The present invention relates to a detector and a classifier for signals that are the additive combination of a few constant-amplitude sinusoidal components.
A multiple frequency (MF) signal is the additive combination of a few constant-amplitude sinusoidal components. Such signals are used in a variety of signaling processes. Dual frequency (DF) signals, also known as dual-tone multiple frequencies (DTMF), are signals that are an additive combination of two equal-amplitude sinusoidal components. Thus, the signal generated by depressing xe2x80x9c1xe2x80x9d on the telephone keypad is the sum of a 697 Hz and a 1209 Hz sine wave, and the signal generated by depressing xe2x80x9c5xe2x80x9d is the sum of a 770 Hz and a 1336 Hz sine wave. DF signals are used for example, for representing telephone numbers and other signaling functions within a telephone system including interactive voice response.
The use of IF signals in signaling processes makes it is necessary to quickly detect and accurately classify such signals, even in a low signal to noise ratio environment, without falsely detecting MF signals within other valid signals. This poses a challenge because short segments of speech occasionally resemble MF signals.
U.S. Pat. No. 5,353,346 to Cox et al. discloses a method for detecting and classifying MF signals. Their method includes filtering the signal to isolate each of the spectral components in the signal, and then determining the frequency of each isolated component. Their method, however, is only applicable when all, of the component frequencies in the MF signal are a priori known to be members in a relatively small set of predetermined frequencies. This would be the case in telephone signaling where each DF signal is composed of two frequencies taken from two predetermined non-overlapping sets of frequencies.
Methods are known in the art for MF signal detection in the absence of a priori knowledge of the frequencies in the signal. A review of such methods may be found in Arslan et at. Proc. IEEE. Vol. II, 1996, pages 884-887. These methods, however, are computationally complex and require relatively long signals.
There is therefore a need in the art for a method of detection and classification of MF signals in the absence of a priori knowledge of the frequencies which is computationally efficient.
In its first aspect, the present invention provides a method for characterizing a DF signal. The characterization of a DF signal, in accordance with the invention, allows rapid and accurate detection of the frequencies of the signal without processing the signal. The methods of the invention may be used in any environment using DTMF signals, such as telephone signaling including interactive voice response.
A digital sine wave of frequency v obtained from an analogue signal by sampling at a sampling frequency vs can be represented by                                           H            v                    ⁡                      (            z            )                          =                  1          -                      2            ⁢                          xe2x80x83                        ⁢            cos            ⁢                          xe2x80x83                        ⁢                          (                                                2                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                                      v                    1                                                                    v                  s                                            )                        ⁢                          xe2x80x83                        ⁢                          z                              -                1                                              +                      z                          -              2                                                          (        1        )            
where z is a complex variable. A DF signal comprising two sine waves of frequencies v1 and v2 can thus be represented by
H(z)=Hv1(z)xc2x7Hv2(Z)=1xe2x88x92xcex1zxe2x88x921xe2x88x92xcex2zxe2x88x922xe2x88x92xcex1zxe2x88x923+zxe2x88x924xe2x80x83xe2x80x83(2)
wherein xcex1 and xcex2 are the real valued parameters                               α          =                      2            ⁢                          {                                                cos                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  2                        ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  v                          1                                                                                            v                        s                                                              )                                                  +                                  cos                  ⁢                                      xe2x80x83                                    ⁢                                      (                                                                  2                        ⁢                                                  xe2x80x83                                                ⁢                        π                        ⁢                                                  xe2x80x83                                                ⁢                                                  v                          2                                                                                            v                        s                                                              )                                                              }                                      ⁢                  
                ⁢                  β          =                                    -              2                        -                          4              ⁢              cos              ⁢                              xe2x80x83                            ⁢                              (                                                      2                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                          v                      1                                                                            v                    s                                                  )                            ⁢              cos              ⁢                              xe2x80x83                            ⁢                              (                                                      2                    ⁢                                          xe2x80x83                                        ⁢                    π                    ⁢                                          xe2x80x83                                        ⁢                                          v                      2                                                                            v                    s                                                  )                                                                        (        3        )            
A DF signal is uniquely determined by the pair of constants xcex1 and xcex2 defined by (3). Thus in accordance with the invention, a DF signal is characterized by this pair of constants. The two constants xcex1 and xcex2 defined by (3) characterizing a DF signal are referred to herein as the xcex1-constant and the xcex2-constant of the DF signal. As described in detail herein below, the xcex1-constant and the xcex2-constant may be used to determine the two spectral frequencies of the DF signal.
In a preferred embodiment, the xcex1-constant and the xcex2-constant of a DF signal are obtained as follows. A digital DF signal obtained by sampling an analog signal at a sampling frequency vs can be represented by the finite sequence of sampled values {x(n)}. It follows from (2) that the sequence {x(n)} satisfies the following sequence of fifth order difference equations:
(x(n)+x(n+2))xcex1+xcex2x(n+1)=x(n+3)+x(nxe2x88x921)xe2x80x83xe2x80x83(4)
Thus, in accordance with the invention, the xcex1-constant and the xcex2-constant of the DF signal are obtained as solutions to the finite sequence of equations (4) that meet a predetermined quality criterion. As will be described herein below, by a specific embodiment of the invention, the predetermined quality criterion consists of minimizing an error function.
In its second aspect, the invention provides a method for determining the two spectral frequencies of a DF signal. Unlike the prior art, in accordance with this aspect of the invention, it is not necessary to first separate the signal into its two spectral components. Moreover, the method is computationally efficient and may be applied when the two spectral components are not presumed to be members of a predetermined set of frequencies.
In accordance with this aspect of the invention, the frequencies v1 and v2 of a DF signal are obtained from the xcex1-constant and the xcex2-constant of the signal using algorithmic expressions expressing the frequencies v1 and v2 as functions of the xcex1-constant and the xcex2-constant. In a preferred embodiment, such algorithmic expressions are obtained as follows. Equations (3) may be rewritten in the form:       α    2    =                    {                              cos            ⁢                          xe2x80x83                        ⁢                          (                                                2                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                                      v                    1                                                                    v                  s                                            )                                +                      cos            ⁢                          xe2x80x83                        ⁢                          (                                                2                  ⁢                                      xe2x80x83                                    ⁢                  π                  ⁢                                      xe2x80x83                                    ⁢                                      v                    2                                                                    v                  s                                            )                                      }            -                        β          +          2                4              =          cos      ⁢              xe2x80x83            ⁢              (                              2            ⁢                          xe2x80x83                        ⁢            π            ⁢                          xe2x80x83                        ⁢                          v              1                                            v            s                          )            ⁢      cos      ⁢              xe2x80x83            ⁢              (                              2            ⁢                          xe2x80x83                        ⁢            π            ⁢                          xe2x80x83                        ⁢                          v              2                                            v            s                          )            
It follows from (5) that   cos  ⁢      xe2x80x83    ⁢      (                  2        ⁢                  xe2x80x83                ⁢        π        ⁢                  xe2x80x83                ⁢                  v          1                            v        s              )  
and   cos  ⁢      xe2x80x83    ⁢      (                  2        ⁢                  xe2x80x83                ⁢        π        ⁢                  xe2x80x83                ⁢                  v          2                            v        s              )  
are solutions of the quadratic equation                                           λ            2                    -                                    α              2                        ⁢            λ                    -                                    β              +              2                        4                          =        0.                            (        6        )            
The solutions xcex1 and xcex2 of (6) are                                           λ            1                    =                                    α              +                                                                    α                    2                                    +                                      4                    ⁢                                          (                                              β                        +                        2                                            )                                                                                            4                          ⁢                  
                ⁢                              λ            2                    =                                    α              -                                                                    α                    2                                    +                                      4                    ⁢                                          (                                              β                        +                        2                                            )                                                                                            4                                              (        7        )            
Hence,                                           v            1                    =                                                    v                s                                            2                ⁢                                  xe2x80x83                                ⁢                π                                      ⁢                          xe2x80x83                        ⁢                          cos                              -                1                                      ⁢                          λ              1                                      ⁢                  
                ⁢                              v            2                    =                                                    v                s                                            2                ⁢                                  xe2x80x83                                ⁢                π                                      ⁢                          xe2x80x83                        ⁢                          cos                              -                1                                      ⁢                          λ              2                                                          (        8        )            
Substitution of equations (7) into (8) yields algorithmic expressions for the frequencies v1 and v2 of the signal as functions of the xcex1-constant and the xcex2-constant of the DF signal.
The invention thus provides a method for characterizing a dual frequency (DF) signal comprising the steps of:
(a) sampling the signal at a sampling frequency vs so as to obtain a sequence of signal samples; and
(b) obtaining an xcex1-constant and a xcex2-constant of the DF signal meeting a predetermined criterion.
The invention also provides a method for determining the two spectral components v1 and v2 of a DF signal comprising the steps off:
(a) sampling the signal at a sampling frequency vs so as to obtain a sequence of signal samples;
(b) obtaining an xcex1-constant and a xcex2-constant of the DF signal;
(c) obtaining v1 and v2 from the xcex1-constant and the xcex2-constant of the DF signal using algorithric expressions expressing v1 and v2 as functions of the xcex1-constant and the xcex2-constant.
The invention still further provides a device for characterizing a dual frequency (DF) signal comprising:
(a) An analog to digital converter sampling the signal at a sampling frequency vs so as to obtain a sequence of signal samples; and
(b) a computer processing unit processing the sequence of sample signals so as to produce an xcex1-constant and a xcex2-constant of the DF signal meeting a predetermined criterion.
The invention also provides a device for determining the two spectral components v1 and v2 of a DF signal comprising:
(a) An analog to digital converter sampling the signal at a sampling frequency vs so as to obtain a sequence of signal samples;
(b) A computer processing unit processing the sequence of signal samples so as to produce an xcex1-constant and a xcex2-constant of the DF signal; the computer processing unit further processing the xcex1-constant and the xcex2-constant so as to calculate v1 and v2 from the xcex1-constant and the xcex2-constant using algorithmic expressions expressing v1 and v2 as functions of the xcex1-constant and the xcex2-constant.