AU662617B2 - A tone filter - Google Patents

Description

I ,66617 P/00/011 28/5/91 Regula~on 3.2

AUSTRALIA

Patcnts Act 1990 t

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ORIGINAL

COMPLETE SPECIFICATION STANDARD PATENT linvention Titlc: "A TO)N 11 F I TrE R" The followving statement is a FUJl deCscit'ion~l Or this invetion, includIing thc best method of performing it known to us:- Im~m~ 2 Technical Field This invention relates to a. method and apparatus flor discriminating between electrical tones. The invention will be described with refrence to an arrangement for identifying each of a plurality of tone signals used in telcphqnc signalling.

Modcrn telephone exchanges use a system of tones consisting of single or inultiple frequencies for signalling and to identify various circuit conditions. Tables in Figures la and lb show examples of various Loncs used in telephone networks. In the table the function of each tone is given in columnn 2, the frequency components in column 3, frequency tolcrance in column 4, signal level in 5, twist in 6, periodicity in 7, line noise in 8, detlection time in 9, and signal tolerance in As can be seen, the requirements of the system include detection of some of the tones within a maximum time of 40 ims, and detection of tones which are only 8-z apart (3801-6 and 40016).

Preferably the d(etectlion should be carried out using digital techniques based on an 8K Hz sampling rate.

Background Art One method which could be used is the fast Fourici Transform (FFT) method.

The FFT can calculate the energy of N evenly spaced frequencies within a range of 0 to fs/2. where fs is the samlpling frequency (81K-1Hz). To be able to distinguish the 20 tones of Figures la and Ib where m inimum separation is 81-1z, an FFT with 512 i points is needed. This mncns that with 8K1-lz sampling the detection time would excccd 40 ins. At 8K1-lz only 320 samples can be evaluated in 40 mis.

H-ence FFT is not suitable at 8KHz.

2 Another possible technique is the Discrete Fourir Transform (DFT) method, applying the following equation: N-1 X(k) x (n)e-.C2 Im N) n=0 whre Ik frequency bin.

An alternative method makes use of the Gocrtzl algorithm, Oppenhcin A.V., Schaffer RW Digital Signal Processing; Prentice -1all, 1975. The Goertzcl algorithmn relics on the periodicity of the signal to rdccuce the computational burden. The Discrete Fourier Transform (DFT) can be considered as the response of a matched digital filter. The matched filter transfer function is: 3 Flk( 2 k zI (1 2cos(2nk/N) z' z 2 z')I where z- z -transform delay operator.

The state.c variables of the ilter is set to zero at the beginning of each analysis frame and so at time t N the output of the filter corrsponds to the required DFT Since the Gortzel algorithm only finds the coefficients for the frequencics of an N point DFT, then as discussd carlier, N must be large to find the X(k)'s close to the freqCuency of intrecst. Note however, that the Gocrtzel algorithm provides the advantage of being able to evaluate the Fouricr transform at a user specified frequency. If such a step is taken then the resolution can be increased considetably and fewer points are required. This can be achieved by modifying the transfer function of the matched filter, as follows: H( c (2 i s) z 1) 2 (1 2cos(2ntf./) z I Z 2 where fi tone frequency Ps sampling frequency 14 Figure 9 shows gain and phase characteristics of the filter.

The poles are located on the unit circle and at the resonant frequency the gain is theoretically infinit. What this means is that the output of the filter will increase without bound as N approaches infinity. The lphase characteristics are linear and \vary betwccn 7t/2 and -n/2 radians per second.

The bandwidth of such a filter is fixed and relatively wide and this allows cxtrancous encrgy remote from the frequency of interest to leak in so false readings may result. Analysis of the poles and zcros of this solution shows that the output increases without limit as N approaches infinity.

Furthermore the wide dynamic range demanded by the telephone signalling system requires substantial scaling in fixed point implementations, hence the detector using the Goertzel algorithm will have added computational complexity.

An alternative approach is the ue of a line enhanccr. This approach increases stability and permits control of bandwidth. This results in a reduction in spectrum leakage and ensures the output does not incicase without bound as N increases.

A block diagram of a line enhancer is shown in Figure A line enhancer functions in a manner similar to a band-pass filter and has a transfer function: L i. L L1 i.

4 H(z) I paz-' 2 2 3 1 caz"' (1 2 Z-2 where a -2cos (2cfi/fs); 0 p a 1; and z is the delay operator transform.

For stability the parameters are chosen so that the poles are inside the unit circle.

The optimisation of this method requires a balance between conflicting clements. The poles should be as close as possible to the unit circle to obtain large cnhancement gain. H-owever, this increases filter delay. To narrow the bandwidth, the zeros should be as close as possible to the poles, but this reduces gain at the frequency of interest.

While the line enhancer technique does permit extraneous energy to leak into the detector, this effect is not as bad as with the Gocrtzcl solution, being reduced by the narrower bandwidth and the fact that energy at the frequency of interest is amplified.

Disclosure of the Invention This specification discloses a method of detecting a wanted frequency in an input signal, the method comprising: filtering the wanted frequency or frequency band out. of the input signal to 20 produce a filtered signal from which the wanted frequency or frequency band has been eliminated; subtracting the filtered signal from the input signal to produce a signal represcnting the wanted frequency or frequency band.

The energy of the wanted signal can then be measured. This may be done by squaring the wanted signal to give a mcasure of its energy content.

This specification also discloses a tone detector comprising a notch filter to i which the input signal is applied wherein the notch filter eliminates the wanted frequency or frequency band to be detec.cd, wherein the output of the no'h filter is S "o applied to a subtraction circuit where it is subtracted from the input signal, the output of the subtraction circuit representing the wanted frequency or frequency band.

Preferably these functions are carried out using digital techniques.

The output from the subtraction circuit may be applied to energy measuring means to give an indication of the energy content at the wanted frequency.

The energy measurement may bc carried out based on the step of squaring the output of the subtraction circuit.

i 1 In the detection of telephone tone signalling, several toncs can be detected siimultanously by performing detection of the specific frequencies in parallel.

Preferably the notch filter has a transfer characteristic which produces a unity gain everywhere except at the frequency of interest where the gain is zero.

Preferably the filter transfer characteristic is: A(z- A(az') q I- az z 2 4 1 az 2 2 Brief Description of the Drawings: Figures Ia and lb show a table of typical tone characteristics used in telephone signalling; Figure 2a shows the pole-zero locations for cquation 3; Figure 2b shows relative pole-zcro locations for the filter transfer function of a filter used in the invention; Figure 3a shows a block dliagram of a second order IIR Notch Filter, implemen ting equation 3.

Figure 3b shows a block diagramr of the filter implementing equatin 4; Figure 4 shows gain versus normalised frequency of a filter according to equation 4; Figure 5 shows a phasc/normalised frequency plot for the filter of Figure 4; Figure 6 shows a block diagram of a tone detctccor embodying the invention; Figure 7 shows a plot of bandwidth and (elay; Figure 8 shows an array of filters for discriminiatin g bclwoeii a plurality of tones; Figure 9 shows the gain and phase characteristics of the filter; Figure 10 shows a block diagram of a line enhaneci.

Best Mode of Carrying Out the Invention Figure 2 shows a pole-zero plot illustrating the characteristics required. for a filter suitable for the prcsnt application, and Figure 3 is a block diagram of an appropriate second order notch filler.

The gain v normalised frequency plot (Figure 4) shows that as a in equation 4 approaches 1, the notch becomes narrower. Thus the filler can be made very scicctive by constraining the poles in Figure 2 to be very close to the unit circle.

This is achieved by appropriate selection of the a parameter (0 a In an analog circuit this is equivalent to improving the Q factor, eg. by reducing filter resistance. In a digital implementation this result may be achieved by narrowing the window of frequencies contained in the notch, ic. if frequency is detected by zerocrossings then the timlle window in Nwhich zero-crossings ;are elinlminated are narrowed.

Figure 5 shows that the phase charactristics of the second order notch filter are in the range -900 to 900 with a polarity change near the notch frequency. The phase at the notch is zero so thcre is no phase distortion at the notch frrcquency. As the phase distortion is minimal and only affects the region near the notch frequency for the ideal case as (r approaches I, it is possible to completely separate a single sinusoid from the spectruum with mininal distortion.

Figure 6 shows a block diagram including a notch filter I, a subtraction circuit 2, and a squaring circuit 3. Input signal u n (u narrow band signals; n noise) is applied to filter I which passes only n. This is subtracted from the input u n at 2, resulting in an output u which is the notch band of filter 1. This is applied to squaring circuit 3 to produce an output E rcprescnting the energy in u.

SPreforably circuits 1, 2 and 3 are implemented in dipital circuitry and u n is a digital signal delrived from sampling an analog signal. The filter is as illustrated in 2 Figure 3. Thc elements of thei filter arc a summing junction I to which the in put signal y(z) is applied; a first delay circuit 2 having a delay I sample period; a second delay circuit 3 having delay I sampine priod; 44 4( a first amplifier 4 having a gain j32 connected from the output of summer I to the summer 6; a second amplificr 5 (gain Pa) conncted from the output of delay 2 to the sunnr 6; the second delay 3 being connected to the second su mner 6; the output of the first delay being applied via third mplift 7 (gain aa) to old- summr= 1; the output of the second sumnet 6 being connectel by fourth aniplificr 8 (gain a 2 to the summer I.

This configuration requires the minifmum number of delay elements, and provides good fixed point performance. The circuit is less sensitive to cocfficicnt quantisation error.

The output v(t) of the filter is given by the equation: r. i -ir~irs- 7 V(t) y(t) pay(t-) P 2 aav(t-1) -a 2 v(t-2) The formula for the output v(t) derives from equation 4. The notch filter formula 4 differs from the line enhancer equation 3 in that the zeros are placed radially outside the poles. For reasons of stability the poles are placed inside the unit circle.

Preferably the zcros are placed on the unit circlc. This climinates two multiplications for each cascaded structure. Furthcr, the gain of the filter at the notch frequency is zero resulting in the complete elimination of the selected frequency under ideal conditions. Thus the desired frequency band can be completely retrievcd after the transient delay of the filter has passed. Transient delay increases as bandwidth narrows so a compromise is necessary. Bandwidth Idepends on the specified tolerances in Figure 1. In our embodiment a delay of 50 samples at 8 kI-lz was chosen.

The notch filter technilquc provides excellent noise cancellation and isolates a.

sinusoidal frequency from the widcband spectrum. This simplifies detectlion and plovides a robust solution.

A single sinlusold with frequency f 1 sampled at a constant interval T seconds can be described by a 2nd order difference cquationll as follows: w x (t I) 2) 6 :1where x(t) sin co t for n co iT and a. -2 cos (i fo, i. 2Tif.T, and Taking the z-1transform yicids: r Xi(z az z 2) F(z 1 7 4 t where is a polynomial of second degree anl reflects the initial conditions. Now considcr a signal consisting of Im inllusoids, 25 II Iti'() C where i 1, in satisfies Equation 6. Taking the z-transform of Equation 8 and using Equation 7 it follows that: F(z) U'(z 1) 9 m n 71 (I a 1 z I +z 2 i -L where is a polynomial of degree 2mn which reflects tile initial conditions. It is now clear that a signal consisting or a sum of mn sinusoidls satisfics thle following (lifference equation: m 17 (1 al Z 1 0 Equation 10 dlescribes a Moving Average (MA) process. The MA model is rn A(z )Fl (I +I-a zI+ z 2 1 where A(z- 1 has complex conjugate roots which lie onl thle unit circle in thle z-plane.

The angular frecquenIcy Of echII sinlusoid is given by thle angle subtended onl the real axis by the root of thle upper hialf-plane.

Now consider a sign a consisting of a.SII sum ofl msinusoids bur1ied inl noise as follows: y(t) uI(t) n1(t) fo r t 1, 2, 12 where n(t) is decfined,", ais a zero man sequecec of indlepell~lnt. and idlentically dlistributed random variab~les wvith variance cr 2 and uI() is a sum of in sinusoids specified by equation 13.

mf A 1(t) E C s in (w r +I 13 1 wher ((pt adC, are both real. Simlple trigonometry shows that thle sinusoids in noise process, Equam~tion 12, can be decscribed by thle followving ARMA model (see Kay aind Marple, 1981):, *A(z 1) y(t) =A(z 1) n(t) 14 This result implies the following Filter structure for- thle eliiniation Of sinusoidal components in thle input signal y(t).

2 (1 Z 2 H n) 171(1 4- a z z z 2 I=i Expanding Equation 15 into polynomial form, it can be re~adily verified that 2mn E 1 H-(z 1= 2m1 Y d (I z wvhere 0 9 a 1 (10 d, 211 and (12m i (I Ifor i m-I, When theC inputL 'Signal1 is passed through H(zl) the result is: Since the poIcs Or Uhe tuna l,1)IC filtcr a re constrainicd to be wvithin the unit, circle, stability is cnsur-cd, Fu rther, dhc sinl iiSOid al comnponen tS, arc completely eliminated by th is filtering process (1c. H-(z 1) ul(t) Hcc it follows that: v(t) H(Z n1(t) 18 Now if a is chosen very close to I will ha,'ve Unity ga9in cvcl'yWhrcj' except A the SinuIsoidl Imquencics wshore the gain wvill be zecro, Th us I-I(z 1) approaches the idlealI notch filter cliaracteristics a.nd so tile broadlband or noise coflipontin is only slightly d istor'ted in tile process (leSCdibed by E(q Un tion 17, Clearly, with a approxiniately cqual1 to I approximately equals ii(t) 19 The notch Filter given by Equationl 1 6 has a :ninimn) I ii mber of lparametcrs wherc III notches a11c ella ra ctLcriscd by III para mectors. In the giv'en Case, the zer-os of the filter are located onl the unit circle while thc position oif the poles arc located on the same raidial line and const rainedl ty thle coefficiet a to be within the unit circle.

Now consider the imiplemental on of seconld order II R notch, filter modules in either cascade Or parallel form. Note that it is desirable to have control over the location of both poles and zeros. The above requirements are satisfied by modifying the filter' structure, Equation 16, as follows: A(1 I pazI rl 2 z I A(cz 1) 1 qaZ I (12Z I where- fi c This arrangement achieves significant improvements over the Goertzel and line enhancer approaches as much of the widcband signal is removed. The filter is suitable for fixed point implementation as little or no scaling is required.

Figure 7 is a plot of bandwidth (Hz) against a, with 13 1 the zero is on the unit circle). This gives an infinite null at the notch ficquency (Figure Thus bandwidth is determined solely by a.

Superimposed on this graph is a plot of delay against a(curved line).

Delay .1 I/In The superimposed plots in Figure 7 enable the optimisation of bandwidth and delay, both of which should be a minimum. The graph shows that with a 0.98, the bandwidth is 50Hz and the delay is 50 samples.

Figure 8 shows a parallel array of filters of the type shown in Figure 6. This array can be used to detect different frequencies.

The majority of tones must be detected within 40 ms (320 samples). With a frame based detection circuit. consideration must be given to the effects of the tone beginning midway through the frame. This is especially so, given the long filter delays experienced with approximately ecqual to 1. y using a small frame size and by accepting a valid tone detection if at least two consecutive frames signal the same S" tone, the effects of a tone starting midway within a fralme and teic subsequent filter 20 delay can be addressed. If we assume that the delay time is approximately 50 samples (a 0,98) and we let the frame size be 100 samples, the effect of a tone commencing anywhere in the first half of the frame is that by the end of the frame, the transient effect will be mostly gone. Thus the next two subsequent frames will detect full signal t energy and a detection will occur. The time taken for detection will be 300 samples (at worst case).

Consider the effect of the tone beginning in the second half of the first frame.

The first frame consists entirely of the transient portion and up to the first half of the 4 1 second frame will be transient also (for the case where the tone begins immediately before the end of the first framic), Thus the energy in the second frame is unreliable and it cannot be assumed only the signal energy is present. The third and fourth frames will detect full signal energy and a tone detection will occur. The maximum time taken for detection is 350 samples greater than 40 ms. By reducing the frame size to 90 the worst case detection time is 3x90 50- 320 samples. Further improvements in detection time is possible if the framc size is decreased, but the smaller frame time leads to less accurate energy determination especially at lower frequencies.

At a frame size of 90 the lowest frequency (350 Hz) has only 4 cycles any less and the energy will vary too much between frames.

The detector operates by computing the energy from every notch filter. The tone energy is simply the sum of the energies of the frequencies that make up the tone.

1 5 A simple comparison is made between tones, and the tone with the highest energy (providing it is above the noise floor) is chosen, Rather than choosing a valid tone based on the energies of the two most recent frames, the median of the last four frames is chosen. This scheme 'smoothes over' any false detections due to random high spectral peaks.

In Figure 6 the combination of notch filter and summing junction significant advantage that wideband energy is largely removed. Standard line enhancement filters amplify the signal of interest and pass wideband signals unaltered. They exhibit unity gain everywhere except the frequency of interest, where the gain is large.

From Figure 6 it is seen that W(z) H(z) S(z) 21 n(z) S(z) W(z) 22 Therefore n(z) S(z) (1 H1(z)) 23 The transfer function for the filter and summing junction is n(z) a(a 1) z (2 l)z j SH" 24 s(z) I az I

C

2 z 2 The gain u frequency is shown in Figure 9. As the gain at the centre frequency is I and approaches 0 elsewhere, the energy measured corresponds to the actual energy. The dynamic range is also minimised as there L. no amplification.

The energy is measured by squaring n(z) and adding over a given data frame.

The data frame is chosen as 90 samples as discussed above,

Claims (12)

1. A digital filter to select a predetermined frequency or frequency band from a widebar,;' signal the filter comprising a second order notch filter to eliminate the predetermined frequency or frequency band from the wideband signal, and subtraction means wherein the output of the notch filter is subtracted from the wideband signal.

2. A filter as claimed in claim 1 wherein the notch filter ias a transfer characteristic (1 az 1 z- 2 (1 -+aaz c'z 2 where a 2 cos 2n fi notch frequency; f, sampling frequency; and 0 c a a controlling the radial position of the complex conjugate poles.

3. A filter as claimed in claim 1 or claim 2 including energy measuring means to measure the output of the subtraction means,

4. A filter as claimed in claim 3 wherein the energy measuring means squares the output of the subtraction means.

A filter as claimed in any one of claims 1 to 4 including an analog to digital converter to convert the wideband signals to digital signals.

6. A filter as claimed in claim 5 wherein the converter samples the wideband signal at greater than twice the frequency of the predetermined frequency,

7. A filter substantially as herein described with reference to the accompanying a drawings.

8. An array of filters for selecting a plurality of predetermined frequencies from a wideband signal, the array comprising a plurality of filters as claimed in any one of the preceding claims, the filters being arranged in parallel.

9. A method of selecting a predetermined frequency from a wideband signal, the method including the steps of sampling the wideband signal at a sampling rate at least twice the predetermined frequency to produce a digitised wideband signal; a0digitally filtering the digitised wideband signal to eliminate the predetermined -v frequency; and i II c~ aa~- ii subtracting the digitally filtered signals from the digitised wideband signal to produce a digital output signal.

A method as claimed in claim 9 wherein the steps of digitally filtering is carried out according to the transfer function where a 2 cos c i 2n fi fi notch frequency; f, sampling frequency; and 0 aC a controlling the radial position of the complex conjugate poles. 0

11. A method as claimed in claim 9 or claim 10 including the steps of squaring the digital output signal to produce an energy signal which is a measure of the energy of the predetermined frequency.

12. A method of selecting a predetermined frequency from a wideband signal substantially as herein described with reference to the accompanying drawings. 1 It 14 4-, ro rr t I t 4- 4-41 £4.4 4 4 4.44£, S 4 DATED THIS FIFTH DAY OF JULY 1995 ALCATEL AUSTRALIA LIMITED I- ABSTRACT A digital filter to sclect a predetermined irequency n(z) from a broadband signal S(z) includes a notch fiter H(z) to eliminate the predetermined frequency from the broadband signal, and summing means in which the filtered broadband signal W(z) is subtracted from the original broadband signal S(z) to produce the predetermined frequency The energy content of the frequency n(z) is measured by squaring the signal so that the presence or absence of a signal of frequency n(z) can be inferred from the level of the energy of the signal. FIGURE 6. 1 Ii I s I I