WO1998038766A1

WO1998038766A1 - Sample rate converter

Info

Publication number: WO1998038766A1
Application number: PCT/US1998/000832
Authority: WO
Inventors: Peter Bo Holmqvist
Original assignee: Ericsson, Inc.
Priority date: 1997-02-26
Filing date: 1998-01-16
Publication date: 1998-09-03
Also published as: CN1249093A; KR100386549B1; HK1026989A1; US5818888A; BR9807771A; EP0963633A1; EP0963633A4; CN1126320C; ES2264193T3; JP2001513295A; EP0963633B1; KR20000075568A; JP4376973B2; BR9807771B1; AU732601B2; AU6027498A; MY123934A; EE9900368A

Abstract

A sample rate converter (200) is described for converting an input data stream including a plurality of input samples (X) at one sample rate to an output data stream including a plurality of output samples (Y) at another sample rate. The converter uses an interpolation approach that utilizes an integer accumulator (220) to track the timing relation between input samples and output samples. Based on the value of the accumulator, the method determines if the correct input samples are being used to calculate the current output sample. If so, the output sample is calculated as a function of the input samples and the accumulator value. The converter provides the robustness of a table based conversion approach without the need to precalculate and store a table, simplifies the calculations involved, and is less sensitive to numeric round off errors.

Description

SAMPLE RATE CONVERTER

FIELD OF THE INVENTION

This invention relates to the field sample rate converting of digital signals.

More particularly, the present invention relates to a sample rate conversion method

that employs an integer accumulator to calculate the timing relation of input and

output samples.

BACKGROUND OF THE INVENTION

In many electronic applications, signals are represented and processed

digitally. Digital words, or samples, represent the value of the data at a regular time

interval. This regular interval is often referred to as the sample rate, and is typically

expressed in units of kilohertz (kHz) representing the reciprocal of the sample

interval time period.

There are situations when the available sample rate of the data is different

from the desired sample rate. Depending on the characteristics of the sample data

and how much the available and desired rates differ, several approaches may be

used to convert the signal at one sample rate to a signal at another sample rate

without intentionally altering the meaning of the signal.

A first common technique for sample rate reduction is called decimation. It is

the method of choice when the available sample rate is an integer multiple of the

desired sample rate. The decimator reduces the input sample rate by an integer

number d to create an output sample rate. If the input signal contains high

frequency components, they must be first removed by a low pass filter to avoid aliasing effects. The rate reduction is performed by simply discarding d-1 input

samples for every .th output samples.

The main drawback of decimation is that the rate reduction is limited to an

integer number. In addition, an anti-aliasing filter, if necessary, may be very

computationally intensive.

A second common technique for sample rate conversion is known as

interpolation. Interpolation is the method frequently used for increasing the sample

rate by an integer multiple. To increase the sample rate by /, the basic interpolator

inserts 1-1 samples with a value of zero between every input sample. The resulting

samples are then filtered through an anti-aliasing low pass filter at the higher rate.

The interpolation method has some of the same basic drawbacks as

decimation. The rate increase is limited to an integer number and the low pass

filtering, which is necessary for interpolation, is costly.

By themselves, interpolation and decimation can only achieve changes in

sample rate of an integer number. In many cases, this does not give the necessary

flexibility. By combining interpolation and decimation, perhaps in several stages, it

becomes possible to fine tune the sample rate conversion. For example, if the input

sample rate is 194.4 kHz and the desired sample rate is 153.6 kHz, the rates do not

differ by an integer factor. Instead, the desired rate is related to the available rate

by the ratio 64/81 . To achieve the desired sample rate, the data may first be

interpolated by a factor of 64 and then decimated by a factor of 81 ; however, large

interpolation and decimation factors put very tough constraints on the required low pass filters. To reduce the filter requirements, the interpolation and decimation may

be performed in several stages, for example: interpolation by 8, followed by

decimation by 9, followed by interpolation by 8, followed by decimation by 9, resulting in a total of a 64/81 conversion. Using a combination of interpolation and

decimation enables a wider range of rate conversions that is not limited to integer

numbers. However, the big drawback of such an approach is the cost of filtering.

Another technique for sample rate conversion method that is useful when

input and output rates are close is known as linear interpolation. This method uses

a first order linear interpolation approach to estimate each output sample as a

function of two input samples and the relative position in time of the input and

output samples. Referring to Fig. 1 , the value of the m:th output sample would be

calculated according to the following formula:

y_m = X_n * k + x_n+1* (1-k)

where k = ((n+1) * T_X - m* T_y)/T_x

In these formulas, x_n is the n:th input sample, y_m is if the m:th output sample,

T_x is the input sample period, and T_y is the output sample period. Given T_x is the

input sample period, the time of the n:th input sample is: tx_n = n * T_x. Similarly, the

time of the m:th output sample is: ty_m = m * T_y. To calculate output sample number

, chose n so that: n * T_X < m * T_y < (n+1) * T_x.

One drawback of the first order interpolation method is that it may be difficult

to tell which particular input samples to use for calculation of an output sample. T_x

and T_y are seldom integers and round off errors may cause the wrong samples to be chosen. The calculation of k, which involves the subtraction of two numbers that

grow very large when m and n grow, also gets susceptible to errors due to limited

numeric precision.

These drawbacks can be mitigated by using a table with / -values.

Continuing with the example of 194.4 kHz input and 153.6 kHz output rate, the

samples relative positions in time repeat over a period of 81 input samples. Thus, it

is possible to pre-calculate and store the k- values in a table. Using a table would

eliminate the need to calculate k for every sample at the expense of storing pre-

calculated values. The drawback with using a pre-calculated table is that the

values for the tables must be pre-calculated and stored, which requires additional

hardware resources. This is particularly problematic when the same converter is to

be used with various input sample rate and output sample rate combinations.

SUMMARY OF THE INVENTION

The present invention is a method and apparatus for sample rate conversion

that overcomes some of the drawbacks of the prior art. The method of the present

invention is an interpolation method that provides the robustness of a table based

approach without the need to pre-caiculate and store a table. The method also

simplifies the calculations involved and is less sensitive to numeric round off errors.

The method utilizes a integer accumulator to generate an output data stream

including a plurality of output samples at one sample rate based on an input data

stream including a plurality of input samples at another sample rate. More

particularly, the method uses the integer accumulator to track the timing relation between input samples and output samples. Based on the value of the

accumulator, the method determines if the correct input samples are being used to

calculate the current output sample. If so, the output sample is calculated as a

function of the input samples and the accumulator value. By employing simple

integer arithmetics to maintain the accumulator value, the present inventive method

avoids unnecessarily large computations otherwise required to confirm that the

proper input samples are being used while maintaining the flexibility and

compactness of a non-table based approach.

The apparatus of the present invention includes an input sample register, an

integer accumulator, and preferably a bit shift register, all configured so as to

practice the present inventive sample rate conversion method.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 is a diagram depicting linear interpolation.

Figure 2 is a logical flowchart of the present sample rate conversion method.

Figure 3 is a diagram depicting the timing relation between input samples

(...x_n.₃, x_n._2l x^, x_n, x_n+1, ...) and output samples (...y_m.₂, y^, y_m, y_m+1, ...).

Figure 4 is a logical flowchart of a simplified sample rate conversion method

applicable when A is known to be smaller than B.

Figure 5 is a logical flowchart of a simplified sample rate conversion method

applicable when A is known to be larger than B. Figure 6 is block diagram of a preferred embodiment of the apparatus for a

sample rate converter.

Figure 7 is a logical flowchart of a preferred embodiment of the controller for

the apparatus of Figure 6 using the method of Figure 4.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is described more fully hereinafter by referring to the

drawings, in which a preferred embodiment is depicted. However, the present

invention can take on many different embodiments and is not intended to be limited

to the embodiments described herein.

The present inventive method is a variation of interpolation that uses an

integer accumulator 220 to facilitate calculation of the relative position in time of

input and output samples. For linear interpolation, the method employs two positive

integer constants, A and B, to calculate the timing relation of two input samples and

one output sample. If the sample period of the input signal is T_x and the sample

period of the output signal is T_y, then A and B are chosen such that the ratio of A

and B satisfies the following equation:

A / B = T_x / T_y

The actual value, or size, of A and B depends on the desired level of precision and

other considerations. In effect, the input sample period T_x is quantized into A steps.

By keeping the steps small (keeping A large), the added quantization noise can be

kept small. However, using a large number of bits to represent A may waste hardware resources. For example, assume that the input signal is available at a

194.4 kHz sample rate and the desired output sample rate is 153.6 kHz, then

A / B = T_x / T_y = ((1/194,400) /(1/153.600)) = 153,600 / 194,400 = 64 / 81

Thus, the input sample period could be quantized into 64 steps (A = 64), or any

multiple of 64 steps and still maintain the proper ratio while allowing both A and B to

be integers. Thus, A could be 1024 if B is 1296. However, if A is 64 then only 6

bits are required to represent the value (2⁶ = 64), but if A is 1024, 10 bits are

required (2¹⁰ = 1024). Note that one additional bit may be required to represent

sign for both.

The values of A and B are employed to iteratively calculate the value of a

variable "ace" which tracks the relative positions in time for a pair of input samples

and a given output sample. In simple terms, ace serves two functions. First, ace is

used to determine if the proper pair of input samples is being used to calculate the

current output sample. Second, ace is used to assign the proper weighting to each

member of the input sample pair so as to properly estimate the output sample

value. The details of how ace performs these functions will become apparent

through the following description.

Figure 2 shows a logical flow chart for the present invention. At the start of

the process, the integer accumulator 220 is set to zero and the variables m and n

are also set to zero (box 10). Variable m is an integer counter representing the

sequence number of the current output sample. Variable n is an integer counter

representing the sequence number of the current input sample. As will become apparent from the following description, the only purpose of m and n in the flow

diagram is to aid the reader in understanding the algorithm by clarifying how the

input and output samples are related. Neither m nor n need be stored or calculated

to practice the present inventive method.

The accumulator 220 contains an integer value representing the variable

"ace." The main processing loop begins by adding A to the integer value in the

accumulator 220 (see box 20). Ace is then checked to see if it is less than zero

(box 30). If so, then n is incremented by one (box 40), the next input sample is

selected to assume the role of the current input sample, and the process returns to

box 20. If ace is not less than zero, then the output sample is calculated (box 50).

In simple terms, the ace value check of box 30 represents a determination of

whether the particular output sample being calculated falls within the current input

sample period, i.e., between the two currently selected input samples (n and n+1)

or exactly at input sample x_n+1.

For purposes of the invention, the current input sample period is defined as

the time period from the current input sample to the next subsequent input sample.

Thus, if the input sample rate is 1 Hz, and the current input sample is number four

(in the sequence zero, one, two, three, four, ... n) then the current input sample

period is from 4 seconds to 5 seconds.

Calculating the output sample (box 50) is accomplished via the formula:

y_m = (ace * x_n + (A - ace) * x_n+1) /A This formula is a modified linear interpolation formula. In this formula, x_n is the

value of the last input sample which occurs before the output sample and x_n+1 is the

value of the, first input sample after the output sample. In the situations where an

output sample falls directly on top of an input sample, then ace will equal the integer

zero and formula will collapse to y_m = (A * x_n+1) / A = x_n+1. Thus, the value of the

properly corresponding input sample, x_n+1, will be used for the output sample (y_m).

Note, however, that for the special case of the very first instance of direct overlap,

at the first input sample (x₀) and first output sample (y₀), ace wiii equal A, therefore

the formula for this one instance will collapse to y₀ = (A * j /A = x₀.

After the output sample is calculated (box 50), the value of ace is

decremented by B (box 60). In box 70, this new value of ace is checked to see if it

is greater than or equal to zero. If so, m is incremented by one and the process

returns to box 50. If not, then the both m and n are incremented by one (box 90).

In simple terms, the ace value check of box 70 represents a determination of

whether the next output sample occurs within the same pair of input samples.

The process continues looping through the main processing loop (box 20-

box 100) until there are no more samples (box 100), at which point it stops (box

110). In this manner the input sample rate of period T_x is converted to an output

sample rate of period T_y.

As an example of the method in action, see Figure 3. Assume that the input

sample rate is faster than the output sample rate, meaning that A is smaller than B.

For sake of discussion assume that A is 10 and B is 14, corresponding to an input sample rate of 1.4 kHz and an output sample rate of 1.0 kHz. Further, assume that

the conversion process is proceeding according to the present invention and is now

processing input sample x_n.₃ and output sample y_m.₂. At this point, entering box 20,

ace equals -4. At box 20, ace is incremented by A such that ace now equals 6 (-4

+10). Because 6 is larger than 0 (box 30), output sample y_m.₂ is calculated (box 50)

based on x_n.₃ and x_n.₂. Now, ace is decremented by 14 (box 60) so as to equal -8

(+6 -14). Because ace is not greater than 0, the main process loop begins again.

During this second pass through the main process loop, the value for y_m.., is

calculated using x_n.₂ and x_n_ and ace is adjusted to be -12 (-8 + 10 -14). At the third

pass through the main process loop, ace is incremented by A so as to equal -2 (-12

+ 10). Now, because ace is still less than 0, the current input sample (x^ at this

point) is discarded, the next input sample x_n assumes the position of current input

sample, and ace is increased to 8 (-2 +10). Output sample y_m is then calculated

using x_n and x_n+1. At the conclusion of the third pass through the main process loop

(box 100), ace equals -6 (8 -14). As shown in Figure 3, the reason input samples x_n

and x_n+1 were used to calculate output sample y_m rather than input samples x^ and

x_n is that y_m fell between x_n and x_n+1.

As can be seen from this explanation, the variable ace is used to dynamically

track the timing relation between input samples and output samples. In this

example, where A is less than B, the input sample sequence is advanced by an

"extra" one or more position when ace is less than zero at box 30. In other

situations, when B is less than A, two or more output samples may be calculated

using the same input sample pair when ace is greater than or equal to zero in box 70. Thus, it can be seen that variable ace is used by the process to verify that the

correct input sample pair is being used to calculate each given output sample.

The algorithm of Figure 2 can be simplified slightly if the constant A is known

to be greater than the constant B, or vice versa. Using the same reference

numbers, Figure 4 shows a simplified logical flow chart for when A is known to be

smaller than B. Figure 5 shows a simplified logical flow chart for when A is known

to be larger than B. The flow charts of Figure 4 and Figure 5 show that a

comparison and loop back step can be eliminated when the relationship between A

and B is known, thereby simplifying the process.

For the above processes, the calculation of the output sample (y_m) calls for

division by the constant A. Because division is sometimes expensive to implement

in hardware, it is possible to pre-calculate the value of 1/A instead, and use

multiplication. Alternatively, and more preferably, a value for A can be selected that

enables easy division. For example, if A is a power of two, the division can be

implemented as a simple binary bit shift.

For purposes of an example, assume that the input sample are available at

194.4 kHz and the desired sample rate is 153.6 kHz. This means that

A / B = T_x / T_y = 153,600 / 194,400 = 64 / 81

Thus, A could equal 64 and B could equal 81. If so, then the input sample period T_x

would be divided into 64 steps. Greater precision could be obtained if, for example,

A were increased to 1536 and B were correspondingly increased to 1944.

Preferably, however, A would be a large power of two such as 1024 (2¹⁰), meaning that B would be 1296. If A is 1024, then division could be implemented as a binary

right shift of ten (10).

The discussion above assumes utilization of a linear interpolation approach.

However, the present inventive method is can also be utilized for other interpolation

approaches, such as second order or cubic or other methods known in the art.

Some of these other interpolation approaches require the use of more than two

input samples to calculate a given output sample. If only two input samples are

required, then only one integer accumulator 220 need be employed. If more than

two input samples are required, a plurality of integer accumulators 220 may be

used to track the various timing relations between input samples and output

samples. Alternatively, one accumulator 220 can be employed to track the

relationship between all the input samples required and the output sample to be

calculated; this is because once a timing relationship to one input sample is known,

the timing relationship to the other input samples will simply be an integer increment

of A farther away. If a different interpolation approach (other than linear) is used,

obviously a different formula would also be employed to calculate each given output

sample. However, the output sample value would still be a function of at least a

plurality of input samples and one or more accumulator values.

A block diagram of a possible hardware implementation of the sample rate

converter 200 is shown in Figure 6. The sample rate converter 200 includes a

controller 210, an integer accumulator 220, a multiplexer 230, adders 240, 250, a

subtractor 260, multipliers 270, 280, an input sample register 290, and a bit shifter

300. The controller 210 controls the overall function of the converter 200. The accumulator 220 tracks the relative position in time of input and output samples

using integer arithmetics. The multiplexer 230 is connected to sources 180, 190 for

values of A and B. The input samples are sequentially fed to the register 290. The

bit shifter 300 performs the appropriate bit shift to reflect division by A and outputs

the output sample value for each output sample.

Alternatively, the functions of the controller 210 may be distributed within the

converter 200 rather than collected in a single device as shown in Figure 6. Also,

two or more of the components of the converter 200, such as the adders 240, 250,

subtractor 260, multipliers 270, 280, and input sample register 290 may be

combined into an integrated arithmetic logic unit, but this may be more costly.

The Figure 7 shows a simplified flowchart of the preferred operation of the

controller 210 of Figure 6 for the method described in Figure 4. Upon initialization,

the controller 210 instructs the accumulator 220 to clear and the input sample

register 290 to load the first input sample (box 310). Note that this action

corresponds to box 10 of Figure 4. Then the controller 210 verifies that the next

input sample is available (box 320). If not, the controller 210 loops until the next

input sample is available. If so, then the controller 210 instructs the multiplexer 230

to load A and causes the accumulator 220 to increment by A (box 330). Note that

this action corresponds to box 20 of Figure 4. The controller 210 then checks the

sign bit of the accumulator 220 (box 340). Note that this action corresponds to box

30 of Figure 4. If the sign bit is positive, the controller 210 causes the output sample

(y_m) to be calculated, the multiplexer to switch to -B, and the accumulator 220 to

add -B to the existing accumulator value (box 350). These actions correspond to boxes 50, 60, and 90 of Figure 4. Either after box 350 or if the sign bit is negative

at box 340, the controller 210 causes the input sample register 290 to load the next input sample (box 360).

The converter 200 of Figure 6 is a simple hardware implementation of the

linear interpolation sample rate conversion method described above for when A is a

power of two. The converter 200 is capable of converting the sample rate of an

input sample stream of x.,, x₂, ... x_n to an output sample stream of y,, y₂, ... y_m

having a different output sample rate using integer arithmetics. By making A and B

programmable constants, the same sample rate converter 200, may be

programmed to operate at several different input to output sample ratios.

Claims

CLAIMSWhat I Claim Is:

1. A sample rate conversion method for converting an input data stream

at a first sample rate to an output data stream at a second sample rate

comprising:

a) receiving an input data stream which includes a plurality of input

samples at a first sample rate; and

b) generating an output data stream which includes a plurality of

output samples at a second sample rate by interpolation of said input samples;

said generation step including:

i) selecting one or more input samples in said input data

stream;

ii) maintaining at least one accumulator total which is

indicative of the timing relationship between a selected input sample and the

output sample to be generated, wherein the value of the accumulator is always an

integer; and

iii) for each output sample, calculating said output sample

as a function of said accumulator total.

2. The method of claim 1 further comprising the step of comparing the

accumulator total to a known reference value so as to determine if the currently

selected input sample has the correct timing relationship to the output sample to

be generated before said calculation step.

3. The method of claim 1 further comprising the step of maintaining a

plurality of accumulator totals wherein each accumulator total is indicative of the

timing relationship between a different input sample in said input data stream and

the output sample to be generated and wherein the value of each accumulator is

always an integer.

4. The method of claim 1 wherein said calculation is a further function of

said currently selected input sample.

5. The method of claim 2 wherein said known reference value is zero.

6. A sample rate conversion method for converting an input data stream

at a first sample rate to an output data stream at a second sample rate

comprising:

a) receiving an input data stream which includes a plurality of input

samples at a first sample rate; and

b) generating an output data stream which includes a plurality of

output samples at a second sample rate by linear interpolation of said input

samples; said generation step including:

i) maintaining at least one accumulator total which is

indicative of the timing relationship between a current input sample in said input

data stream and the output sample to be generated, wherein the value of the

accumulator is always an integer; and

ii) for each output sample, calculating said output sample

as a function of the accumulator total.

7. The method of claim 6 further comprising the step of comparing the

accumulator total to a known reference value so as to determine whether the

output sample to be generated falls within a current input sample period before said calculation step.

8. The method of claim 6 wherein said calculation is a further function of

the current input sample and the next input sample.

9. The method of claim 8 further comprising the steps of:

a) establishing integer values A and B such that the ratio A / B is

equal to T_x / T_y where T_x is the input sample period and T_y is the output sample

period; and

b) calculating the output sample value Y_m of the m th output sample

according to the formula

Y_m = (L * X_n + (A - L) * X_n+1) / A

where L is the current value of said accumulator, X_n is the value of the current

input sample, and X_n+1 is the value of the next input sample after X_n.

10. The method of claim 9 further comprising the step of decrementing the

value of said accumulator by B after calculating an output sample value.

11. The method of claim 9 further comprising the step of incrementing the

value of said accumulator by A before calculating an output sample value.

12. The method of claim 9 wherein A is a power of two.

13. The method of claim 7 wherein said known reference value is zero.

14. A sample rate conversion method for converting an input data stream

at a first sample rate to an output data stream at a second sample rate

comprising:

a) receiving an input data stream which includes a plurality of input samples at a first sample rate;

b) generating an output data stream which includes a plurality of

output samples at a second sample rate by linear interpolation of said input

samples; said generation step including:

i) establishing integer values A and B such that the ratio

A / B is equal to T_x / T_y where T_x is the input sample period and T_y is the output

sample period;

ii) maintaining an accumulator total which is indicative of

the timing relationship between a current input sample in said input data stream

and the output sample to be generated, wherein the value of the accumulator is

always an integer; and

iii) for each output sample, comparing the accumulator

total to a known reference value so as to determine whether the output sample to

be generated falls within a current input sample period; if so, calculating said

output sample as a function of the accumulator total, the current input sample,

and the next input sample according to the formula

Y_m = (L _* X_n + (A - L) _* X_n+1) / A where Y_m is the value of the m:th output sample, L is the current value of said

accumulator, X_n is the value of the current input sample, and X_n+1 is the value of

the next input sample after X_n; and

iv) setting L to zero initially and then incrementing L by A

before calculating the first output sample value and decrementing L by B after

calculating each output sample value.

15. The method of claim 14 wherein A is a power of two.

16. The method of claim 14 wherein said known reference value is zero.

17. A sample rate converting device for converting an input data stream

which includes a plurality of input samples at a first sample rate to an output data

stream which includes a plurality of output samples at a second sample rate

comprising:

a) an input sample register;

b) at least one integer accumulator for calculating the timing

relation between input samples and output samples using integer arithmetics;

wherein the value of each of said output samples is calculated as a function of

said accumulator total and a plurality of said input samples.

18. The apparatus of claim 17 wherein said calculation is according to the

formula:

the next input sample after X_n; and A is an integer value such that A and integer

value B have a ratio A to B of T_x to T_y where T_x is the input sample period and T_y

is the output sample period.

19. The device of claim 17 further comprising a bit shifter for the division

portion of said calculation.