Paper Dtmf

The DTMF Detection Group Page 59

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A DISCRETE FOURIER TRANSFORM BASED DIGITAL DTMFDETECTION ALGORITHM

Jimmy H. Beard, Steven P. Given, and Brian J. Young

The Digital Signal Processing GroupDepartment of Electrical and Computer Engineering

Mississippi State UniversityMississippi State, Mississippi 39762

{beard, given, byoung}@ee.msstate.edu

ABSTRACT

We present a new type of d ig i ta l Dua l -ToneMultifrequency(DTMF) detection scheme based on theGoertzel DFT algorithm. This detection scheme is morerobust and cost-effective than conventional analogdetection techniques. This algorithm is designed toprovide optimal performance and exceed BellCore[2]specifications for DTMF detection. The problemsassociated with closely spaced signal frequencies andshort tone duration are overcome by proper window andframe selection. Adaptive thresholding is provided tominimize false outputs due to noise and speech.

The algorithm was tested with a variety of dataincluding speech, music, and DTMF tones. We find thatthis detector is efficient, reliable, and exceeds BellCorestandards.

1. INTRODUCTION

The first touch tone telephone installation was in1963[3]. DTMF signaling uses voiceband tones to sendaddress signals and other digital information from push-button telephones and other devices such as modemsand fax machines[2]. Analog DTMF detection is doneusing bandpass filter banks with center frequencies atthe DTMF signal frequencies.

Analog receivers have wide tolerances to compensatefor distortion caused by aging transmitters, variations inkeying characteristics, and transmission line distortion.These distortions compound the problem of digitalDTMF detection[4].

The in t roduc t ion o f d ig i ta l pu lse codemodulation(PCM) switches in 1976 signaled thebeginning of the end of the analog telephone network. Inthe past 20 years telephone networks have been rapidlymoving from totally analog to totally digital. In digitalswitching systems is desirable to treat all signalsuniformly, bringing all signals through A/D convertersand switching them through the PCM system[4].Therefore the need for digital DTMF detection isjustifiable to avoid the costs of hardware and D/A

conversion needed to use analog detectors. With tconstant advances in VLSI dr iv ing DSP costdownward, it is economically sound to replace analodetectors with their digital counterparts which are moreliable, maintenance cost effective, and spatialminimal.

Several techniques for digital DTMF detection havbeen used, but most designers have settled on eitdigital filtering or discrete fourier transform(DFT)[4]. Indigital filtering, DTMF signals are passed througdigital bandpass filters centered at the signalinfrequencies(shades of analog). The power at eafrequency is then measured repeatedly to detect tDTMF tones. A DSP then interprets and translates thefor the proper switching. The DFT also measures signpower at the signaling frequencies but has the additionneed to check for signals of some minimum duratioThis will help to ensure robustness toward speech anoise. The DFT is the technique that is outlined in thpaper.

While the actual DFT is based on the aforementioneGoertzel algorithm, the windowing, level detection, antiming logic involved in developing a working designensure that digital DTMF detection is a non-triviaproblem.

As can be seen in Table 1, the DTMF signalinfrequencies are very closely spaced. It is obvious ththe bandwidth of the filter used for detection must bnarrow enough to avoid any bleeding of adjacenfrequencies. An even more limited bandwidth iintroduced when one considers that some of todayDTMF signal generators(phones, modems, etc.) apoor ly made to such an extent that the actufrequencies generated are not as shown in Table 1.

MS State DSP Conference Fall’95


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N 1–

∑ 0 1 … N 1–, , ,= =

Equation 1: Discrete Fourier Transform

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On the other hand, the design must be efficient enouto run in real time. So we have a trade-off between thnumber of DFT points that must be taken to give propbandwidth(and accurate spectrum) compared with tamount of time it takes to evaluate that number opoints. BellCore[2] specifies that the bandwidth of thdetection filter be within +-1.5% of the designed centefrequency and must accept frequencies that fall withthat range. There is also what is referred to as a rejectbandwidth beyond which the filter must attenuate anfrequencies. This bandwidth is +-3.5% of the designecenter frequency.

Determining whether DTMF signals are present or nis done using an adaptive level detection schemBellCore specifies that for adaptive thresholding, thsignal frequency must be present at a power level of 9dgreater than that of the other signal frequencies in tsame group(high or low, see Table 1). The other powlevel consideration is twist. Twist is the differencebetween the power of the signal frequency in the logroup and that of the signal frequency in the high grouTwist is defined as positive when the high frequencpower level exceeds that of the low frequency annegative if the opposite is true. BellCore‘s specificatiofor twist is +4 dB to -8 dB. Once a valid level is found, itis desirable to know how long the signal is presentthat level.

Timing is another important issue when doing DTMFdetection. The duration of the signal is critical to thaccuracy of the detector. BellCore. specifies severtiming constraints: signal duration, interdigit time, ancycle time. According to BellCore, a DTMF detectoshould recognize tones of 40ms or greater. Alternativethe detector can recognize tones with durations as low23ms. Any signal with a duration < 23ms must brejected. This specification is instrumental for ensurinrobustness to noise and speech. Interdigit time is t

HIGH

LOW 1209 1336 1477 1633

697 1 2 3 A

770 4 5 6 B

852 7 8 9 C

941 * 0 # D

Table 1: DTMF Frequencies andCharacter Assignments

MS State DSP Conference

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time between the end of one signal and the beginningthe next. Signals with interdigit times of at least 40mmust be recognized but the interdigit t ime maalternatively be allowed to approach zero. The cyctime is the time from the start of one signal to the startthe next. The minimum specification for cycle time i93ms, but it also may be allowed to approach zero. Wplaced no bounds on interdigit or cycle time in ouDTMF detector.

2. THEORY

The problem addressed in this paper is how, givendigital single-channel data stream, to detect the preseof valid DTMF tones. The algorithm must be capable oaccurately determining 1) which of the eight DTMFfrequencies are present, 2) the relative signal powereach of the frequencies, and 3) the duration that thesignals are present. These signal characteristics mthen be compared to industry standard criteriadetermine whether a valid DTMF tone is present.

Several methods exist for determining the componenta signal at a given frequency[10]. The technique choshere is the Discrete Fourier Transform (DFT). The DFallows us to represent an aperiodic discrete signal asalgebraic sum of its frequency components. The DFhas the form

.where x(n) is a finite duration sequence of length N, anw is the normalized radian frequency[9].

Consider a signal

The sampled signal is then

,as

The DFT of this signal is given by

Fall’95


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Which becomes[10]

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In this manner the amplitude of an individual frequenccomponent can be computed.
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The signal power is then A2.

2.1. Finite Sampling Effects

A consequence of approximating the infinite duratiosignal x(t) with the finite duration sequence x(n) olength Nis distortion. Consider again the signal x(t) = Asin(w0t). In the frequency domain, this signal can brepresented as X(F) = 0.5*A*delta(w+-w0). The FourieTransform of this signal X(w) is

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Equation 2: Rectangular (Uniform)TimeWindow

w n( )2

nN 1–------------- n

N2----<,

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=

Equation 3: Triangular (Bartlett)TimeWindow

Note that X(F)!= X(w). X(w) is a sinc function centeredaround w0 with a main lobe width of 1/PI = 2*fs/N.Thus, X(w) approaches X(F) with increasing N.

2.2. Choice Of N

There are several factors which together constrain tchoice of N. First, it is clearly evident in equation 3 thathe bandwidth of X(w) is inversely proportional to N.Given the BellCore requirement that the bandwidth bless than 3% of the center frequency, N must be chosnot less than 380. Other constraints on the choice ofinclude the DTMF tone duration. Recall that N is thnumber of signal samples from which the DFT icomputed. A large portion of the sampled signal macontain portions of multiple key presses, which coulsignificantly alter the resulting spectrum. Because valDTMF tones may be as brief as forty ms, with tone ttone separation of forty ms, a value of N samples greathan 321 samples may span multiple key presses. Textent to which errors are induced depend on a numbof factors, including the relative power levels of theinput signal, the amount of overlap onto the adjaceDTMF tone, and the window function used[14]

A third factor influencing the choice of N is therequirement that the DTMF detector operate in retime. Recall that the computation of the DFT issummation of N terms. The time complexity of the bessequential algorithm for the computation of the DFT iO(N log N) [9]. Obviously, as N increases, the amounof computational effort required to compute the DF


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increases as well. Therefore, the value of N mustchosen sufficiently small to ensure that the detector wrun in real time.

3. WINDOWS

Windowing is an essential consideration wheperforming spectral estimation. It is used to control thsidelobes of the spectral estimator[11]. The magnituof sidelobe attenuation is a large factor in DTMFdetection. A DTMF detector cannot tolerate sidelobleakage, but neither can it tolerate large mainlobbandwidths. This is where a good balance of mainlobandwidth versus sidelobe attenuation must bachieved. Since the two are inversely related, thproblem of windowing must be given ser iousconsideration.

The windows that were considered with this DTMFdetector were: rectangular(uniform), triangle(BartlettHamming(raised cosine) and Hann(squared cosinComplete testing was only performed using threctangular, triangular, and Hamming windows as allthe others were close derivatives of the Hamming atherefore provided insigni ficant performancedifferences.

Equations 2, 3, and 4 are the weighting functions for threctangle, triangle, and Hamming windows[11]. Thfrequency response of these functions can be seenFigure 1.

Table 2 shows some characteristics of the windows th

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Figure 1: Frequency response for: a) Rectangular Window, b) Triangular Window, and c) Hamming Window


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were tested. This table shows why the sidelobattenuation characteristics of the Hamming windowere preferable to the others given the slight differenin bandwidth.

4. GOERTZEL’S ALGORITHM

4.1. The Algorithm

The algorithm we used to compute the Fourietransform X(w) is based substantially on Goertzelalgorithm. Goertzel’s Algorithm. This algorithm modelsthe computation of the DFT as a linear filteringoperation [9]. This operation takes the form of a parallbank of resonators, where each resonator selects onthe frequencies of the DFT [8]. The output of each otheses filters at n=N yields the value of the DFT at thfrequency wk = 2*PI*k/N.

The advantages of this approach over other algorithmare two-fold: 1) it is computationally more efficient, and2) the value of the DFT can be computed at anfrequency desired. The extent to which the Goertzalgorithm is more efficient than other algorithms (sucas Fast Fourier Transforms) depends on the numberfrequencies at which the DFT is to be computed[9Each iteration of the Goertzel algorithm requires onreal multiplication and two real additions. If the value othe DFT is required at M points, then the total cost focomputing the DFT is M*N multiplications and 2*M*Nadditions. For values of M < Log N, Goertzel’salgorithm is less expensive computationally than an FFalgorithm which is O(N*Log N).

A second advantage to Goertzel’s algorithm is thaunlike FFT algorithms require N and N to be equal andpower of 2[9], Goertzel’s algorithm places no artificiaconstraints on these values. Hence, Goertzel’s algorit

WindowHighestSidelobe

Level

Equivalent BW

1/2PowerBW

Rectangle -13.3 dB 1.00 0.89

Triangle -26.5 dB 1.33 1.28

Hamming -43 dB 1.36 1.30

Table 2: Characteristics of Windows


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may be used to compute the value of the DFT at afrequency, and with any value of N. This is critical inDTMF detection because the resolution betweefrequencies decreases as the value of N decreases. IFFT were used, the value of the DFT could be computonly at N equally spaced frequencies, which may or mnot correspond to the frequencies of interest. The fathat any value of N may be used with Goertzel’algorithm is also highly beneficial, because, as will bshown later in this paper, the optimal range of N is abo150 - 400.

Three primary factors led to the selection of thitechnique. First, the DFT has been shown by Proakisto be a linear operation, i.e. any noise that is containin the time-domain signal representation is not amplifiein the frequency-domain by the DFT. Secondly, the DFis well-studied, and several efficient algorithms exist tcompute the DFT.

4.2. The Modifications

As previously stated, the algorithm presented herebased heavily on Goertzel’s algorithm. Severasubstantial modifications were made, however,improve the overall computational efficiency of theDTMF detector. First, we recognize that we arinterested in computing the DFT at a very small setfrequencies. We create an array of size eight containionly the values of k corresponding to the eighfrequencies with which we are interested. The algorithwas then modified to compute the DFT at only thesfrequencies.

Secondly, we recognized that the values of k need notrestricted to integers. This results directly from the fathat X(w) is continuous in w [9]. By allowing k to takeon floating point values, the DFT can be computedprecisely the frequency of interest, within roundoferror, regardless of the value of N. This singlmodification eliminated altogether the problemassociated with frequency resolution.

A third improvement came from the realization thaGoertzel’s algorithm was designed to handle a complinput data sequence x(n). However, the real ancomplex portions of the computations are separatedthe algorithm. Because samples of a real signal are revalued, many of the computations were unnecessary awere eliminated. This effectively halved the number ocomputations required for each iteration.

A fourth modification that was made was to precomputhe phase factors Wk. This saves sixteen trigonometevaluations per DFT computation, at a cost of thstorage of sixteen floating point numbers.

Finally, the algorithm was modified to extract the inpu

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sequence x(n) from a circular buffer. The originalGoertzel algorithm assumes that the data is stored in avector with x(0) located in element 0 of the vector.LiNear storage of the data proved to be awkward, atbest. The entire vector had to be reconstructed each timethe DFT was to be recomputed. Using a circular buffer,only `stale’ data need be changed as new data isreceived, while updating the pointers appropriately.

5. EVALUATION

5.1. Different Window Functions

One of the most important issues that was contendedwith was which window yields the best results. The keyparameter focused on during testing was the windowsize(N)[11]. We tested each window using values of Nranging from 50 to 450(figure 4). These were the valuesthat we determined would keep us within bandwidthspecification and still allow us to run in real time.

Certain other values of N were chosen to optimize theplacement of the zero locations in the frequencydomain. Figures 4-6 illustrate the relative sidelobeattenuation for the rectangular, triangular, and Hammingwindows. It can be seen that the Hamming windowprovides superior sidelobe attenuation at the adjacentDTMF signal frequencies[14].

5.2. Data Generation

Several methods were used to produce data which wasused to test the DTMF detector. Computer programswere written in C++ to generate a sampled sinusoidalsignal sequence. The amplitudes and frequencies of thesinusoidal signals were varied and approximately 100files were generated containing a variety of tones, tonespacings, and tone durations.

A simulation was then done using each file as input datato the DTMF detector and the results were recorded.Next, a noise file of approximately ten second durationwas recorded using an inexpensive clock-radio tuned tono station as a noise source. This file was then summedwith each of the computer-generated signal files to formnoisy data files of specified signal-to-noise ratio.Simulations were done with SNRs ranging from -30 to30, in steps of 5 dB, and the results were recorded. RealDTMF data was then collected by originating a normalvoice call over the public switched network, andrecording the keypresses using the Sony DAT system.Several recordings were made, using several differenttelephone sets. DTMF tones were generated by cyclingthrough the keypad several times, as well as by enteringvalid seven- and eleven-digit telephone numbers. The

algorithm was simulated using these recorded files, athe results were noted. Each of these files was thcombined in various ratios with the noise file previousdescribed to again create noisy data. Simulations wedone with SNRs ranging from -30 to 30 and the resulwere noted.

Figure 3 shows the signal-to-noise ratio versus perceerror for various windows. The detector performperfectly for SNRs down to 10 dB as can be seenfigure 2.

Software Generated Data 100 files 7 windows100 files with noise

7 windows

Recorded Data Phone 13 files(92 key presses)

Phone 2 2 files(124 keypresses)Phone 3 1 file(99 key presses)

Speech Data 151 files(0 key presses)

Music and Speech Data 25 files(0 key presses)

Table 3: Testing Database

Windows

SNR Rectangle TriangleHammin

g

30 0 0 0

23 0 0 0

20 0 0 0

10 0 0 0

0 7 11 11

-10 84.5 89.7 92.2

-20 100 100 100

-30 100 100 100

Table 4: Percent Error for different SNRs and Window




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SNR

0.0

20.0

40.0

60.0

80.0

100.0

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Triangular

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Figure 2: Percent Error VS SNR



0.0 100.0 200.0 300.0 400.0N

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40.0

60.0

80.0

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Figure 3: Percent Error VS N



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Figure 5: Triangular Window N=330



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Figure 6: Hamming Window N=330


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The DTMF detector was also evaluated for real timeoperation. Data was taken from a touch-tone telephonevia a microphone and an A/D converter. The narecordprogram was used to set the channel preference andsample frequency and pipe the sampled data to thedetector. The pipe command was also utilized to sendfiles to the input of the detector for real time testing.

The two parameters that affected real time operationwere N(total number of points computed) and the size ofsliding window(number of points computed eachiteration). Real time performance deteriorates as Ngrows large(>400) or the sliding window size growssmall(<64). This highlights the interdependencebetween parameters. Decrease N for real time and thebandwidth grows large accordingly.

6. SUMMARY

Testing and evaluation resulted in the Hamming windowbeing chosen for this detector. The frame size used isN=330. For this value: the bandwidth is acceptable, realtime operation is achieved, and the adjacent frequenciesfall in or very near to the null.A sliding window size of80 was chosen because this value was small enoughensure that the detector would always detect signaldurations of 40ms. Lower values of N compromisespeech and noise immunity. Higher values of N slowprocessing and decrease the bandwidth to the extent thattelephones with any deviation from ideal DTMF signalfrequencies cannot be detected.

Testing revealed inadequacies in the generation ofDTMF frequencies by signalling devices. It was foundthat several telephones that were tested actuallyproduced frequencies that were significantly out ofspecified ranges. Because of this fact, we began to lookfor windows with wider bandwidths to compensate forthis deviation and increase detector accuracy.

This detector was tested extensively with computergenerated and real data. It performed flawlessly on alldata in table 3. It registered zero misses on data withsignal-to-noise ratios as low as 10dB. The detectorexperienced no failures due to music or talk-off.

This detection scheme is more robust and cost-effectivethan conventional analog detection techniques. Thealgorithm was tested with a variety of data includingspeech, music, and DTMF tones. We find that thisdetector is efficient, reliable, and exceeds BellCorestandards for DTMF detection.

7. ACKNOWLEDGEMENTS

We would like to thank Dr. Joseph Picone for higuidance and patience throughout this project. Wwould also like to thank Dr. and Mrs. Picone for theihelp in data collection and the use of their telephonand recording equipment.

We wish to thank Dr. William J. Ebel for his supportideas, and the use of his personal library. We also wato acknowledge the staff of ISIP for their technicasupport, and especially Mary Weber for her help iscanning images.



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REFERENCES

Telephony:

1. Digital Simulation Test Tape.” Bell CommunicationResearch Technical Reference TR-TSY-D00763,Issue 1, July 1987.

2. “Dual-Tone Multifrequency Receiver GenericRequirements for End-to-End Signaling Over Tan-dem-Switched Voice Links.” Bell CommunicationsResearch Technical Reference TR-TSY-000181,Issue 1, March 1987.

3. Noll, A. Michael. Introduction to Telephones andTelephone Systems. Artech House, Inc., 1986.

4. Keiser, Bernhard E. and Strange, Eugene.DigitalTelephony and Network Integration.Van NostrandReinhold Company, 1985, pp. 289-90, 306-7.

5. Freeman, Roger L.Telecommunication System Engi-neering: Analog and Digital Network Design.JohnWiley & Sons, 1980, pp. 377-8.

Digital Signal Processing:

6. Blahut, Richard E.Fast Algorithms For Digital SignalProcessing.Addison-Wesley Publishing Co., Inc.,1985, pp. 131-2.

7. Manolakis, Dimitris G. and John G. Proakis.DigitalSignal Processing.2nd edition. Macmillan Publish-ing Co., 1992.

8. Burrus, C. S. and T. W. Parks.DFT/FFT and Convolution Algorithms: Theory and Implementations.Texas Instruments, Inc., 1985, pp. 32-36.

9. Marple, S. Lawrence Jr.Digital Spectral Analysis.Prentice-Hall, Inc., 1987, pp. 136-44.

10. Oppenheim, Alan V. and Schafer, Ronald W.DigitalSignal Processing. Prentice-Hall of India, 1989.

Systems:

11. Fannin, D. Ronald, Tranter, William H., Ziemer,Rodger E.Signals and Systems: Continuous and

Discrete, 3rd Ed. MacMillan Publishing Incorpo-rated, 1993, pp. 486-501, 523-525.

12. Tranter, W. H. and Ziemer, R. E.Principles of Com-munications Systems, Modulation and Noise.Houghton Mifflin Company, 1990.

WWW Sites:

13. TI. http://www.ti.com.

14. Programming in C. http://arachnid.cs.sf.ac.uk/DavC/CE.html.

15. Introduction to Signal Processing. http://wwwece.rutgers.edu/gopher/ftp/pub/sjo/intro2sp.html.


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