling rates;

selecting, in response to an output sample request, coefficients stored in a second memory element according to the fractional part;

computing filter coefficients according to the fractional part of the ramp signal and the selected coefficients; and

producing, in response to an output sample request, an output sample as a sum of products of the selected input samples and the computer filter coefficients.

30. The method of claim 29, wherein the step of generating the periodically overflowing ramp signal comprises the steps of:

generating a coarse periodically overflowing ramp signal at the second sampling rate, having an average slope proportional to the first sampling rate; and

filtering the coarse periodically overflowing ramp signal to obtain the periodically overflowing ramp signal at the second sampling rate.

31. The method of claim 30, wherein the step of filtering involves using a modulo integrator having an input and an output and comprises the steps of:

computing a difference between the output of the modulo integrator and the coarse periodically overflowing ramp signal;

scaling the computed difference; and

applying the scaled computed difference to the input of the modulo integrator.

32. The method of claim 31, wherein the step of computing a difference comprises the steps of:

providing both the output signal of the modulo integrator and the coarse periodically overflowing ramp signal as two positive N-bit signals; and

producing a twos complement N+1 bit number indicative of the difference between the two positive N-bit signals, wherein the N least significant bits of the N+1 bit number are the computed difference.

33. The method of claim 32, further comprising the step of adding a constant to the scaled computed difference applied to the modulo integrator.

34. The method of claim 33, wherein the step of generating the coarse periodically overflowing ramp signal comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof;

sampling the number at the second sampling rate, to produce the coarse periodically overflowing ramp signal.

35. The method of claim 33, wherein the step of generating the coarse periodically overflowing ramp signal further comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof;

sampling the number at the second sampling rate;

receiving a high frequency signal with pulses occurring at a frequency independent of and substantially higher than the first and second sampling rates;

counting a first number of pulses of the high frequency signal that occur between an arrival of an input sample and an arrival of an immediately subsequent output sample request;

counting a second number of pulses of the high frequency signal that occur between arrivals of two consecutive input samples;

dividing, at the arrival of each output sample request the first number by the second number to obtain a quotient; and

combining the sampled number, as an integer, with the quotient, as a fraction, to provide the coarse periodically overflowing ramp signal.

36. The method of claim 30, wherein the step of generating the coarse periodically overflowing ramp signal comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof; and

sampling the number at the second sampling rate, to produce the coarse periodically overflowing ramp signal.

37. The method of claim 30, wherein the step of generating the coarse periodically overflowing ramp signal further comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof;

sampling the number at the second sampling rate;

receiving a high frequency signal with pulses occurring at a frequency independent of and substantially higher than either of the first and second sampling rates;

counting a first number of pulses of the high frequency signal that occur between an arrival of an input sample and an arrival of an immediately subsequent sample request;

counting a second number of pulses of the high frequency signal that occur between arrivals of two consecutive input samples;

dividing, at the arrival of each output sample request the first number by the second number to obtain a quotient; and

combining the sampled number, as an integer, with the quotient, as a fraction, to provide the coarse periodically overflowing ramp signal.

38. The method of claim 30, wherein the step of filtering comprises the steps of:

computing a difference between the coarse periodically overflowing ramp signal and feedback input;

a first step of filtering the difference to obtain a first output signal which is the feedback input;

a second step of filtering the difference to obtain a second output signal; and

adding the first and second output signals to obtain a sum which is the periodically overflowing ramp signal.

39. The method of claim 38, wherein the first step of filtering comprises using a modulo integrator having an input and an output providing the first output signal and the steps of:

scaling the computed difference;

applying the scaled difference to the input of the modulo integrator; and

the step of adding a constant to the scaled computed difference.

40. The method of claim 39, wherein the step of generating the coarse periodically overflowing ramp signal comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof; and

sampling the number at the second sampling rate, to produce the coarse periodically overflowing ramp signal.

41. The method of claim 39, wherein the step of generating the coarse periodically overflowing ramp signal further comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof;

sampling the number at the second sampling rate;

receiving a high frequency signal with pulses occurring at a frequency independent of and substantially higher than either of the first and second sampling rates;

counting a first number of pulses of the high frequency signal that occur between an arrival of an input sample and an arrival of an immediately subsequent output sample request;

counting a second number of pulses of the high frequency signal that occur between arrivals of two consecutive input samples;

dividing, at the arrival of each output sample request the first number by the second number to obtain a quotient; and

combining the sampled number, as an integer, with the quotient, as a fraction, to provide the coarse periodically overflowing ramp signal.

42. The method of claim 38, wherein the step of generating the coarse periodically overflowing ramp signal comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof; and

sampling the number at the second sampling rate, to produce the coarse periodically overflowing ramp signal.

43. The method of claim 38, wherein the step of generating the coarse periodically overflowing ramp signal further comprises the steps of:

incrementing a number at a rate proportional to the first sampling rate and generating a signal indicative thereof;

sampling the number at the second sampling rate;

receiving a high frequency signal with pulses occurring at a frequency independent of and substantially higher than either of the first and second sampling rates;

counting a first number of pulses of the high frequency signal that occur between an arrival of an input sample and an arrival of an immediately subsequent output sample request;

counting a second number of pulses of the high frequency signal that occur between arrivals of two consecutive input samples;

dividing, at the arrival of each output sample request the first number by the second number to obtain a quotient; and

combining the sampled number, as an integer, with the quotient, as a fraction, to provide the coarse periodically overflowing ramp signal.

44. The method of claim 38, wherein the first step of filtering comprises using a modulo integrator having an input and an output providing the first output signal and the steps of:

scaling the computed difference; and

applying the scaled difference to the input of the modulo integrator.

45. The method of claim 44 further comprising, the steps of:

providing both the first output signal of the modulo integrator and the coarse periodically overflowing ramp signal as two positive N-bit signals; and

producing a twos complement N+1 bit number indicative of the difference between the two positive N-bit signals, wherein the N least significant bits of the N+1 bit number are the computed difference.

46. The method of claim 30, further comprising:

determining a scaling value for each output sample request according to a ratio of the second sampling rate to the first sampling rate; and

wherein the step of selecting coefficients includes the step of scaling the fractional part of the ramp signal by the scaling value to chain an address for accessing a first coefficient from the second memory element.

47. The method of claim 29, wherein the step of selecting input samples comprises the step of adding the increment value to the integer part of the periodically overflowing ramp signal to obtain a sum and the step of using the sum to select the input samples.

48. The method of claim 29, further comprising:

determining a scaling value for each output sample request according to a ratio of the second sampling rate to the first sampling rate; and

wherein the step of selecting coefficients includes the step of scaling the fractional part of the ramp signal by the scaling value to obtain an address for accessing a first coefficient from the second memory element.

49. The method of claim 29, wherein the second memory element is a read only memory.

50. A method for converting a sequence of input samples at a first sampling rate defining an input period to a sequence of output samples at a second sampling rate, using a set of filter coefficients stored in a memory comprising the steps of:

measuring a time period between an arrival of an input sample and an immediately subsequent output sample request by receiving a signal having pulses occurring at a rate independent of and substantially higher than the first and second sampling rates and counting the pulses of the received clock signal occurring between an arrival of an input sample and an arrival of an immediately subsequent output sample request;

selecting a plurality of filter coefficients according to a first coefficient address defined by a ratio between the measure of the time period and the input period, and an increment value related to the first and second sampling rates; and

computing an output sample as a sum of products of the selected filter coefficients and the sequence of input samples.

51. The method of claim 50, wherein the step of selecting further comprises:

determining a scaling value according to a ratio of the second sampling rate to the first sampling rate; and

scaling the first coefficient address by the scaling value to obtain an address to access a first filter coefficient form the memory.

52. A method for converting a first sequence of input samples at a first sampling rate to a second sequence of output samples at a second sampling rate using a set of filter coefficients stored in a memory, given a first coefficient address related to the first and second sampling rates comprising the steps of:

generating a first coefficient address related to the first and second sampling rates and a phase difference between the first sequence and the second sequence;

determining a scaling value according to a ratio of the second sampling rate 19 the first sampling rate; and

computing, in response to an output sample request, such output sample requests occurring at the second sampling rate, a sum of products of the first sequence of input samples and selected filter coefficients, including scaling the first coefficient address by the scaling value to obtain an address to select a first filter coefficient from the memory, and accessing grid selecting the filter coefficients from the memory according to the scaled first coefficient address and the scaling value.

53. The method of claim 52, wherein the scaling value is unity when the second sampling rate is faster than the first sampling rate and wherein the scaling value is approximately the ratio of the second sampling rate to the first sampling rate when the second sampling rate is slower than the first sampling rate.

54. The method of claim 53, further comprising the step of scaling the sum of products of the input samples and the filter coefficients by the scaling value.

55. The method of claim 52, wherein the step of determining the scaling value comprises the steps of:

counting a number of input samples arriving at the first sampling rate;

counting a number of output sample requests received at the second sampling rate;

periodically resetting both of the numbers counted;

sampling the number of output sample requests counted;

filtering the sampled number;

limiting the filtered sampled number to be less than or equal to unity, which limited number is the scaling value.

56. The method of claim 55, wherein the step of sampling includes the step of:

determining a difference between the number of output sample requests counted and a previously sampled number;

sampling the number of output sample requests counted when the counted numbers are reset and when the determined difference is higher than a predetermined threshold.

57. A method for convening a sequence of input samples arriving at a first sampling rate defining in input period to a sequence of output samples at a second sampling rate, using a set of filter coefficients stored in a memory, comprising the steps of:

receiving a clock signal comprised of pulses occurring at a rate independent of and substantially higher than the first and second sampling rates;

counting a number of pulses occurring between an arrival of an input sample and an arrival of an immediately subsequent request for an output sample;

selecting and accessing some of the filter coefficients from the memory according to a ratio between the number of pulses counted and the input period and a ratio between the first and second sampling rates; and

producing an output sample as a sum of products of the sequence of input samples and the selected filter coefficients.