DE102021207339B3 - Method and device for analyzing a time signal with periodic signal components and computer program product and computer program - Google Patents

Abstract

The invention relates to a method for analyzing a time signal ((x(t)) with periodic signal components, in which frequencies and signal parameters (HNR) assigned to the frequencies are determined from the time signal ((x(t ). (t)) via a sum and difference formation in the time signal ((x(t)) at points in time that are offset by one period according to the current frequency (ƒc); b) determination of the signal parameter (HNR) for the current frequency (ƒc ) as a quantity indicating the ratio of a signal strength measure of the first filter signal (yp) to a signal strength measure of the second filter signal (ym);c) determining a control rsignals (cs(n)) indicating whether a phase difference between the first filter signal (yp) and the second filter signal (ym) is positive or negative,d) modification of the current frequency (ƒc) by increasing it if the Control signal (cs(n)) indicates a negative phase difference, and by decreasing it when the control signal (cs(n)) indicates a positive phase difference, using the modified frequency as the current frequency (ƒc) in the next iteration loop.

Description

The invention relates to a method and a device for analyzing a time signal with periodic signal components, as well as a computer program product and a computer program.

Time signals with periodic signal components occur both in nature and in a variety of technical applications. In the context of processing such signals, the periodicity represents important information, so there is a need to extract corresponding fundamental frequencies from these signals. Examples of natural signals with periodic signal components are acoustic signals such as speech signals, music and the like. Technical examples of such signals are time signals in mechanical or electrodynamic systems, such as high-frequency waves.

So-called PLL methods (PLL=phase-locked loop) are known from the prior art for detecting and estimating the periodicity in time signals. However, PLL-based methods cannot be used for any signal form. Above all, they are suitable for sinusoidal signals.

Also known from the prior art are DLL methods (DLL=Delay-Locked Loop) which use internal delays for the detection and estimation of periodic signals. These methods are also not suitable for detecting periodic signals with any waveform.

The pamphlet U.S. 5,812,737A discloses a method for estimating the frequency in a periodic signal based on a closed loop using a frequency error signal to improve the frequency estimate.

The pamphlet BITTNER, Rachel M.; WANG, Avery; BELLO, Juan P.: Pitch contour tracking in music using Harmonic Locked Loops. In: Proc. of the 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). 5th-9th March 2017, pp. 191-195 discloses a method for pitch tracking in a music signal using an HLL control loop (HLL = Harmonic Locked Loop).

The object of the invention is to create a method for analyzing a time signal, with which the fundamental frequencies of periodic signal components in a time signal can be estimated easily and reliably.

This object is achieved by the method according to patent claim 1. Further developments of the invention are defined in the dependent claims.

The method according to the invention analyzes a time signal with periodic signal components. The time signal thus represents the signal processed in the method according to the invention. The method is preferably implemented digitally as a computer-aided or computer-implemented method. In this case, the time signal is a digital signal or a signal digitized from an analog signal, which supplies a signal value at corresponding sampling times. Nevertheless, the method can also be implemented, at least in part, as an analog method if necessary. In particular, analog filters are known with which the determination of the first and second filter signals described further below can be carried out.

As part of the method according to the invention, frequencies and signal parameters assigned to the frequencies are extracted from the time signal for successive points in time in the time signal by means of one or more iterations, starting from an initial frequency. For a current frequency in a current iteration loop of a respective iteration, the steps a) to d) explained below are carried out within the scope of the method according to the invention for a current point in time of the successive points in time. The order of the steps can be arbitrary, as long as one step does not use the result of another step.

In step a), a first filter signal and a second filter signal are determined based on an input signal. The input signal can be the original time signal or a smoothed time signal. In the case of a smoothed time signal, the method thus also includes a corresponding smoothing step. As can be seen from the following description, other smoothed quantities or signals can also be processed in the method according to the invention. If reference is made below to corresponding smoothed signals or variables, this should always be understood to mean that a corresponding smoothing step is carried out for these signals or variables in the method according to the invention will lead. The smoothing can be implemented in different ways. A low-pass IIR filter or a low-pass FIR filter is preferably used, as will be described in more detail below. Nevertheless, other smoothing methods (eg arithmetic averaging) can also be used.

The first filter signal determined in step a) represents the sum of the input signal at the current point in time and the input signal at the (earlier) point in time, which is one period according to the current frequency before the current point in time. In contrast, the second filter signal represents the difference between the input signal at the current point in time and the input signal at the (earlier) point in time, which is one period according to the current frequency before the current point in time.

In step b) of the method according to the invention, the signal parameter for the current frequency is determined as a variable which is the ratio or the smoothed ratio of a signal strength measure or a smoothed signal strength measure of the first filter signal or a smoothed first filter signal to a signal strength measure or a smoothed signal strength measure of the second filter signal or a smoothed second filter signal. The signal strength measure can be defined differently depending on the configuration. For example, the signal strength measure can represent the absolute value or the square of the corresponding first or second (possibly smoothed) filter signal. The signal parameter based on the ratio of signal strength measures defined above indicates how strong the proportion of a periodic component in the time signal is at the current frequency.

In step c) of the method according to the invention, a control signal is determined which indicates whether a phase difference is positive or negative, the phase difference being the phase difference between the first filter signal or the smoothed first filter signal and the second filter signal or the smoothed second filter signal. Alternatively, this phase difference can also be a smoothed phase difference, i.e. the corresponding phase difference after smoothing has been carried out.

Finally, in step d) of the method according to the invention, the current frequency is modified by being increased if the control signal indicates a negative phase difference and by being reduced if the control signal indicates a positive phase difference, the modified frequency being used as the current frequency in the next iteration loop of the respective iteration is used.

The frequencies and signal parameters obtained using the method according to the invention can be stored in a suitable manner (preferably digitally) and optionally output as information via a user interface

The method according to the invention makes it possible to use a novel control signal in a simple manner to create a control loop which is quickly and reliably adjusted to a fundamental frequency in the processed time signal. In particular, the method according to the invention also delivers good results in the case of heavily noisy signals, as the inventor was able to demonstrate based on simulated signals.

In a particularly preferred embodiment, in the event that the signal parameter in the current iteration loop or over a plurality of iteration loops comprising the current iteration loop and a predetermined number of previous iteration loops, or the signal parameter averaged over the plurality of iteration loops exceeds a predetermined threshold value, the current frequency as one Fundamental frequency is identified in the time signal. This fundamental frequency can be stored in a suitable manner (preferably digitally) and optionally output as information via a user interface. The appropriate determination of the level of the threshold is within the scope of professional action. For example, a threshold of 6 dB has proven to be practical.

In a further preferred embodiment, the smoothed time signal and/or the smoothed first filter signal and/or the smoothed second filter signal and/or the smoothed ratio and/or the smoothed signal strength measure of the first filter signal or of the smoothed first filter signal and/or the smoothed signal strength measure of the second filter signal or the smoothed second filter signal and/or the smoothed phase difference is determined by smoothing based on a low-pass IIR filter (IIR=infinite impulse response), preferably with a first-order low-pass IIR filter.

wobei s(n) das eingehende Signal zum aktuellen Zeitpunkt ist;
wobei s_g (n) das geglättete Signal zum aktuellen Zeitpunkt ist;
wobei s_g (n - 1) das zum vorhergehenden Zeitpunkt bestimmte geglättete Signal ist; wobei α = e^-T/τ ist und T die Abtastperiode der Zeitpunkte ist und τ die Zeitkonstante des Filters ist.Such low-pass IIR filters are well known to those skilled in the art. These filters work recursively, whereby the smoothed signal at the current time (i.e. the current sampling time) consists of the incoming signal (i.e. the signal to be smoothed) at the current time and possibly incoming signals at one or more earlier times using one or more smoothed signals is determined, which were determined in previous recursion loops. In a manner known per se, a first-order low-pass IIR filter is defined based on the following rule: $$s_G\left(n\right)=\left(1-a\right)\cdot s\left(n\right)+a{s}_G\left(n-1\right)$$

where s(n) is the incoming signal at the current time;
where s _g (n) is the smoothed signal at the current time;
where s _g (n-1) is the smoothed signal determined at the previous instant; where α = e ^-T/τ and T is the sampling period of the instants and τ is the time constant of the filter.

The strength of the smoothing or filtering is defined via the time constant τ. The appropriate choice of this time constant is within the scope of professional action. In particular, the time constant in the method according to the invention for the smoothing of different signal types or sizes can also be defined differently. The time constant is preferably of the order of the period of the current frequency.

Corresponding calculation rules for higher-order low-pass IIR filters are known analogously. These filters are also characterized by a time constant. When smoothing, however, you not only consider the incoming signal at the current time, but also previous incoming signals. In this case, earlier incoming signals are preferably taken into account at a fixed time interval from the respective reference times, which are described in the detailed description with reference to FIG 2 be explained.

The modification of the current frequency in step d) carried out in the method according to the invention can be designed in different ways. In a preferred variant, the modification is carried out using a factor greater than one, with the current frequency being multiplied by the factor to increase it and the current frequency being divided by the factor to reduce it. The factor preferably depends on the current frequency and becomes greater the greater the current frequency.

$$adc\left(n\right)=arg\left(c\left(n\right)\cdot c*\left(n-1\right)\right)$$

$$cs\left(n\right)={\langle adc\left(n\right)\rangle }_{\mathrm{\tau }}\text{ oder }cs\left(n\right)=adc\left(n\right)$$

wobei n den aktuellen Zeitpunkt und n - 1 den Zeitpunkt der letzten, vor dem aktuellen Zeitpunkt liegenden Iterationsschleife der jeweiligen Iteration repräsentiert,
wobei y₁ (n) das erste Filtersignal oder das geglättete erste Filtersignal in der aktuellen Iterationsschleife ist;
wobei y₂ (n) das zweite Filtersignal oder das geglättete zweite Filtersignal in der aktuellen Iterationsschleife ist;
wobei cs(n) das Steuersignal in der aktuellen Iterationsschleife ist;
wobei 〈adc(n)〉 ein geglätteter Wert von adc(n) ist, wobei die Glättung vorzugsweise mittels eines Tiefpass-IIR-Filters oder eines Tiefpass-FIR-Filters durchgeführt wird.According to the invention, the control signal, which indicates the sign of the phase difference or the smoothed phase difference, can be defined in different ways. In a particularly preferred variant, the control signal is determined as follows: $$c\left(n\right)=y_1\left(n\right)+i{y}_{\mathrm{e.g}}\left(n\right)$$

$$a\mathrm{i.e}c\left(n\right)=a\mathrm{right}G\left(c\left(n\right)\cdot c*\left(n-1\right)\right)$$

$$cs\left(n\right)={〈a\mathrm{i.e}c\left(n\right)〉}_{\mathrm{\tau }}\text{or}cs\left(n\right)=a\mathrm{i.e}c\left(n\right)$$

where n represents the current time and n - 1 represents the time of the last iteration loop of the respective iteration before the current time,
where y ₁ (n) is the first filter signal or the smoothed first filter signal in the current iteration loop;
where y ₂ (n) is the second filter signal or the smoothed second filter signal in the current iteration loop;
where cs(n) is the control signal in the current iteration loop;
where 〈adc(n)〉 is a smoothed value of adc(n), the smoothing preferably being performed using a low-pass IIR filter or a low-pass FIR filter.

However, other variants for determining the control signal are also conceivable, provided the control signal indicates whether the corresponding phase difference or smoothed phase difference is positive or negative.

In a further preferred embodiment, a number of periodic signal components contained therein are extracted simultaneously from the corresponding time signal. In this case, several of the above iterations are performed simultaneously, with each iteration having a different initial frequency.

The method according to the invention can be used to analyze any time signals. In a particularly preferred embodiment, the inventive method is an acoustic Signal and in particular a voice signal processed as a time signal, in which case the initial frequency of each iteration is between 80 Hz and 400 Hz.

In addition to the method described above, the invention relates to a device for analyzing a time signal with periodic signal components, the device being set up to carry out the method according to the invention or one or more preferred variants of the method according to the invention. In other words, the device contains appropriate means for carrying out the method according to the invention or preferred embodiments of this method. These means are preferably implemented using suitable program code on a computer.

In addition to the method described above, the invention also includes a computer program product with a program code stored on a machine-readable carrier for carrying out the method according to the invention or one or more preferred variants of the method according to the invention when the program code is executed on a computer. The invention also relates to a computer program with a program code for carrying out the method according to the invention or one or more preferred variants of the method according to the invention when the program code is executed on a computer.

Exemplary embodiments of the invention are described in detail below with reference to the attached figures.

• 1 ein Ablaufdiagramm, das die Schritte einer Ausführungsform des erfindungsgemäßen Verfahrens wiedergibt;
• 2 ein Diagramm, welches die Integration eines Phasensignals zur Bestimmung von Zeitpunkten offenbart, die bei der Glättung verschiedener Größen in dem Verfahren der 1 berücksichtigt werden können;
• 3 ein Diagramm, das die Filterung verdeutlicht, die im Verfahren der 1 zur Erzeugung entsprechender Filtersignale genutzt wird; und
• 4 eine Darstellung, die mit dem Verfahren der 1 erzielte Ergebnisse für verschiedene simulierte Signale verdeutlicht.

Show it:

• 1 a flow chart showing the steps of an embodiment of the method according to the invention;
• 2 a diagram which discloses the integration of a phase signal for determining points in time which are used in the smoothing of various variables in the method of FIG 1 can be taken into account;
• 3 a diagram showing the filtering used in the method of 1 is used to generate corresponding filter signals; and
• 4 a representation made with the method of 1 obtained results for various simulated signals.

The aim of the embodiment of the method according to the invention described here is to find the fundamental frequencies of these components in a time signal which is represented by signal values along the time axis and contains periodic components, with the fundamental frequencies being able to change over time. The method can be used for any time signals in a wide variety of application areas. In a preferred embodiment, the method is used for acoustic signals in a frequency range between 80 Hz and 400 Hz, but the method can also be used for other types of signals, such as high-frequency signals.

In the embodiment described here, the steps of the method are carried out digitally, so that the time signal represents a digital or digitized signal. This time signal, which is the input signal for the method described here, is used in the flowchart of FIG 1 denoted by x(t), where t represents time. The method is described below using an example in which a single fundamental frequency is extracted from the signal x(t) by means of an iteration. However, the method can also be easily extended to the extraction of a plurality of fundamental frequencies, with a plurality of iterations then being carried out in parallel or in series, which differ sufficiently in their initial frequencies so that they converge towards different fundamental frequencies.

The method is based on a model for a corresponding periodic signal component in the time signal, with the model assuming a time-varying fundamental frequency ƒ ₀ (t) of the signal component. The corresponding signal component is described by the following sum: $$\begin{array}{l}x\left(t\right)={\displaystyle \sum _{n=1}^{N_p}{a}_{\text{n}}\text{sin}\left(n\phi \left(t\right)-{\mathrm{<figure-callout\; id="0"\; label="\phi "\; filenames="DE102021207339B3\_0024.png,DE102021207339B3\_0025.png"\; state="\{\{state\}\}">\phi </figure-callout>}}_{\mathrm{0,}\text{n}}\right)}\\ {ƒ}_0\left(\text{t}\right)=\frac{1}{2\pi }\frac{\mathrm{i.e}\phi \left(t\right)}{\mathrm{i.e}t}\end{array}$$

Here ƒ ₀ (t) is the corresponding fundamental frequency, which is calculated as a derivative of the instantaneous phase φ(t). In addition to the fundamental frequency (n=1), the signal component contains several harmonics (n=2, . . . , Np) of the fundamental frequency. The corresponding amplitudes for the fundamental frequency and the harmonics are denoted by a _n in equation (1), whereas the phases are denoted by φ _0,n .

As part of the method described here, a frequency is continuously changed so that it adjusts to the basic frequency ƒ ₀ (t) or the corresponding period T ₀ = 1/ƒ ₀ . In contrast to known PLL methods, no reference signal is required as a modulator for deriving a control signal. Instead, the signal model above is used explicitly to define a period-synchronous modulation filter which, when applied to the time signal x(t), provides a phase-based control signal with which a control loop is suitably adjusted. The method adjusts very quickly to an estimate of the fundamental frequency ƒ ₀ (t). In other words, corresponding frequency estimates ƒ _c (t)=ƒ̂ ₀ (t) for the fundamental frequency are determined iteratively in the method explained below, with the method also delivering the actual fundamental frequency of the corresponding signal component after a short time.

Before describing the individual steps of the procedure of 1 First, the concept of period-synchronous integration for obtaining reference times from the estimated frequency ƒ _c (t) is explained. This period-synchronous integration can be used in the smoothing of various variables within the framework of the method described here.

The aim of period-synchronous integration is that sampling values or sampling times for smoothing a corresponding signal are synchronously adapted to the changing frequency ƒ _c . The following phase function Φ(t) is determined by numerical integration: $$\varphi \left(t\right)={\displaystyle {\int }_0^t{ƒ}_c}\left(t\text{'}\right)\mathrm{i.e}t\text{'}$$

An example of such a phase function, normalized over 2π and modulo 1, is shown in the diagram of 2 played back. The case of a frequency ƒ _c is shown, which increases linearly over time t. This frequency is represented by the line L1, with the corresponding frequency values in 2 are plotted along the left ordinate. The phases resulting for this frequency profile are indicated by dashed lines L2, the corresponding phase values along the right ordinate of the 2 are reproduced. As you can see, the phase regularly falls back to the value 0, which in 2 is indicated by corresponding vertical lines L3. Due to the linear increase in frequency ƒ _c along time t, the corresponding zero points of the phase show a decreasing distance. The points in time at which the phase becomes zero represent reference points in time. A number of n consecutive reference points in time is described by the following time series: $$T_s\left(t\right)=\left\{t_{s\mathrm{,1}},t_{s\mathrm{,2}},t_{s\mathrm{,3}},\cdots ,t_{s,n}\right\}$$

$$b_{SI}\left(t\text{'}\right)=l{p}_{\tau }\left(s\left(t_{s,n}+t\text{'}\right),s\left(t_{s,n-1}+t\text{'}\right),s\left(t_{s,n-2}+t\text{'}\right),\dots ,s\left(t_{s,n-N}+t\text{'}\right)\right)$$

$$s_{SI}\left(t\right)=b_{SI}\left(t\text{'}\right)$$

In this case, t _s,1 designates the first reference time and t _s,n the last reference time before the current time t currently under consideration occurs. With the above reference times, period-synchronous smoothing of a signal s(t) that changes over time can generally be carried out as follows: $$t\text{'}=t-t_{s,n}$$

$$b_{SI}\left(t\text{'}\right)=l{p}_{\tau }\left(s\left(t_{s,n}+t\text{'}\right),s\left(t_{s,n-1}+t\text{'}\right),s\left(t_{s,n-2}+t\text{'}\right),...,s\left(t_{s,n-N}+t\text{'}\right)\right)$$

$$s_{SI}\left(t\right)=b_{SI}\left(t\text{'}\right)$$

In the above equations, t denotes the current time, whereas t' represents the time elapsed since the last reference time t _s,n occurred. l _{p τ} (·) is a per se known low-pass IIR filter with the time constant τ. Alternatively, a low-pass FIR filter with an appropriate time constant can also be used. The (period-synchronous) smoothed signal is denoted by s _SI (t). Equation (4b) above means that the signal segment starting at each reference instant is continuously averaged in a signal buffer, which amplifies the waveform of a periodic signal portion corresponding to the (stabilized) period of the consecutive reference instants, while other signal components are suppressed. The order of the low-pass IIR filter used corresponds to the number of signal values considered in equation (4b).

As a result, reference times before the current time are only relevant if the order of the low-pass IIR filter is greater than one. In the embodiment described here, a first-order low-pass IIR filter was used. However, the method can also be used with higher-order low-pass IIR filters without any problems, with a number of signals corresponding to equation (4b) then flowing into such filters.

The following are based on 1 explains the individual steps of an iteration to determine a corresponding fundamental frequency in the time signal x(t). The iteration is started in step S0 with an initial frequency ƒ _c,0 . The initial frequency is chosen as a function of the processed time signal x(t) in such a way that it lies within the frequency spectrum of the time signal. The iteration is carried out in successive iteration loops, with the initial frequency ƒ _c,0 being processed as the current frequency ƒ _c with the corresponding period T _c in the first iteration loop, whereas in the next iteration loop the current frequency ƒ _c is that frequency which was adapted in the last iteration loop, as will be explained in more detail below. In general, a current iteration loop according to steps S1 to S4 is explained below, with the current frequency ƒ _c used in this case coming from the last iteration loop or the initial frequency being ƒ _c,0 .

$$y_m\left(t\right)=x\left(t\right)+x\left(t-T_c\right)$$

$T_c=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${ƒ}_c$}\right.$

ist die aktuelle Periode. Das erste Filtersignal y_p (t) stellt dabei die Ausgabe eines perioden-konstruktiven Filters und das zweite Filtersignal y_m(t) die Ausgabe eines perioden-suppressiven Filters dar. Wenn die Grundfrequenz ƒ₀ des Signals mit der aktuellen Frequenz ƒ_c übereinstimmt, ist die Ausgabe des perioden-konstruktiven Filters doppelt so groß wie die Eingabe, wohingegen die Ausgabe des perioden-suppressiven Filters verschwindet.In step S1 of the iteration, a first filter signal y _p (t) and a second filter signal y _m (t) are determined for the current point in time t based on the following equations (5a) and (5b): $$y_p\left(t\right)=x\left(t\right)+x\left(t-T_c\right)$$

$$y_m\left(t\right)=x\left(t\right)+x\left(t-T_c\right)$$

$T_c=\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{${ƒ}_c$}\right.$

is the current period. The first filter signal y _p (t) represents the output of a period-constructive filter and the second filter signal y _m (t) represents the output of a period-suppressive filter. If the fundamental frequency ƒ ₀ of the signal matches the current frequency ƒ _c , the output of the period-constructive filter is twice the input, while the output of the period-suppressive filter vanishes.

3 clarifies the transfer function |H| and the phase Φ/2π of the period constructive filter and the period suppressive filter according to equations (5a) and (5b) above. The transfer function |H| is in 3 is represented along the left ordinate, while the phase is along the right ordinate. The solid lines LP and LP' refer to in 3 to the period constructive filter providing the first filter signal, whereas the dashed lines LM and LM' refer to the period suppressive filter providing the second filter signal. The line LP represents the transfer function of the period constructive filter and the line LP' its phase. In contrast, the line LM represents the transfer function of the period-suppressive filter and the line LM' its phase.

der Filtersignale kleiner als für den Fall, dass ƒ_c und ƒ₀ übereinstimmen. Dieses Verhältnis nimmt ab, je größer der Unterschied zwischen ƒ_c und ƒ₀ ist. Aus 3 erkennt man ferner, dass die Phasendifferenz zwischen dem ersten Filtersignal y_p(t) (Linie LP') und dem zweiten Filtersignal y_m(t) (Linie LM') +90° ist, wenn ƒ₀ kleiner als ƒ_c, ist, wohingegen die Phasendifferenz im Falle, dass ƒ₀ größer als ƒ_c ist, +90° beträgt. Es tritt somit ein Sprung in den Phasendifferenzen auf, wenn ƒ₀ = ƒ_c gilt. Dieser Sprung tritt sowohl bei der Grundfrequenz als auch bei deren Harmonischen auf.If the fundamental frequency ƒ ₀ in the time signal is less than the current frequency ƒ _c (indicated by the frequency ƒ _0.1 in 3 ) or if the fundamental frequency ƒ ₀ is greater than the current frequency ƒ _c (indicated by the frequency ƒ _0.1 in 3 ), is the ratio of the amplitudes $\left|\frac{y_p\left(t\right)}{y_m\left(t\right)}\right|$

of the filter signals is smaller than if ƒ _c and ƒ ₀ match. This ratio decreases as the difference between ƒ _c and ƒ ₀ increases. Out of 3 one can also see that the phase difference between the first filter signal y _p (t) (line LP') and the second filter signal y _m (t) (line LM') is +90° when ƒ ₀ is smaller than ƒ _c , whereas the phase difference in case ƒ ₀ is larger than ƒ _c is +90°. A jump in the phase differences thus occurs when ƒ ₀ = ƒ _c applies. This jump occurs at both the fundamental frequency and its harmonics.

According to the invention, the above phase difference is used as a control signal in order to iteratively approximate the current frequency ƒ _c to the fundamental frequency ƒ ₀ in the signal x(t). As described in more detail below, the current frequency ƒ _c is reduced when the phase difference is positive, whereas it is increased when the phase difference is negative.

Before the control signal is calculated, in the embodiment described here, steps S2 and S3 of 1 carried out. In step S2 of the iteration, a smoothed first filter signal y _p,SI and a smoothed second filter signal y _m,SI according to the smoothing based on the above Equations (4a) to (4c) determined. The time constant τ of the low-pass IIR filter lp _τ (·) was set to 1.0 · T _c . Then, in step S3, the HNR ratio (HNR = Harmonics to Noise Ratio) is determined for these smoothed filter signals, which is given as follows: $$HNR\left(t\right)=\frac{{〈{\left|y_{p,SI}\left(t\right)\right|}^2〉}_{\mathrm{\tau }}}{{〈{\left|y_{p,SI}\left(t\right)\right|}^2〉}_{\mathrm{\tau }}}$$

In this case, 〈·〉 _τ again designates smoothing with the low-pass IIR filtering according to equation (4b) above, with the time constant being set to τ=0.5·T _c . In the embodiment described here, the HNR ratio itself has been smoothed again using the low-pass IIR filtering according to equation (4b) above, with the time constant set to τ=0.05*T _c .

The HNR ratio determined according to step S3 provides information as to whether the current frequency ƒ _c is converging toward the fundamental frequency ƒ ₀ . This is the case when the HNR ratio stabilizes at a constant value significantly greater than 0. This information can be used to identify the current frequency ƒ _c as the fundamental frequency ƒ ₀ , as will be explained further below.

After the HNR ratio has been determined, the control signal cs(n) is calculated in step S4 of the iteration. It is essential that the control signal indicates whether the phase difference between the filter signal y _p,SI (t) and the filter signal y _m,SI (t) is positive or negative. In the case of a negative phase difference, the actual fundamental frequency ƒ ₀ is larger than ƒ _c , whereas in the case of a positive phase difference, the actual fundamental frequency ƒ ₀ is smaller than ƒ _c . This means that in the case of a negative phase difference the frequency ƒ _c must be increased and in the case of a positive phase difference the frequency ƒ _c must be decreased in order to approach the fundamental frequency ƒ ₀ of the signal.

$$adc\left(n\right)=arg\left(c\left(n\right)\cdot c*\left(n-1\right)\right)$$

$$cs\left(n\right)={\langle adc\left(n\right)\rangle }_{\mathrm{\tau }}$$

The above phase difference or the corresponding control signal cs(n) is determined in the embodiment described here based on the following equations: $$c\left(n\right)=y_{p,SI}\left(n\right)+i{y}_{m,SI}\left(n\right)$$

$$a\mathrm{i.e}c\left(n\right)=a\mathrm{right}G\left(c\left(n\right)\cdot c*\left(n-1\right)\right)$$

$$cs\left(n\right)={〈a\mathrm{i.e}c\left(n\right)〉}_{\mathrm{\tau }}$$

In the above equations, n denotes the current iteration loop or the current point in time in the time signal and n-1 denotes the previous iteration loop or the previous point in time in the time signal. According to the above equation (7a), a complex number is formed which includes the filter signal y _p,SI (n) as the real part and the filter signal y _m,SI (n) as the imaginary part. Multiplying this complex number by its complex conjugate at the previous time indicates whether the complex number vector is moving counter-clockwise (positive phase difference) or clockwise (negative phase difference). Accordingly, the sign of the variable adc(n) indicates whether there is a positive phase difference (positive sign) or a negative phase difference (negative sign). In this case, the control signal is the variable adc(n) after smoothing has been carried out with the time constant τ, the smoothing in turn being carried out using the low-pass IIR filter described above in accordance with equation (4b). In the exemplary embodiment described here, the time constant τ for smoothing adc(n) was set to 0.1*T _c .

wobei ƒa der Faktor, ƒ_s die Abtastfrequenz des digitalen Zeitsignals x(t) und ƒ_c die aktuelle Frequenz ist.The information about the positive and negative phase difference is used in step S4 to adapt ƒ _c . In general, ƒ _c is increased in the case of a negative phase difference and reduced in the case of a positive phase difference. In the exemplary embodiment described here, this enlargement or reduction is achieved using a factor which is greater than one. In the case of a negative phase difference, ƒ _c is multiplied by the factor, whereas in the case of a positive phase difference, ƒ _c is divided by the factor. Appropriate choice of this factor is within the skill of the art. In a preferred variant, the factor is selected as follows: $$ƒ{\text{a=2}}^{1/16\cdot {ƒ}_c/{ƒ}_s}$$

where ƒa is the factor, _ƒs is the sampling frequency of the digital time signal x(t) and _ƒc is the current frequency.

After appropriate adaptation of the frequency ƒ _c in step S4, a new iteration loop is started with step S1, the frequency previously determined in step S4 now being used as the new current frequency ƒ _c .

In the event that the HNR ratio stabilizes at a higher value, it can be assumed that the current frequency corresponds to the fundamental frequency. In one embodiment of the invention, this can be used in such a way that if the HNR ratio in the current iteration loop or possibly in the current and several previous iteration loops exceeds a predetermined threshold value, the current frequency ƒ _c is identified as the fundamental frequency ƒ ₀ and is output, for example, via a corresponding user interface.

The method described above was tested by the inventor using a number of simulated time signals. It could be proven that the basic frequencies contained in the corresponding time signal can be recognized well. An example is the result of a corresponding simulation in 4 played back. This figure shows a total of six diagrams DI1, DI1', DI2, DI2', DI3 and DI3'. All diagrams refer to the processing of a signal in the form of a harmonic complex tone with a duration of 400 ms and a fundamental frequency ƒ ₀ which changes abruptly from 98.5 Hz to 101 Hz at 200 ms. Diagrams DI1 and DI1' relate to a signal with a signal-to-noise ratio of 21.5 dB, diagrams DI2 and DI2' to a signal with a signal-to-noise ratio of 7.5 dB and diagrams DI3 and DI3' to a signal with a signal-to-noise ratio of 1.5 dB. In other words, the signal-to-noise ratio of the signals increases 4 from the left to the right diagrams. The upper diagrams DI1 to DI3 show the development of the frequency ƒ _c over time, which is extracted from the corresponding signal using a variant of the method according to the invention. The difference between ƒ _c and the frequency value ƒ _0,min = 96 Hz is shown. The lower diagrams DI1' to DI3' show the development of the HNR ratio over time, which is obtained from the corresponding signal with the variant of the method according to the invention.

As can be seen very clearly from the diagrams DI1 to DI3 above, the method very quickly converges to the fundamental frequency of 98.5 Hz (ƒ _c - ƒ _0,min = 2.5 Hz) contained in the signal. The abrupt frequency change at 200 ms to 101 Hz is also very well recognized (ƒ _c - ƒ _0,min = 5 Hz). Furthermore, the lower diagrams DI1' to DI3' clearly show that the HNR ratio drops briefly when the frequency changes and then quickly stabilizes again at a high level. In addition, in 4 clear that the method recognizes the corresponding fundamental frequencies even with poor signal quality and a low signal-to-noise ratio.

The embodiment of the method according to the invention described above has a number of advantages. In particular, the method approaches the fundamental frequencies of periodic signal components in the processed time signal very quickly. Discontinuities in the periodicity of the signal are easily recognized by a drop in the determined HNR ratio. In addition, the method is robust against noise in the processed time signal, i.e. even with a poor signal-to-noise ratio, the method adjusts to the corresponding fundamental frequencies.

Claims (12)

Method for analyzing a time signal ((x(t)) with periodic signal components, in which frequencies and the signal parameters (HNR) assigned to the frequencies are determined for successive points in time in the time signal ((x(t)) by means of one or more iterations, starting from a initial frequency (ƒ _c,0 ) are extracted from the time signal ((x(t)), the following steps being carried out for a current frequency (ƒ _c ) in a current iteration loop of a respective iteration for a current point in time of the successive points in time a ) Determining a first filter signal (y _p ) and a second filter signal (y _m ) based on an input signal which is the time signal ((x(t)) or a smoothed time signal, the first filter signal (y _p ) being the sum of the represents the input signal at the current time and the input signal at the time which is one period according to the current frequency (f _c ) before the current time, and wob ei the second filter signal (y _m ) represents the difference between the input signal at the current time and the input signal at the time which is one period according to the current frequency (ƒ _c ) before the current time; b) Determination of the signal parameter (HNR) for the current frequency (ƒ _c ) as a quantity representing the ratio or the smoothed ratio of a signal strength measure or a smoothed signal strength measure of the first filter signal (y _p ) or a smoothed first filter signal (y _p,SI ) to a signal strength measure or indicates a smoothed signal strength measure of the second filter signal (y _m ) or a smoothed second filter signal (y _m,SI ); c) determining a control signal (cs(n)) which indicates whether a phase difference is positive or negative, the phase difference being the phase difference or a smoothed phase difference between the first filter signal (y _p ) or the smoothed first filter signal (y _p,SI ) and the second filter signal (y _m ) or the smoothed second filter signal (y _m,SI ); d) modification of the current frequency (ƒ _c ) by increasing it when the control signal (cs(n)) indicates a negative phase difference and decreasing it when the control signal (cs(n)) indicates a positive phase difference, where the modified frequency is used as the current frequency (ƒ _c ) in the next iteration loop. procedure after claim 1 , characterized in that in the event that the signal parameter (HNR) in the current iteration loop or over a plurality of iteration loops comprising the current iteration loop and a predetermined number of earlier iteration loops or the signal parameter (HNR) averaged over the plurality of iteration loops exceeds a predetermined threshold value, the current frequency (ƒ _c ) is identified as a fundamental frequency (ƒ _o ) in the time signal ((x(t))). procedure after claim 1 or 2 , characterized in that the smoothed time signal and/or the smoothed first filter signal (y _p,SI ) and/or the smoothed second filter signal (y _m,SI ) and/or the smoothed ratio and/or the smoothed signal strength measure of the first filter signal ( y _p ) or the smoothed first filter signal (y _p,SI ) and/or the smoothed signal strength measure of the second filter signal (y _m ) or the smoothed second filter signal (y _m,SI ) and/or the smoothed phase difference by means of smoothing based on a Low-pass IIR filter can be determined. Method according to one of the preceding claims, characterized in that the current frequency (ƒ _c ) in step d) is modified by a factor greater than one, the current frequency (ƒ _c ) being multiplied by the factor to increase it and being reduced the current frequency (ƒ _c ) this is divided by the factor. procedure after claim 4 , characterized in that the factor depends on the current frequency (ƒ _c ) and becomes greater the greater the current frequency (ƒ _c ). Method according to one of the preceding claims, characterized in that the control signal is determined in step c) as follows: $$c\left(n\right)=y_1\left(n\right)+i{y}_{\mathrm{e.g}}\left(n\right)$$

$$a\mathrm{i.e}c\left(n\right)=a\mathrm{right}G\left(c\left(n\right)\cdot c*\left(n-1\right)\right)$$

$$cs\left(n\right)={〈a\mathrm{i.e}c\left(n\right)〉}_{\mathrm{\tau }}\text{or}cs\left(n\right)=a\mathrm{i.e}c\left(n\right)$$

where n represents the current point in time and n - 1 represents the point in time of the last iteration loop of the respective iteration lying before the current point in time; where y ₁ (n) is the first filter signal (y _p ) or the smoothed first filter signal (y _p,SI ) in the current iteration loop; where y ₂ (n) is the second filter signal (y _n ) or the smoothed second filter signal (y _m,SI ) in the current iteration loop; where cs(n) is the control signal (cs(n)) in the current iteration loop; where 〈adc(n)〉 is a smoothed value of adc(n). Method according to one of the preceding claims, characterized in that several iterations are carried out simultaneously, each iteration having a different initial frequency. Method according to one of the preceding claims, characterized in that the method is used to process an acoustic signal as a time signal (x(t)) and the initial frequency of a respective iteration is between 80 Hz and 400 Hz. Device for analyzing a time signal ((x(t)) with periodic signal components, the device being set up for carrying out a method in which frequencies and the frequencies associated signal parameters (HNR) are extracted from the time signal ((x(t)) starting from an initial frequency (ƒ _c,0 ), whereby for a current frequency (ƒ _c ) in a current iteration loop of a respective iteration for a current point in time the the following steps are carried out at successive points in time: a) determining a first filter signal (y _p ) and a second filter signal (y _m ) based on an input signal which is the time signal ((x(t)) or a smoothed time signal, the first Filter signal (y _p ) represents the sum of the input signal at the current time and the input signal at the time one period according to the current frequency (ƒ _c ) before the current time, and the second filter signal (y _m ) represents the difference between represents the input signal at the current time and the input signal at the time which represents a period according to the current frequency (ƒ _c ) before the current time pu not lying; b) Determination of the signal parameter (HNR) for the current frequency (ƒ _c ) as a quantity representing the ratio or the smoothed ratio of a signal strength measure or a smoothed signal strength measure of the first filter signal (y _p ) or a smoothed first filter signal (y _p,SI ) to a signal strength measure or a smoothed signal strength measure of the second filter signal (y _m ) or a smoothed second filter signal (y _m,SI ); c) determining a control signal (cs(n)) which indicates whether a phase difference is positive or negative, the phase difference being the phase difference or a smoothed phase difference between the first filter signal (y _p ) or the smoothed first filter signal (y _p,SI ) and the second filter signal (y _m ) or the smoothed second filter signal (y _m,SI ); d) modification of the current frequency (ƒ _c ) by increasing it when the control signal (cs(n)) indicates a negative phase difference and decreasing it when the control signal (cs(n)) indicates a positive phase difference, where the modified frequency is used as the current frequency (ƒ _c ) in the next iteration loop. device after claim 9 , characterized in that the device for carrying out a method according to one of claims 2 until 8th is set up. Computer program product with a program code stored on a machine-readable carrier for carrying out a method according to one of Claims 1 until 8th , if the program code is run on a computer. Computer program with a program code for carrying out a method according to one of Claims 1 until 8th , if the program code is run on a computer.

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