1. Chapter 17 DTMF generation and detection Dual Tone Multiple Frequency
DSP C5000
Chapter 17
DTMF generation and detection
Dual Tone Multiple Frequency

2. Learning Objectives DTMF signaling and tone generation.
DTMF signal generation
DTMF tone detection techniques and the Goertzel algorithm.
Implementation of the Goertzel algorithm for tone detection on DSP

3. Introduction
Dual Tone Multi-Frequency (DTMF) is a widespread used signalling system: telephone services use commonly key strokes for options selection
DTMF is mainly used by touch-tone digital telephone sets which are an alternative to rotary telephone sets.
DTMF has now been extended to electronic mail and telephone banking systems
It is easily implemented on a DSP as small part of the tasks.

4. DTMF Signaling
In a DTMF signaling system a unique combination of two normalized frequency tones
Two types of signal processing are involved:
Coding or generation.
Decoding or detection.
For coding, two sinusoidal sequences of finite duration are added in order to represent a digit.

5. Dual tone Generation A key stroke on « 9 » will generate
2 added tones, one at
852Hz low frequency
and one at 1477Hz
The 2 tones are
Both audible.

6. Tones Generation
Dual tone generation can be done with 2 sinewave sources connected in parallel.
Different method can be used for such implementation:
Polynomial approximation
Look-up table
Recursive oscillator
DTMF signal must meet certain duration and spacing requirements
10 Digits are sent per second.
Sampling is done via a codec at 8Khz
Each tone duration must be >40msec and a spacing of 50ms minimum between two digits is required

7. 2 and 9 digit signal sequence

8. DTMF generation implementation
Tone generation of a DTMF is generally based on two programmable, second order digital sinusoidal oscillators, one for the low fl the other one for the high fh tone.
Two oscillators instead of eight reduce the code size.
Coefficient and initial conditions are set for each particular oscillation + +
y(n)
Low freq
Z-1 +
Z-1 +
High
freq
Z-1 +
Z-1

9. Digital oscillator parameters
2 pole resonator filter with 2 complexe poles on the unit cercle (unstable)
Output signal:
Y(n)= -a1y(n-1)-y(n-2)
Initial conditions:
Y(-1)=0
Y(-2)=-A sin(w0)
w0=2Pf0/fs
f0 is the tone freq
fs is the sampling freq

10. C55 sine generator code
Frames of data stream of 120 samples (15msec) long contain either DTMF tone samples or pause samples.
The encoder is either in idle mode, not used to encode digits or active and generates DTMF tones and pauses
The sine equation is implemented in assembly language:
Mov a1/2, T1 ; coded in Q15
Mpym *AR1+,T1,AC0; ;AR1 y(n-1); AR y(n-2)
sub *AR1-<<#16,AC0,AC ;AC1= a1/2*y(n-1)-y(n-2)
Add AC0,AC1 ; AC1= a1*y(n-1)-y(n-2)
||delay *AR1 ;y(n-2)=y(n-1)
Mov rnd(hi(AC1)),*AR1 ;y(n-1)=y(n)
; output signal pointer is AR1

11. Oscillator parameters at fs=8Khz

12. DTMF Tone Detection
Goertzel algorithm is the more efficient detection algorithm for a single tone.
To detect the level at a particular frequency the DFT is the most suitable method:
The Goertzel algorithm is a recursive implementation
of the DFT ,
16 samples of the DFT are computed for 16 tones
See DTMF.pdf file for a complete description

13. Goertzel Algorithm Implementation
To implement the Goertzel algorithm the following equations are required:
The only coefficient needed to compute output signal level is
Cos(2pfk/fs)

14. Goertzel Algorithm Implementation
Get N input samplex(n)
Compute recursive part:
Wk(n), n=0 to N-1
For 8 frequencies
Calculate X2(k) for 8 freq
Tests:
Magnitude
Harmonic
Total Energy
Output Digit

15. Goertzel Algorithm Implementation
The value of k determines the tone we are trying to detect and is given by:
Where: fk = frequency of the tone.
fs = sampling frequency.
N is set to 205.
Then we can calculate coefficient 2cos(2**k/N).

16. Goertzel Algorithm Implementation
Frequency k
Coefficient
(decimal)
(Q15)
1633 42
0x479C
1477 38
0x6521
1336 34
0x4090*
1209 31
0x4A70*
941 24
0x5EE7*
852 22
0x63FC*
770 20
0x68AD*
697 18
0x6D02*
N = 205
fs = 8kHz
During fixed point implementation this will prevent overflow
* The decimal values are divided by 2 to be represented in Q15 format (a1/2<1).

17. Goertzel Algorithm Implementation
wn = x(n) - wn a1*wn-1; n<N-1
= sum prod1
Where: a1= 2cos(2k/N) and N=205
This gives 205 MACs+ 205 ADD
The last computation gives the energy of the tone and is done with:
2 SQRS and one multiplication
|Yk(N) |2 = Q2(N) + Q2(N-1) - a1*Q(N)*Q(N-1)

18. Goertzel Algorithm Implementation
void Goertzel (void) {
static short delay;
static short delay_1 = 0;
static short delay_2 = 0;
static int N = 0;
static int Goertzel_Value = 0;
int I, prod1, prod2, prod3, sum, R_in, output;
short input;
short coef_1 = 0x4A70; // For detecting 1209 Hz
R_in = mcbsp0_read(); // Read the signal in
input = (short) R_in;
input = input >> 4; // Scale down input to prevent overflow
prod1 = (delay_1*coef_1)>>14;
delay = input + (short)prod1 - delay_2;
delay_2 = delay_1;
delay_1 = delay;
N++;
if (N==206)
prod1 = (delay_1 * delay_1);
prod2 = (delay_2 * delay_2);
prod3 = (delay_1 * coef_1)>>14;
prod3 = prod3 * delay_2;
Goertzel_Value = (prod1 + prod2 - prod3) >> 15;
Goertzel_Value <<= 4; // Scale up value for sensitivity
N = 0;
delay_1 = delay_2 = 0; }
output = (((short) R_in) * ((short)Goertzel_Value)) >> 15;
mcbsp0_write(output& 0xfffffffe); // Send the signal out
return;
‘C’ code
This first implementation facilitates debugging

19. C54 assembly programme Goertzel tone detection routine
;Assume input signal x(n) is read through an I/O port at address 100h
;Output level Y(k)2 is sent to a port at address 1001h
;Scratch RAM reservation
.bss wn,2 ;w(n-1) andw(n-2)
.bss xn,1 ; input signal xn
.bss Y,1 ; tone Energy
.bss alpha,1 ;coefficient storage
; Constant initialisation
alphap .word 0x68ADh ; a2/2 coefficient value at fs=8khz ; (prog memory)
N .set 205 ;value of N
;DSP modes initialisation
SSBX FRCT ;Product shift for Q15 format
SSBX SXM ;Sign extension during shift
RSXB OVA ; no overflowmode for A and B
RSXB OVB

20. C54 assembly programme ;Data pointers Initialisation
LD #wn,AR2 ; AR2 is pointing w(n-1)
LD #xn,AR1
LD #Y,AR4
LD #alpha,AR3
MVPD #alphap,*AR3 ;Move alpha value to data RAM
RPTZ #1 ;Accumulator A=0
STL A,*AR2+ , w(0) and w(-1) are set to 0
MAR *AR2- ; AR2 is pointing w(n-2)

21. Algorithm Core STM #N-1,BRC ; repeat block number RPTB loop-1
PORTR 100h,*AR1
LD *AR1,16,A ; AccH=x(n)
SUB *AR2,16,A ;A=x(n)-w(n-2)
MAC *AR2,*AR3,A ;A=x(n)-w(n-2)+alphaw(n-1)
MAC *AR2,*AR3,A ;A=x(n)-w(n-2)+2alphaw(n-1)
delay *AR2 ;w(n-2)=w(n-1) tap delay
STH A,*AR2+ ;w(n-1)=w(n) tap delay
Loop ;end of loop

22. Energy calculation LD *AR2,16,A ;A=w(N-1)
MPYA *AR2- ;T=w(N-1) B=w(N-1)^2
MPY *AR2,A ;A=w(N)*w(N-1)
LD *AR3,T ;T=alphap
MPYA A ;A=alphap*w(N)*w(N-1)
SUB A,1,B ; substract with a left shift to ;obtain 2alphap
; B=w(N-1)^2-2alphap*w(N)*w(N-1)
LD *AR2,T ;T=w(N)
MAC *AR2,B ;B=w(N-1)^2-2alphap*w(N)*w(N-1)+w(N)^2
STH *AR4 ;save to Y
PORTW *AR4,101h ;copy output level

23. Universal Multifrequency Tone Generator and detector (UMTG)
This software module developed by SPIRIT Corp. for the TMS320C54x and TMS320C55X platform
It can be used into embedded devices for generating various telephone services used in intelligent network systems
Or as a simple tone generator for custom applications
It is fully compliant with TMS Algorithm standard rules
See SPRU 639 and SPRU 638 AN

24. Follow on Activities Application 7 for the TMS320C5416 DSK
Uses a microphone to pick up the sounds generated by a touch phone. The buttons pressed are identified using the Goerztel algorithm and their values displayed on Stdout. The frequency response of each Goertzel filter is given using Matlab.