WO1982003144A1

WO1982003144A1 - Energy band discriminator

Info

Publication number: WO1982003144A1
Application number: PCT/US1982/000228
Authority: WO
Inventors: Electric Co Inc Western; Charles William Kevin Gritton; Timothy James Zebo
Original assignee: Western Electric Co Inc
Current assignee: AT&T Corp
Priority date: 1981-03-05
Filing date: 1982-02-24
Publication date: 1982-09-16
Anticipated expiration: 1983-09-05
Also published as: DE3235915C2; FR2501439B1; DE3235915T1; IT1150253B; NL8220092A; GB2095519A; FR2501439A1; IT8219972A0; GB2095519B

Abstract

Energy in a received signal is distinguished as being whole band energy or partial band energy in an energy discriminator (103) by comparing an average value of the received signal to a modified magnitude value of the received signal. When the modified magnitude value exceeds the average value, the received signal includes whole band energy, otherwise the received signal includes only partial band energy. This technique is employed in an echo canceler (100) to enable updating an echo path estimate during intervals that the received signal includes whole band energy and to inhibit updating of the echo estimate being generated when the received signal includes only partial band energy.

Description

ENERGY BAND DISCRIMINATOR

Technical Field

This invention relates to an energy band discriπinator useable in an echo canceler which comprises an adjustable signal processing circuit coupled to a first transmission path for generating an echo estimate signal, a combining network coupled to a second transmission path for combining a signal in the second path with the echo estimate signal to generate an error signal, first circuitry responsive to the error signal for adjusting the processing circuit, and second circuitry for supplying the error signal to the adjustable processing circuit. Background of the Invention Echoes commonly occur because of imperfect coupling of incoming signals at 4-to-2 wire junctions in communications systems- The echoes typically result because of imperfect impedance matching to the 2-wire facility in the 4-to-2 wire junction causing the incoming signal to be partially reflected over an outgoing path to the source of incoming signals.

Self-adapting echo cancelers have been employed to mitigate the echoes by generating an estimate of the reflected signal or echo and subtracting it from the outgoing signal. The echo estimate is updated in response to the outgoing signal for more closely approximating the echo to be cancelled. Heretofore, the updating of the echo estimate has been inhibited when near end speech signals are being transmitted or when no significant far end energy is being received. However, the echo estimate was allowed ^' to be updated when any significant far end energy was being received, whether it was speech, noise, single frequency tones, multifrequency tones or the like.

It has been determined that allowing the canceler to update the echo estimate during intervals that the received far end signal includes energy occupying only a portion of a frequency band of interest, for example, a single frequency tone, multifrequency tone or the like (hereinafter designated parti'al.- band energy), results in an undesirable condition of the communications circuit including the canceler. Specifically, the canceler includes a self-adapting processor which can adjust to a large number of transfer functions in order to generate the echo estimate which best approximates the echo. A problem with allowing the processor to adjust the transfer function when partial band energy is being received is that although the transfer function arrived at is optimized for the frequency components of the partial band energy it may not be optimum for the remaining frequency components in the frequency band of interest, for example, the voice band. Indeed, the transfer function adjusted to at frequencies other than those in the partial band energy may be significantly different from the desired optimum adjustment which would be obtained when adjusting on a whole band signal, i.e., speech or Gaussian noise. Consequently, a so-called low return loss path is established at frequencies other than the partial band energy. This low return loss can lead to oscillations in the co nunications circuit. These oscillations are extremely undesirable and must be avoided. The problem of low return loss and other problems of prior echo canceler arrangements results from allowing the canceler to adjust the echo estimate during intervals that partial band far end energy is being received. Summary of the Invention The problem is solved in accordance with the invention in one specific embodiment in which an energy band discriminator interconnecting the combining network to the circuitry for discriminating between whole band energy and partial band energy in a received signal in the first transmission path and for generating a control signal indicative thereof, the energy band discriminator including a first filter circuit for generating a first signal representative of an average value of the received signal, a second filter circuit for generating a second signal representative of a magnitude of the received signal, and control circuit for comparing the first and second signals and to generate a first state of the control signal when the second signal is greater than the. first signal, the control signal being supplied to the second circuitry for enabling supplying the error signal to the adjustable signal processing circuit during intervals that the control signal first state is generated. Brief Description of the Drawing

The invention will be more fully understood from the following detailed description of an illustrative embodiment taken in connection with the appended figures in which:

FIG. 1 shows in simplified block diagram form an echo canceler including an embodiment of the invention;

FIG. 2 depicts in simplified form details of the energy discriminator employed in FIG. 1; FIG. 3 shows details of the control circuit employed in the. discriminator of FIG. 2; and

FIG. 4 is a state diagram useful in describing operation of the discriminator of FIG. 2 and control circuit of FIG. 3. FIG. 5 shows details of another version of the control circuit employed in the discriminator of FIG. 2.

FIG. 6 depicts in simplified form details of the filter employed in the control circuit of FIG. 5. Detailed Description Echo canceler 100 including an embodiment of the invention is shown in simplified block diagram form in FIG. 1. However, unlike prior echo canceler arrangements, such as disclosed in U. S. Patent Nos. 3,499,999 and 3,500,000 and a article entitled "Bell's Echo-Killer Chip", IEEE Spectrum, October, 1980, pages 34-37 canceler 100 includes energy discriminator 103 for controllably enabling updating of an echo signal estimate, in accordance with an aspect of the invention, when a far end signal received over a first transmission path includes a certain class of signals including so-called whole band energy. Stated another way, updating of the echo signal estimate is inhibited when the far end signal includes significant energy which is only partial band. Broadly, in one embodiment of the invention an average magnitude of the received signal is compared to a modified magnitude of the received signal and if the modified magnitude is greater than the average, the received signal is considered to include whole band energy. If so, the updating or adapting of the echo signal estimate is enabled. Otherwise, updating of the echo estimate is inhibited. This enables the echo canceler adapting to a transfer function only when the received signal includes whole band energy and inhibits updating the transfer function when only partial band energy is being received, which would result in possible low return loss for other frequency components in the frequency band of interest e.g., the voice frequency band. Consequently, unwanted oscillations and other problems in the transmission network are avoided.

Briefly, canceler 100 includes an adjustable signal processor having a closed loop error control system which is self-adapting in that it automatically tracks signal variation in an outgoing path. Mo.re specifically, canceler 100 employs echo estimator 101 including a transversal filter arrangement for synthesizing a linear approximation of the echo, i.e., an echo estimate.

To this end, far end incoming signal X(K) is usually supplied from a far end talking party over a first transmission path, e.g., lead 102, to a first input of echo canceler 100 and therein to an input of echo estimator 101, an input of. nergy discriminator 103 and a first input of speech detector 104. Far end signal X(K) may be, for example, a digitally sampled speech signal, where K is an integer identifying the sampling interval. Far end signal X(K) is also supplied via lead 105, perhaps through some conversion circuitry, e.g., an analog-to-digital converter not shown, to a first input of hybrid 106. It is usually desirable for the input signal to hybrid 106 from lead 105 to be supplied over bidirectional path 107 to a near listening party. However, because of an impedance mismatch in hybrid 106, typically caused by balance impedance 108 not exactly matching the impedance of bidirectional path 107 a portion of the hybrid input signal appears on outgoing lead 109 and is reflected to the far end signal source as ^' an echo. The echo is supplied from an output of hybrid 106 over lead 109 to a second input of canceler 100 and therein to a second input of speech detector 104, and a first input of combining network 110. Lead 109 may also include conversion apparatus, e.g., an analog-to-digital converter not shown. A second input to combining network 110 is a signal estimate of the echo generated by echo estimator 101. The echo estimate is supplied via lead 111 from an output of echo estimator 101 to the second input of combining network 110. Combining network 110 generates error signal E(K) corresponding to the algebraic difference between the echo estimate and the output from hybrid 109 including the undesirable echo. Error signal E(K) is supplied over a second transmission path, e.g., lead 112 to the far end source and to controllable switching gate 113. Gate 113 is controlled to be enabled or inhibited by an output signal from AND gate 114. A first state of the output from AND gate 114, e.g., a logical 1 enables gate 114 to supply error signal E(K) to estimator 101 while a second state of the output from AND gate 114, e.g., a logical 0 inhibits gate 114 from supplying error signal E(K) to estimator 111.

Heretofore, gate 113 was controlled to inhibit supplying error signal E(K) to estimator 101 when significant far end energy was not present, when near end speech was present or when a prescribed relationship between error signal E(K), far end signal X(K) and a status signal indicates the presence of near end speech signals as described in ϋ. S. Patent 4,129,753. As indicated above far end signal X(K) could include speech, noise, any of a number of individual tones, multifrequency tones or the like. Thus, in prior arrangements error signal E(K) was only inhibited when no significant far end energy was detected or when near end speech was detected. On the other hand, error signal E(K) was supplied to estimator 101 during intervals that significant far end energy in signal X(K) was detected. This energy could be partial band energy, i.e., a single frequency tone, multifrequency tones or the like. Consequently, estimator 101 was allowed to adapt or otherwise be adjusted during the intervals that only partial band energy was being received. As indicated above such an adjustment results in undesirable results. Specifically, the transfer function to which estimator 101 may adjust to for the frequency components of the partial band signal would possibly result in a low return loss for other frequency components in the frequency band of interest. This, in turn, may cause unwanted oscillations in the communications circuits. The undesirable oscillations and other problems arise from allowing estimator 101 to be adjusted when partial band energy is present are avoided, in accordance with an aspect of the invention, by employing energy discriminator 103 to distinguish whether far end signal X(K) includes only partial band energy or whole band energy. If it is determined that X(K) is not whole band energy, e.g., speech or noise, or stated another way, if X(K) is partial band energy, e.g., a single frequency tone, multifrequency tones or the like, discriminator 103 generates an output which inhibits A.ND gate 114. On the other hand, when whole band energy is detected, discriminator 103 generates an output which enables AND gate 114. AND gate 114, in turn, generates a control signal for controlling gate 113 and, hence, the supply of E(K) to estimator 101. Specifically, a first state of the control signal from gate 114, e.g., a logical 1 enables gate 113 while a second state of the control signal, e.g., a logical 0 inhibits gate 113. Consequently, the echo estimate generated by estimator 101 remains constant during intervals that only partial band energy is present and an undesirable adjustment of the canceler transfer function is avoided.

Estimator 101 includes a so-called tapped delay line comprised of delay units 115-1 through 115- for realizing desired delays at the taps corresponding to convenient Nyquist intervals. Therefore, delayed replicas X(K-l) through X(K-N) of incoming far end signal X(K) are generated at the corresponding taps. The signal at each tap position, namely X(K-l) through X(K-N) as well as X(K) , is adjusted in response to error signal E(K). More particularly, signals X(K) through X(K-N) are individually weighted in response to E(K) via a corresponding one of adjustment networks 116-0 through 116-N, respectively. Adjustment networks 116-0 through 116-N each include multipliers 117 and 118, and feedback loop 119. Feedback loop 119 adjusts the tap weight to a desired value in a manner which will be apparent to those skilled in the art and explained in the above-noted references. The weighted replicas of X(K) from adjustment networks 116-0 through 116-N are summed via summing network 120 to generate the echo estimate signal approximating the echo to be cancelled. The echo estimate is supplied via lead 111 to the second input of combining network 110.

FIG. 2 shows in simplified block diagram form one embodiment of energy discriminator 103 which may be utilized, in accordance with an aspect of the invention, to determine whether significant energy in received signal X(K) is whole band and, hence, not only partial band. In this example not to be construed as limiting the scope of the invention, the frequency band of interest is the telephone voice frequency band of approximately 300 Hz to 4000 Hz. Whole band energy is, for example, speech,

Gaussian noise or the like, i.e., signals having frequency components across the whole frequency band. Partial band energy is, for example, single frequency tones, multifrequency tones or the like, i.e., signals having frequency components in relatively narrow frequency portions of the frequency band of interest. Accordingly, received signal X(K) is supplied via buffer amplifier 201 to rectifier 202. Any one of a number of precision full wave rectifiers known in the art may be employed for this purpose. If X(K) is a digital signal, for example, representative of a μ-law sample, a y-law to linear digital converter, not shown, would be used after rectifier 202. In this example, it is assumed that X(K) is an analog signal.

Rectified version MAG of X(K) is supplied to first filter 203 and to second filter 204. Filters 203 and 204 are employed to obtain prescribed characteristics of received signal X(K) in order to distinguish whether X(K) includes whole band energy or only partial band energy. In this example, filter 203 is used to obtain an average value of MAG while filter 204 is used to obtain a modified magnitude of MAG. To this end, filter 203 is a low pass filter having a first prescribed time constant while filter 204 has a second prescribed time constant. Since filter 204 in this example generates modified magnitude MOD MAG of MAG in accordance with a prescribed criterion, the second time constant is zero and filter 204 is essentially an attenuator. In this example, MOD MAG is 9 dB less than MAG, i.e., MOD MAG=MAG-9 dB.

Filter 203 generates essentially the running average of MAG and has a short time constant, illustratively on the order of 8 to 16 milliseconds.

Specifically, filter 203 is an active resistor-capacitor (RC) filter (not shown) having a prescribed exponential characteristic to generate an exponentially mapped past (EMP) version of MAG. It is noted that other filter characteristics may be equally employed in obtaining the EMP of MAG. A variety of arrangements and techniques may be employed for generating the short term running average of signal MAG. As indicated above, one technique is to obtain the exponentially mapped past (EMP) of the signal. EMP averaging is particularly useful in control or detection situations where interest is directed at the recent past behavior of a process and is described in IRE Transactions on Automatic Control, Vol. AC-5, January 1960, pages 11-17. The EMP average of a continuous signal is determined by weighting the recent signal occurrence more heavily than the less recent signal occurrence. The relative weighting of a continuous signal is, for example, an exponential function.

Both signal EMP and signal MOD MAG are supplied to control circuit 205 for generating in accordance with prescribed criteria signal ADAPT, signal ADAPT in this example is employed to control enabling and disabling AND gate 113 (FIG. 1) and, hence, enabling and disabling updating of the echo estimate being generated by echo estimator 101 (FIG. 1). Specifically, when ADAPT is a first state, e.g., a logical 1 signal X(K) includes whole band energy and when ADAPT is a second state, e.g., a logical 0 signal X(K) includes partial band energy.

FIG. 3 shows details of one type of control circuit 205. Accordingly, EMP is supplied to a first input of comparators 301 and 302. MOD MAG is supplied to a second input of comparator 302 while signal TH is supplied to a second input of comparator 301. Comparator 301 is employed to detect whether received signal X(K) includes significant far end energy. Thus, if EMP exceeds a predetermined threshold TH, X(K) is assumed to include significant energy. In this example TH = -50 dBmO. An output from comparator 301 is supplied to timer 303. Timer 303 is employed to determine whether the significant far end energy is present for at least a first predetermined interval T . In this example, timer 303 provides a wait interval of T^ = 24 milliseconds. This is to protect against erroneously generating ADAPT = 1 during the initial interval of received signal X(K) while filter 203 (FIG. 2) output is in a transient state. An output from timer 303 is supplied to a first input of AND gate 304. Thus, AND gate 304 is disabled until EMP is greater than TH for interval i. Comparator 302 compares MOD MAG to EMP. When MOD

MAG is greater than EMP comparator 302 generates a logical 1 output. An output from comparator 302 is supplied to a second input of AND gate 304. Thus, AND gate 302 is inhibited until MOD MAG is greater than EMP. • An output from AND gate 304 is supplied to timer

305. Timer 305 is responsive to a logical 1 from AND gate 304 to generate an ADAPT = 1 output immediately and to generate the ADAPT = 1 output for an additional second predetermined interval T2 upon a transition from logical 1 to logical 0 output from AND gate 304. Interval T₂ is a so-called hangover interval and adds in this example, 24 milliseconds to the logica-1 1 output from AND gate 304. This generates ADAPT = 1 for a sufficiently long interval for canceler 100 to update the echo estimate being generated.

Operation of energy discriminator 103 is summarized in the state diagram shown in FIG. 4. Simply, ADAPT = 0 until EMP > TH for T_χ, and MOD MAG > EMP. When the above conditions are all met X(K) includes whole band energy and ADAPT = 1 for an interval equal to at least interval T₂-

Thus, it is seen that ADAPT = 0 during intervals that EMP > TH but MOD MAG < EMP. When this occurs, the energy is partial band and updating of the echo estimate is inhibited.

FIG. 5 shows details of another type of control circuit 205. Accordingly, EMP(K) is supplied to a first input of digital comparators 501 and 502. MOD MAG(K) is supplied to a second input of comparator 502 while threshold signal TH is supplied to a second input of comparator 501. Comparator 501 is employed to detect whether received signal X(K) includes significant far end

c energy. Thus, if EMP(K) exceeds a predetermined threshold TH, X(K) is assumed to include significant energy. In this example, TH is 16 of a 4079.5 full scale linear' range. An output from comparator 501 is supplied to timer 503. Timer 503 is employed to determine whether the significant far end energy is present for at least a first predetermined interval T^. in this example, timer 503 provides a wait interval of T-_j_ = 24 milliseconds. This is achieved by counting 192 8-kHz frames to generate HC(K) = 1, otherwise HC(K) = 0. This is to protect against erroneously generating ADAPT(K) _.= 1 during the initial interval of received signal X(K) when transients may be present. Output HC(K) from timer 503 is supplied to a first input of AND gate 504. Thus, AND gate 504 is disabled until EMP(K) is greater than TH for interval T--_.

Comparator 502 compares MOD MAG(K) to EMP(K) on a sample by sample basis. When MOD MAG(K) is greater than EMP(K) comparator 502 generates a logical 1 output. For speech, i.e., whole band energy, MOD MAG(K) should be greater than EMP(K) approximately once every pitch period. An output from comparator 502 is supplied to a second input of AND gate 504. Thus, AND gate 504, when enabled via HC(K) = 1, supplies a logical 1-0 pattern d(K) representative of the result of the EMP(K) to MOD MAG(K) comparison to digital filter 505.

Digital low pass filter 505 is used, in accordance with an aspect of the invention, so that the comparison threshold between EMP and X' (K) can be lowered thereby improving performance in detecting when whole band energy is being received. This is possible because some wrong EMP to MOD MAG decisions can be made without affecting the decision to generate ADAPT(K) = 1 because of the filter function. Filter 505 generates digital output f(K) which is supplied to one input of digital comparator 506. Details of filter 505 are shown in FIG. 5 and described below.

OM? Comparator 506 in conjunction with threshold selector 507 provides, in accordance with an aspect of the invention, hysteresis in the decision to- generate the first and second states of control signal ADAPT(K) .* Specifically, threshold selector 507 is responsive to a first state of ADAPT(K), namely, ADAPT(K) = 1, to supply a first predetermined threshold TH1 to a second input of comparator 506 and to a second state of ADAPT(K), namely, ADAP (K) = 0, to supply a second predetermined threshold TH2 to the second input of comparator 506. The threshold values are selected in relationship to scaling factor F of d (K) in filter 505 as described below. In one example, F is selected to be 512 and TH1 is selected to be 4F = 2048 while TH2 is selected to. be 2F = 1024. Thus, it is seen that hysteresis is provided in the generation of ADAPT(K). Specifically, since TH1 is 4F = 2048, F(K) must exceed this higher value before ADAPT = 1 is generated. This allows for some errors in the EMP to MOD MAG comparison because of transients and the like without prematurely generating ADAPT = 1 and allowing updating of the echo estimate on an improper signal. Also, since TH2 is selected to be 2F = 1024, once ADAPT = 1 is generated, it will be maintained until f(K) drops below the lower threshold TH1. This provides hysteresis in the generation of ADAPT = 1. Consequently, the ADAPT = 1 condition, once generated, remains for an interval significantly longer than with the use of a hangover timer. Consequently, ADAPT = 1 is maintained longer without returning to the ADAPT = 0 condition and thereby causing the updating of the echo estimated to be inhibited less often.

FIG. 6 sho-js in simplified form details of digital filter 505. For clarity of description timing signals have not been shown. In this example, serial bit flow is assumed, although the filter can equally be implemented employing parallel bit flow. Digital filter 505 is a low pass digital filter and is enabled via signal HC(K) being a logical 1 to filter signal d (K) according to f (K+l ) = ( l- β) f (K) + βd ( k) (1 )

where = 1/512 and K is the currently generated sample When HC(K) is a logical 0

f(K+l) = f(K) (2)

Accordingly, output d (K) from AND gate 504 (FIG. 5) is supplied to one input of multiplier 401 while scaling factor F is supplied to a second input to generate scaled version Fd(K) of d (K) . Scaling factor F is a number selected so that f(K) is an integer and still has a desired precision. In experimental practice, the scaling function is realized by approximately timing of d (K) until a desired value is obtained, for example, F=512. Signal Fd (K) is supplied to a first input of adder 402 while a signal representative of (l-β)f(K) is supplied to a second input. An output of adder 402 is current sample f(K) and, then, the next sample output is f(K+l). Signal f(K) is supplied to shift register 403. When enabled via HC(K) = 1, shift register 403 generates βf(K) at one output and f(K) at another output. The number of stages in shift register 403 is selected to realize β , in this example, β = 1/512. When HC(K) = 0 shift register 403 is inhibited.

Signal βf(K) is supplied via inverter 405 to a first input of ADDER 404 while signal f(K) is supplied to a second input. ADDER 404 generates a signal representative of (l-β)f(K) which is supplied to the second input of ADDER 402.

Although the invention is described as being employed in an echo canceler, it can equally be used with other adaptive filters or in any application .in which the type of the received energy must be classified as either partial band or whole band.

Claims

Cl aims

1. An energy band discriminator useable in an echo canceler which comprises: an adjustable signal processing circuit (101) coupled to a first transmission path (105) for generating an echo estimate signal, a combining network (110) coupled to a second transmission path (109) for combining a signal in the second path with the echo estimate signal to generate an error signal ( E(k) ), first circuitry (117) responsive to the error signal ( E(k) ) for adjusting the processing circuit, and second circuitry (113) for supplying the error signal to the adjustable processing circuit, CHARACTERIZED IN THAT an energy band discriminator interconnecting the combining network (110) to the circuitry (117) for discriminating between whole band energy and partial band energy in a received signal in the first transmission path (105) and for generating a control signal indicative thereof, the energy band discriminator including a first filter circuit (203) for generating a first signal representative of an average value of the received signal, a second filter circuit (204) for generating^'a second signal representative of a magnitude of the received signal, and control circuit (205) for comparing the first and second signals and to generate a first state of the control signal when the second signal is greater than the first signal, the control signal being supplied to the second circuitry (113) for enabling supplying the error signal ( E(k) ) to the adjustable signal processing circuit during intervals that the control signal first state is generated.

2. An echo canceler as defined in claim 1 CHARACTERIZED IN THAT the second filter circuit (204) includes means for modifying the magnitude of the received signal in accordance with a prescribed criterion.

3. An echo canceler as defined in claim 2 CHARACTERIZED IN THAT the second filter circuit (204) includes an attenuator for generating the modified magnitude in a prescribed relationship to the magnitude of the received signal.

4. An echo canceler as defined in claim 1 CHARACTERIZED IN THAT the first filter circuit (203) includes means for obtaining a short term running average value of the received signal.

5. An echo canceler as defined in claim 4 CHARACTERIZED IN THAT the first filter circuit (203) includes low pass filter means having a predetermined time constant.

6. An echo canceler as defined in claim 4 CHARACTERIZED IN THAT the first filter circuit (203) includes means for obtaining the exponentially mapped past average value of the received signal.

7. An echo canceler as defined in claim 6 CHARACTERIZED IN THAT the second filter circuit (204) includes means for attenuating said magnitude of the received signal by a predetermined amount.

8. An echo canceler as defined in claim 7 CHARACTERIZED IN THAT the control circuit (205) further includes means for generating the first state of the control signal for at least a predetermined interval.

9. An echo canceler as defined in claim 8

o.:?l CHARACTERIZED IN THAT the energy band discriminator further includes means for inhibiting generation of the control signal first state until the first signal has a magnitude which exceeds a.predetermined threshold level for a predetermined interval.

10. An energy band discriminator in accordance with claim 1

CHARACTERIZED IN THAT the control circuit (205) further comprises: a filter circuit (505) having a prescribed characteristic for generating the control signal.

11. An energy band discriminator in accordance with claim 10 CHARACTERIZED IN THAT the filter circuit (505) includes a low pass filter.

12. An energy band discriminator in accordance with claim 10 CHARACTERIZED IN THAT the control circuit (205) further comprises: a comparator (506) supplied with an output signal from the filter (505) and a predetermined threshold value for generating a first state of the control signal indicative that whole band energy is not being received when the value of the filter output signal amplitude is less than the threshold value and a second state of the control signal indicative that whole band energy is being received when the filter output signal amplitude value is equal to or greater than the threshold value.

13. An energy band discriminator in accordance with claim 10

CHARACTERIZED IN THAT the first threshold value is greater than the second threshold value.