JP2006166375A - Howling canceller - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a howling canceller equipped with an adaptive filter that distinguishes a sustained sound of a musical sound with constant frequency from a howling, and does not attenuate an input signal by the musical sound. <P>SOLUTION: A waveform analyzing unit 8 performs a fast Fourier-transform on an audio signal inputted from a microphone 1 to detect a peak frequency and a harmonic frequency. Then, it compares them with a howling waveform pattern stored in a waveform storage unit 9. A cross-correlation function of both waveforms is calculated. When a cross-correlation value is a predetermined threshold or more, it is determined that the audio signal is a howling. When the value is the threshold or less, it is determined that the audio signal is not a howling. When the audio signal is determined not to be a howling, the adaptive filter 7 is instructed to suspend adaptive processing. This enables the suppression of only howling without canceling the sustained sound of a musical sound with constant frequency. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention relates to a howling canceller that suppresses howling without reducing musical sound in a loudspeaker system installed in a lecture hall or hall.

  In general, when a loudspeaker is used in a lecture hall, a hall, or the like, sound output from a speaker is input to a microphone again through an acoustic path having a certain transfer function. That is, a closed loop is formed by the path of microphone-amplifier-speaker-acoustic path-microphone. When the gain of the closed loop exceeds 1, the sound returned from the speaker to the microphone increases, and howling occurs.

  In order to efficiently prevent this howling, a howling canceller that uses an adaptive filter (adaptive digital filter) to prevent howling has been proposed (for example, see Non-Patent Document 1).

  FIG. 6 is a view showing the above howling canceller. The microphone 101 and the speaker 104 are installed in the same acoustic space such as a lecture hall or a hall. Here, the audio signal input from the microphone 101 is amplified by a front-end microphone amplifier and then converted into a digital signal y (k) by an A / D converter.

  The signal y (k) is supplied to the amplifier 103 via the adder 102 and amplified. G (z) is a transfer function of the amplifier 103. The signal x (k) output from the amplifier 103 is sounded from the speaker 104 after being converted into an audio signal by the D / A converter.

  The sound generated from the speaker 104 returns to the microphone 101 via the acoustic feedback path 105. The acoustic return path 105 is an acoustic path from the speaker 104 to the microphone 101. H (z) is a transfer function of the acoustic feedback path 105. A feedback signal d (k) fed back through the acoustic feedback path 105 is input to the microphone 101 together with a sound source signal s (k) generated by a sound source such as a speaker. The microphone 101 converts the input voice into a digital signal and outputs it as y (k).

  In such a loudspeaker, a closed loop is formed by the path of the microphone 101 -the amplifier 103 -the speaker 104 -the acoustic feedback path 105 -the microphone 101. When the gain of the closed loop exceeds 1, the feedback signal d (k) is increased and howling occurs. The loudspeaker shown in FIG. 1 has a howling canceller including a delay circuit 106, an adaptive filter 107, and an adder 102 in order to prevent the occurrence of such howling.

  The delay circuit 106 gives a delay time τ corresponding to the time delay of the acoustic feedback path 105 to the output signal x (k) of the amplifier 103 and outputs it to the adaptive filter 107 as a signal x (k−τ). The adaptive filter 107 includes a filter unit 107a and a filter coefficient estimation unit 107b as shown in FIG. 7, and the signal x (k−τ) is input to both the filter unit 107a and the filter coefficient estimation unit 107b. .

  In the filter unit 107a, the filter coefficient is set so that the signal input from the microphone 101 is attenuated by the transfer function F (z) simulating the transfer function H (z) of the acoustic feedback path 105. Therefore, the signal do (k) output from the adaptive filter 107 is a signal obtained by filtering the signal x (k−τ) with the transfer function F (z) simulating the transfer function H (z) of the acoustic feedback path 105. Therefore, the feedback signal d (k) transmitted from the speaker 104 through the acoustic feedback path 105 and re-input to the microphone 101 is simulated.

  The adder 102 is a signal do (k) simulating the feedback signal d (k) from the signal y (k) input from the microphone 101 (where y (k) is a signal obtained by adding the sound source signal and the feedback signal). ) Is subtracted. Thereby, the feedback signal is removed from the input signal, and howling can be canceled.

The filter coefficient estimating unit 107b uses an adaptive algorithm so that the transfer function F (z) matches or approximates the transfer function H (z) based on the signals x (k−τ) and e (k). Are sequentially updated. As a result, a signal do (k) simulating the signal d (k) is obtained, and howling can be prevented.
Inazumi, Imai, Konishi: "Preventing howling in loudspeakers using the LMS algorithm", Proc. 417-418 (1991, 3)

  By the way, although howling appears as a high-level signal of a sine wave (pure tone) having a constant frequency, the howling canceller described in Non-Patent Document 1 adapts a filter to this howling and attenuates the frequency peak of the signal. A simulation signal do (k) is generated. That is, the howling canceller determines that a component similar to the signal delayed by the delay circuit 106 among the signals input from the microphone is a feedback signal, and updates the filter coefficient of the adaptive filter so as to attenuate it. Therefore, the howling canceller can prevent the howling by canceling the feedback signal before the howling, and can also quickly attenuate the howling sound when the howling occurs.

  As described above, the howling canceller with a built-in adaptive filter has a characteristic in which a component similar to a delayed signal among signals input from the microphone is regarded as a feedback signal and attenuated. For this reason, for example, musical tones of musical instruments that emit continuous sounds such as violins and flutes are high-level signals that are close to pure tones with a constant frequency similar to howling signals, and are therefore sound source signals (source sounds) input from a microphone. However, there was a problem that it was canceled by the howling canceller.

  An object of the present invention is to provide a howling canceller including an adaptive filter that distinguishes between a continuous sound of a musical tone having a constant frequency and a howling, and attenuates only howling without attenuating the input due to the musical tone, in view of the above circumstances. To do.

  The invention according to claim 1 is a howling canceller including an adaptive filter that estimates a transfer function of an acoustic feedback path from a speaker to a microphone and cancels a feedback audio signal from an input signal of the microphone, and has a constant frequency. When a peak signal, which is a signal having a peak value, is input, an input signal determination means for determining whether or not the peak signal is an input signal based on a musical sound, and a peak signal is input, and the input signal determination means And control means for controlling the adaptive filter so as not to cancel the input signal when it is determined that the input signal is a musical sound.

  In the present invention, there is provided an input signal determining means for determining whether or not the audio signal input from the microphone is an input signal based on a musical sound. The input signal determination means determines whether or not the input signal is an input signal based on a musical sound when a continuous sound having a constant frequency is detected. When it is determined that the input signal is a musical sound, the adaptive filter is set so as not to cancel the signal input from the microphone. The filter coefficient is updated so that the process of the adaptive filter is stopped or the adaptive process of the adaptive filter is slowed down.

  According to a second aspect of the present invention, in the above invention, when the peak signal is input, the input signal determination means determines whether the peak signal is howling by determining whether or not the peak signal is howling. It is characterized by determining whether or not there is.

  In this invention, the input signal determination means determines whether or not the input signal is an input signal by howling when a continuous sound having a constant frequency is detected. When it is determined that it is not an input signal by howling, it is determined that the input signal is an input signal by musical sound.

  According to a third aspect of the present invention, in the above invention, the input signal determining means determines whether or not the peak signal is a tone or howling by comparing the peak signal with a reference waveform pattern. And

  In the present invention, a signal input from a microphone is compared with a reference waveform. The reference waveform is a musical tone waveform, a howling waveform, or the like. In the comparison method, for example, a cross-correlation function between a signal input on the time axis and a reference waveform is calculated, and the calculation result is used. What is necessary is just to calculate the product sum of an input signal waveform and a reference waveform in a predetermined time domain. If the value of the cross-correlation function is large, it can be determined that the reference waveform is approximated. Also, the audio signal input from the microphone is subjected to fast Fourier transform (hereinafter referred to as FFT) to obtain a peak frequency at which the sound pressure value shows a peak and a harmonic frequency of the frequency, and a frequency spectrum of the waveform of the input signal and a reference You may compare the frequency spectrum of a waveform. As a comparison method, a pattern matching technique such as HMM (Hidden Markov Model) is used. As a result, it is determined whether or not the input signal is an input signal based on a musical sound.

  According to a fourth aspect of the present invention, in the above invention, the input signal determining means sets a predetermined threshold value for the peak width value at the peak frequency of the frequency spectrum of the input signal, and based on the peak width value, It is characterized by determining whether a peak signal is a musical sound or howling.

  In the present invention, an audio signal input from a microphone is subjected to FFT, a peak frequency and its harmonic frequency are obtained, and a peak width is obtained. A predetermined threshold is set for the peak width, and if the peak width is larger than the threshold, it is determined that the input signal is a musical sound and the input signal is not canceled. If the peak width is smaller than the threshold, the signal is close to a sine wave, so that it is determined as howling.

  As described above, according to the present invention, the input peak signal is distinguished from the input signal by howling by determining whether or not the input peak signal is a musical sound. By not canceling, it is possible to suppress only howling without suppressing a continuous tone of a constant frequency.

  DESCRIPTION OF EMBODIMENTS Hereinafter, a loudspeaker system with a built-in adaptive howling canceller according to an embodiment of the present invention will be described in detail with reference to the drawings.

  FIG. 1 is a block diagram of a loudspeaker system with an adaptive howling canceller. As shown in the figure, the microphone 1, the adder 2, the amplifier 3, the speaker 4, the acoustic feedback path 5, the delay circuit 6, the adaptive filter 7, the waveform analysis unit 8, and the waveform storage unit 9. 4 is arranged in a lecture hall or hall. The audio signal input via the microphone 1 is converted into a digital signal y (k) by A / D conversion processing and input to the amplifier 3 via the adder 2. The amplifier 3 is for amplifying the input signal y (k). G (z) is a transfer function of the amplifier 3.

  The signal x (k) output from the amplifier 3 is converted into an analog audio signal by D / A conversion processing, and sounds are produced from the speaker 4. The sound produced from the speaker 4 returns to the microphone 1 via the acoustic return path 5. The acoustic return path 5 is an acoustic path from the speaker 4 to the microphone 1. H (z) is a transfer function of the acoustic feedback path 5. A feedback signal d (k) fed back through the acoustic feedback path 5 is input to the microphone 1 together with a sound source signal s (k) generated by a sound source such as a speaker. The microphone 1 converts the input voice into a digital signal and outputs it as y (k).

  The signal x (k) output from the amplifier 3 is also input to the delay circuit 6. The delay circuit 6 gives a time delay to the input signal x (k) and outputs it. Here, the delay circuit 6 gives a time delay τ that estimates the time delay of the feedback signal fed back from the speaker 4 to the microphone 1. To do. The signal x (k−τ) output with the time delay τ given by the delay circuit 6 is input to the adaptive filter 7.

As shown in FIG. 2, the adaptive filter 7 includes a filter unit 7a and a filter coefficient estimation unit 7b. The filter unit 7a and the filter coefficient estimation unit 7b each receive a signal x (k−τ) output from the delay circuit 6. ) Is entered. The filter unit 7a outputs a signal do (k) simulating the feedback signal d (k) from the speaker 4 to the microphone 1, and receives the feedback signal d (k) from the signal y (k) re-input from the microphone 1. The simulated signal do (k) is subtracted. A signal do (k) simulating the feedback signal d (k) is determined based on the signal x (k−τ) output from the delay circuit 6 according to the transfer function F (z). The filter coefficient estimation unit 7b uses the signal x (k−τ) output from the delay circuit 6 and the signal do (k) simulating the feedback signal d (k) among the signals transmitted from the microphone 1 to the amplifier 3. Based on the subtracted signal e (k), an adaptive algorithm is used to filter the filter coefficient of the filter unit 7a so that the signal do (k) simulating the feedback signal matches or approximates the actual feedback signal d (k). Is to be updated. As the adaptive algorithm, for example, an LMS (Least Mean Square) algorithm is used. If the root mean square value of the signal e (k) is J = E [e (k) ² ] (where E [•] is an expected value), a filter coefficient that minimizes J is estimated by calculation. The filter coefficient of the filter unit 7a is updated using the estimated filter coefficient.

  If the delay circuit 6 is not provided, the signal input to the microphone 1 is input to the adder 2 and also input to the adaptive filter 7 without delay. Since the adaptive filter 7 updates the filter coefficient so as to reduce the error signal e (k), the signal input from the microphone is canceled by the output signal of the adaptive filter 7 in the adder 2 as the filter coefficient is updated. Will come to be. Therefore, the delay circuit 6 is indispensable in order to cancel the feedback signal d (k) by the signal do (k) while preventing cancellation of the sound source signal s (k).

  As described above, the adaptive filter 7 simulates the feedback signal d (k) among the signal x (k−τ) output from the delay circuit 6 and the signal y (k) transmitted from the microphone 1 to the amplifier 3. Since the filter coefficient is updated based on the signal e (k) obtained by subtracting the signal do (k), it is possible to cancel the signal d (k) among the signals input from the microphone 1. When the gain of the closed loop formed by the path of microphone 1 -amplifier 3 -speaker 4 -acoustic feedback path 5 -microphone 1 exceeds 1, the sound pressure value of a certain frequency in the feedback signal d (k) passes over time. It increases along with this to form a peak on the frequency spectrum, resulting in howling. The adaptive filter 7 updates the filter coefficient so as to attenuate this peak, and the generated simulated signal do (k) is used as the input signal y. Subtract from (k). Accordingly, when the signal y (k) obtained by adding the sound source signal s (k) input from the microphone and the feedback signal d (k) is a continuous sound having a constant frequency, the filter coefficient is sequentially updated to obtain the continuous sound. Can be attenuated.

  The waveform analyzer 8 performs FFT on the signal y (k) input from the microphone 1 to obtain a signal Y (f). Further, the peak frequency is detected for the FFTed signal Y (f). As a method for detecting the peak frequency, for example, a peak frequency may be set as a maximum frequency in a frequency region where the sound pressure value is equal to or greater than a predetermined threshold. Further, the lowest peak frequency among the detected peak frequencies is set as a primary peak of the input signal, and a frequency that is an integral multiple of the primary peak is set as a harmonic peak.

  When the detected peak frequency is continuously input for a predetermined time or longer, the spectrum shape near each peak frequency is analyzed to determine whether the signal Y (f) is a signal due to howling. If it is determined that the signal is not due to howling, it is determined that the signal is a continuous tone of music and the adaptive filter 7 is instructed not to cancel the signal input from the microphone 1. Here, the filter unit 7b of the adaptive filter 7 shown in FIG. 2 is set to stop updating the filter coefficient.

  The input signal analysis method is performed in the following two modes.

[First aspect]
FIG. 3 is a flowchart showing the operation of the first mode of the analysis method. The waveform analyzer 8 starts this operation when a signal is input to the microphone 1. As shown in the figure, the waveform analyzer 8 first takes in the signal y (k) input from the microphone 1 and performs FFT (s1). Further, the waveform of the FFTed signal Y (f) is examined to detect the peak frequency (s2). Thereafter, it is determined whether or not the peak frequency has been detected (s3). If the peak frequency cannot be detected, the process is repeated from the input signal capture (s3 → s1). Further, it is determined whether or not the peak frequency is continuously generated for a predetermined time (s4). If the peak frequency does not continue for a predetermined time or longer, the process is repeated from the input signal capture (s4 → s1).

  When the peak frequency is detected and continues for a predetermined time or longer, sine waveform data corresponding to the detected peak frequency is read from the waveform storage unit 9 as a storage device (s5). Note that the sine waveform data may be calculated instead of being read from the waveform storage unit 9. Thereafter, the waveform of the signal input from the microphone 1 and the cross-correlation function are calculated (s6). The cross-correlation function may be calculated for a signal that has passed through a frequency bandpass filter corresponding to the peak frequency detected for the input signal. In addition to the detected peak frequency, the calculation may be performed for the harmonic peak frequency. The waveform storage unit 9 may be any type as long as it can store waveform data. For example, a flash memory or the like may be used. In addition, when calculating sine waveform data, the waveform storage unit 9 may be omitted.

  The cross-correlation function represents the degree of similarity between two signals, and approaches zero when the two signals are completely different. Since the howling waveform is a continuous sound with a constant frequency, the correlation with the sine waveform is high. Therefore, when the value of the cross-correlation function with the sine waveform is large, it can be determined that the signal is due to howling. When the value of the cross-correlation function is small, it can be determined that the signal is not due to howling. Here, a predetermined threshold value is set for the value of the cross-correlation function, and when it is equal to or greater than the threshold value, it is determined that the signal is due to howling, and the analysis operation is stopped. (S7). Instead of obtaining the value of the cross-correlation function with the sine waveform, the cross-correlation function with the tone waveform may be found to determine whether the signal is a tone signal. In this case, when it can be determined that the signal is a musical sound, it may be determined that it is not howling.

  If it is determined that the signal is not a howling signal, the adaptive filter 7 is set so as not to cancel the input signal (s8). Here, the adaptive filter 7 is instructed to stop the adaptive processing so as not to reduce the frequency components of the detected primary peak and harmonic peak. In addition, you may make it set so that the adaptive process of the adaptive filter 7 may be blunted.

  The transfer function of the adaptive filter 7 is represented by F (z), and this transfer function is updated with a coefficient called a forgetting coefficient λ or a step size α. The forgetting factor λ is a factor that multiplies the transfer function so far, and is set in the range of 0-1. If the forgetting factor λ is reduced, the transfer function up to that point is deleted and the update is promoted. The step size α is a coefficient representing the magnitude of correction. When the step size α is increased, the corrected transfer function is used more and the update is promoted. The corrected transfer function F ′ (z) is expressed by the following formula: F ′ (z) = λF (z) + αΔF (z) (where ΔF (z) is a filter difference).

  Therefore, when it is determined that it is not howling, the values of the forgetting factor λ and the step size α are set to around zero. When the values of the forgetting factor λ and the step size α are set to 0, the transfer function F ′ (z) is close to 0, and the output signal do (k) of the adaptive filter 7 is also close to 0. Therefore, the input signal y (k) from the microphone 1 is not canceled. Further, the value of the forgetting factor λ may be increased and the value of the step size α may be decreased. When the value of the forgetting factor λ is increased and the value of the step size α is decreased, the transfer function is not updated, so that it is possible to prevent the continuous sound input signal from being reduced.

  When a certain primary peak is determined to be a musical sound, the determination process for the harmonic peak may be omitted. As a method for calculating the similarity between two signals, a pattern matching method such as an HMM may be used instead of the cross-correlation function. In this case, it may be determined whether or not the signal is due to howling compared to the sine waveform data, or it may be determined whether or not the signal is based on musical sound compared to the waveform data of musical sound.

[Second embodiment]
FIG. 4 is a flowchart showing the operation of the second mode of the analysis method. The waveform analyzer 8 starts this operation when a signal is input to the microphone 1. As shown in the figure, first, a signal input from the microphone 1 is captured, and a frequency spectrum is calculated by FFT (s9). The calculated frequency spectrum is examined to detect the peak frequency (s10). Thereafter, it is determined whether or not the peak frequency has been detected (s11). If the peak frequency cannot be detected, the process is repeated from the input signal capture (s11 to s9). Further, it is determined whether or not the peak frequency is continuously generated for a predetermined time or more (s12). If the peak frequency does not continue for a predetermined time or more, the process is repeated from the input signal capture (s12 → s9).

  When the peak frequency is detected and continues for a predetermined time or longer, the frequency of the peak shape at a sound pressure value lower than the peak sound pressure value by a predetermined value from the peak shape corresponding to the detected peak frequency in the frequency spectrum The peak width which is the width of is calculated (s13).

  FIG. 5 is a diagram for explaining the frequency spectrum. As shown in FIG. 6A, the sound pressure value at the detected peak frequency is acquired, and a peak width calculation sound pressure value that is a sound pressure value lower than the peak sound pressure value by a predetermined value is calculated. The peak width calculation sound pressure value may be set in any way, but may be, for example, a half value of the peak sound pressure value. The frequency width of the peak shape in this sound pressure value is calculated, and this frequency width is set as the peak width.

  The smaller the calculated peak width, the steeper peak spectral shape. Since the howling waveform is close to a sine waveform, the peak width is small, and the peak shape of the frequency spectrum at the peak frequency is steep. Therefore, a predetermined threshold value is set for the peak width, and when it is less than the threshold value, howling is determined and the analysis operation is stopped (s14 → END). (S14).

  If it is determined that it is not howling, the adaptive filter 7 is corrected so as not to cancel the input signal (s15). Also in this example, the adaptive filter 7 is instructed to stop the adaptive processing so as not to reduce the frequency component of the detected peak frequency. In addition, you may make it set so that the adaptive process of the adaptive filter 7 may be blunted. As described above, the value of the forgetting factor λ and the step size α may be set close to 0, or the value of the forgetting factor λ may be increased so as not to update the transfer function, and the value of the step size α may be set small. As a result, it is possible to prevent the continuous sound input signal from being reduced.

  In addition to the two modes described above, for example, howling may be determined based on the left-right symmetry of the peak waveform of the frequency spectrum. Since the howling waveform has high left-right symmetry around the peak frequency, it can also be determined whether or not it is howling. Moreover, you may investigate distribution of deviation. As shown in FIG. 5B, in a predetermined frequency width centered on the peak frequency, the total value of the values obtained by multiplying the square value of the deviation from the peak frequency at each frequency by the sound pressure value is determined as the variation value. To do. Since the howling waveform has a steep peak shape of the frequency spectrum, the variation value is small. Therefore, if the variation value is small, it can be determined that howling. Any analysis method capable of distinguishing the howling waveform from the musical tone waveform may be used.

  In this embodiment, when the peak frequency is detected and it is determined that it is not howling, the adaptive filter processing is stopped or delayed so that the input signal is not canceled. It is not limited. A band cut filter or the like for attenuating a signal in an arbitrary frequency band may be provided between the adaptive filter and the adder, and control may be performed so as to attenuate the output signal of the adaptive filter according to the detected peak frequency. In this way, it is possible to prevent the adaptive filter from operating in the band of the input musical sound signal.

  As described above, the speech enhancement system with a built-in adaptive howling canceller according to the present invention performs FFT on the audio signal input from the microphone, and determines whether the signal input from the microphone is howling based on the waveform near the peak frequency and the harmonic frequency. If it is determined that it is not howling, the adaptive filter is instructed not to cancel the audio signal. As a result, when a continuous sound having a constant frequency such as a violin is input, it is possible to suppress only howling without canceling the musical sound.

  Further, the input signal is not limited to the input from the microphone, but may be any signal as long as it collects a sound source signal of a speaker such as a vibration sensor. Further, the frequency analysis method is not limited to the FFT described above, and any method may be used as long as it is a method capable of calculating a frequency peak. For example, a band pass filter or the like may be used.

The block diagram which shows the structure of the sounding system with a built-in adaptive howling canceller in this embodiment The figure which shows the structure of the adaptive filter in this embodiment in detail Flowchart showing the operation of the first aspect of the analysis method Flowchart showing the operation of the second mode of the analysis method Diagram explaining frequency spectrum Block diagram showing the configuration of a conventional loudspeaker system The figure which shows the structure of the conventional adaptive filter in detail

Explanation of symbols

1-microphone 2-adder 3-amplifier 4-speaker 5-acoustic feedback path 6-delay circuit 7-adaptive filter 7a-filter unit 7b-filter coefficient estimation unit 8-waveform analysis unit 9-waveform storage unit 101-conventional Microphone 102 in loudspeaker system-Adder 103 in conventional loudspeaker system-Amplifier 104 in conventional loudspeaker system-Speaker 105 in conventional loudspeaker system-Acoustic feedback path 106 in conventional loudspeaker system-Delay circuit 107 in conventional loudspeaker system- Adaptive filter in conventional loudspeaker systems

Claims (4)

A howling canceller including an adaptive filter that estimates a transfer function of an acoustic feedback path from a speaker to a microphone and cancels a feedback audio signal from a microphone input signal,
When a peak signal, which is a signal having a constant frequency, is input, input signal determination means for determining whether or not the peak signal is an input signal based on a musical sound;
Control means for controlling the adaptive filter so as not to cancel the input signal when the peak signal is input and the input signal determination means determines that the peak signal is an input signal based on music;
A howling canceller characterized by comprising   The input signal determining means, when a peak signal is input, determines whether or not the peak signal is a musical sound by determining whether or not the peak signal is howling. Item 3. A howling canceller according to item 1.   3. The howling according to claim 1, wherein the input signal determination unit determines whether the peak signal is a tone or howling by comparing the peak signal with a reference waveform pattern. 4. Canceller.   The input signal determining means sets a predetermined threshold value for the peak width value at the peak frequency of the frequency spectrum of the input signal, and determines whether the peak signal is a musical sound or howling based on the peak width value. The howling canceller according to claim 1 or 2, characterized in that:

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