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Dialogic ADPCM Algorithm
Abstract
VOX file format specification
ADPCM Encoding
ADPCM Decoding
Calculation of Step Size
Initial Conditions
Abstract
This application note describes the implementation of Adaptive Differential Pulse Code Modulation (ADPCM) as used in Dialogic Voice Processing Applications. The following topics are covered.
- File format for voice data files.
- ADPCM encoding algorithm.
- ADPCM decoding algorithm.
- Step size determination.
- Initial and reset conditions.
VOX file format specification
VOX files are flat binary files containing digitized voice data samples. Each byte contains two samples. There is a direct relationship between any positional offset within the file and time, expressed in the following formula:
T(i) = 2i * 1/SR
where: T(i) is the time offset in seconds from the beginning of the file of byte number "i" within the file. SR is the sampling rate in samples per second.
The encoding within each byte is as follows:
Bit 7 6 5 4 3 2 1 0
OUI
Sample N Sample N+1
UUI
The encoding within each sample is Adaptive Differential Pulse Code Modulation (ADPCM). This is a differential coding scheme in which each sample approximates the difference between the present input value and the previous one. The weighting of the magnitude portion of the difference is adaptive (non-linear). That is, it can change after each sample.
Bit 3 2 1 0
OUI
Sign Magnitude
UUI
Sign: Positive (0) or negative (1) sample.
Magnitude: Change (0 to 7) from previous sample.
ADPCM Encoding
Figure 1 shows a block diagram of the ADPCM encoding process. A linear input sample X(n) is compared to the previous estimate of that input X(n-1). The difference, d(n), along with the present step size, ss(n), are presented to the encoder logic. This logic, described below, produces an ADPCM output sample. This output sample is also used to update the step size calculation, ss(n+1), and is presented to the decoder to compute the linear estimate of the input sample.
Figure 1
The encoder accepts the differential value, d(n), from the comparator and the step size, and calculates a 4-bit ADPCM code. The following is a representation of this calculation in pseudocode.
let B3 = B2 = B1 = B0 = 0
if (d(n) 0)
then B3 = 1
d(n) = ABS(d(n))
if (d(n) = ss(n))
then B2 = 1 and d(n) = d(n) - ss(n)
if (d(n) = ss(n) / 2)
then B1 = 1 and d(n) = d(n)-ss(n) / 2
if (d(n) = ss(n) / 4)
then B0 = 1
L(n) = (10002 * B3) + (1002 * B2) + (102 * B1) + B0
Note: For the calculation of ss(n), see Calculation of Step Size.
ADPCM Decoding
Figure 2 shows a block diagram of the ADPCM decoding process. An ADPCM sample is presented to the decoder. The decoder computes the difference between the previous linear output estimate and the anticipated one. This difference is added to the previous estimate to produce the linear output estimate. The input ADPCM sample is also presented to the step size calculator to compute the step size estimate.
Figure 2
The decoder accepts ADPCM code values, L(n), and step size values. It calculates a reproduced differential value, and accumulates an estimated waveform value, X. Here is a pseudocode algorithm:
d(n) = (ss(n)*B2)+(ss(n)/2*B1)+(ss(n)/4*B0)+(ss(n)/8)
if (B3 = 1)
then d(n) = d(n) * (-1)
_ _
X(n) = X(n-1) + d(n)
Note: For the calculation of ss(n), see Calculation of Step Size.
Calculation of Step Size
For both the encoding and decoding process, the ADPCM algorithm adjusts the quantizer step size based on the most recent ADPCM value. The step size for the next sample, n+1, is calculated with the following equation:
ss(n+1) = ss(n) * 1.1M(L(n))
This equation can be implemented efficiently as a two-stage lookup table. First the magnitude of the ADPCM code is used as an index to look up an adjustment factor as shown in Table 1) . Then that adjustment factor is used to move an index pointer in Table 2. The index pointer then points to the new step size. Values greater than 3 will increase the step size. Values less than 4 decrease the step size.
Table 1 - M(L(n)) Values
L(n) Value M(L(n))
1111 or 0111 +8
1110 or 0110 +6
1101 or 0101 +4
1100 or 0100 +2
1011 or 0011 -1
1010 or 0010 -1
1001 or 0001 -1
1000 or 0000 -1
Table 2 - Calculated Step Sizes
No. Step Size No. Step Size No. Step Size No. Step Size
1 16 13 50 25 157 37 494
2 17 14 55 26 173 38 544
3 19 15 60 27 190 39 598
4 21 16 66 28 209 40 658
5 23 17 73 29 230 41 724
6 25 18 80 30 253 42 796
7 28 19 88 31 279 43 876
8 31 20 97 32 307 44 963
9 34 21 107 33 337 45 1060
10 37 22 118 34 371 46 1166
11 41 23 130 35 408 47 1282
12 45 24 143 36 449 48 1411
49 1552
This method of adapting the scale factor with changes in the waveform is optimized for voice signals, not square waves or other non-sinusoidal waveforms.
Initial Conditions
When the ADPCM algorithm is reset the step size ss(n) is set to the minimum value (16) and the estimated waveform value X is set to zero (half scale). Playback of 48 samples (24 bytes) of plus and minus zero (10002 and 00002) will reset the algorithm. Twenty four bytes of 08 Hex or 80 Hex will satisfy this requirement. It is necessary to alternate positive and negative zero values because the encoding formula always adds 1/8 of the quantization size. If all values were positive or negative, a DC component would be added that would create a false reference level.
Dialogic Corporation
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