JP2010283779A - High-frequency amplifier and predistortion compensation method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a high-frequency amplifier of a compact size and low consumed power, and a predistortion compensation method. <P>SOLUTION: A digital predistortion circuit DPD2 includes a bandwidth of B/3 or wider within an assigned frequency band B. A white noise generator WNGen21 generates a test signal from white noise at the center frequency fc of the frequency band B, and outputs the test signal to a power amplifier 8. The test signal output amplified by the power amplifier 8 and the original test signal output are input to a comparator 25 to derive a difference. A control processing unit Cont22 refers to the obtained difference pattern and difference patterns stored beforehand in a database PB to make a predistortion signal generator PGen24 output a predistortion signal for eliminating the difference. Calibration of the predistortion signal that is to be added to an input signal by a mixer 23 is conducted. <P>COPYRIGHT: (C)2011,JPO&INPIT

Description

  The present invention relates to a broadband high-frequency amplifier and a predistortion compensation method.

  A transmission signal of a radio wave of mobile communication or digital broadcasting is required to be a signal having a wide signal transmission band and good linearity, and various distortion compensation methods are applied. In particular, in an amplifier that re-converts a radio signal digitally processed at baseband or IF frequency to a required radio frequency and transmits it, the signal component that cancels the distortion generated in the high-frequency amplifier circuit is given to the input signal in advance. DPD (Digital Pre-Distortion) that corrects distortion is effective. In this method, a test signal generation circuit that calibrates in order to examine how the distortion exists is provided, and an output obtained by amplifying the test signal is compared with a reference signal to compensate for the difference. (For example, Patent Document 1).

  However, the state of occurrence of distortion changes depending on, for example, the temperature condition of the equipment caused by, for example, when the operating band of the amplifier is different, or immediately after switching on or during continuous operation. The DPD has an advantage that the change in distortion can be corrected by performing a calibration operation every time such a change, but there is a problem that the calibration signal generation circuit becomes complicated and large.

  There is no problem with large-scale devices such as mobile phone base stations, but the calibration signal generation circuit is miniaturized in small devices such as repeaters and repeaters that are installed in places with poor radio wave environments such as densely populated areas and underground shopping centers. In addition, there is a problem that the power consumption must be reduced.

JP 2004-253834 A

  A conventional high frequency amplifier using a DPD has a problem that the calibration signal generation circuit becomes complicated and large.

  The present invention has been made to solve the above problems, and an object thereof is to provide a small-sized, low power consumption high frequency amplifier and a predistortion compensation method.

  In order to achieve the above object, the high-frequency amplifier of the present invention measures an input signal transmitted in a predetermined frequency band within an allowable maximum frequency band by measuring and calibrating its own distortion characteristic with a test signal. In a high-frequency amplifier that performs predistortion compensation and amplification, a predistortion signal obtained by synthesizing an input signal and a predistortion signal is generated and output to an amplification unit, and a predistortion input from the synthesis unit An amplifying unit that amplifies and outputs the compensation signal, and generates white noise, and outputs the generated white noise as a test signal in the center frequency of the maximum frequency band and in the test signal band within the maximum frequency band. A test signal output means, a comparison for inputting the test signal input from the test signal output means and the output signal of the amplifying unit to which the test signal is input, and outputting difference information of both inputs to the control means And when the calibration is performed, the output test signal is input to the amplifying unit, the difference information input from the comparison unit, and a database storing a predistortion signal for eliminating the difference The control information for outputting and calibrating the control information for outputting the predistortion signal that eliminates the inputted difference to the predistortion signal generating means, and after the calibration is completed, the amplifying unit sends the predistortion from the synthesizing means. Control means for performing control for switching so as to input a compensation signal; and predistortion signal generating means for outputting the predistortion signal for generating the predistortion compensation signal by inputting the control information to the synthesizing means; It is characterized by comprising.

  Further, the predistortion compensation method for a high-frequency amplifier according to the present invention includes a test signal output unit, a comparison unit, a predistortion signal generation unit, and a transmission unit in order to transmit in a predetermined frequency band within an allowable maximum frequency band. And a control unit, a synthesis unit, and an amplification unit. The amplification unit measures a predistortion signal obtained by synthesizing a predistortion signal with respect to a transmission input signal by measuring and calibrating its own distortion characteristic using a test signal. In the predistortion compensation method for a high-frequency amplifier to be amplified, the test signal output means converts the white noise to be generated into a test signal having a flat peak portion at a center frequency of the maximum frequency band over a band of 1/3 or more. The comparison means inputs a test signal from the test signal output means and a signal obtained by amplifying the test signal, and outputs difference information of both inputs to the control means. The control input When performing the calibration, the stage inputs the output test signal to the amplifying unit, and stores the difference information input from the comparison unit and a database storing a predistortion signal for eliminating the difference. Control for outputting and calibrating the control information for outputting the predistortion signal that eliminates the inputted difference to the predistortion signal generating means, and after the calibration, the amplifying unit inputs the predistortion compensation signal. The predistortion signal generating means outputs the predistortion signal to be combined with the input signal in accordance with the input control information to the combining means, and the predistortion signal is input. The combining means generates the predistortion compensation signal by combining the transmission input signal and the predistortion signal, and outputs the predistortion signal to the amplifier.

  According to the present invention, a small-sized, low power consumption high frequency amplifier and a predistortion compensation method can be provided.

The functional block diagram explaining operation | movement of the high frequency amplifier concerning the Example of this invention. The functional block diagram explaining the internal operation | movement of DPD. The conceptual diagram of the channel allocation for every 1 provider of a mobile telephone. The conceptual diagram which shows the channel allocation of 1 provider, and the relationship of the zone | band of the test signal in a present Example. Image diagram explaining the relationship between the distortion generated in the amplifier and the ideal test signal The figure explaining the frequency band of the test signal in the Example of this invention. The functional block diagram explaining the operation processing procedure of DPD. The flowchart of the control procedure which Cont of DPD implements.

  Embodiments of the present invention will be described below with reference to the drawings.

  FIG. 1 is a functional block diagram for explaining the operation of the high-frequency amplifier according to the embodiment of the present invention.

  In FIG. 1, a high-frequency amplifier R includes a pre-stage circuit 1, a digital predistortion circuit 2 (hereinafter abbreviated as DPD2), and a quadrature demodulation unit (QDEM) 3 that separate an input signal of a radio signal to be transmitted into I and Q channels. , Digital / analog converter 4 (hereinafter abbreviated as DAC), LPF 5, modulator (hereinafter abbreviated as MOD) filters 7 a and 7 b, power amplifier 8, coupler 9, terminator 10, and analog / digital converter 11. (Hereinafter abbreviated as ADC 11), an amplifier 12, a switch 13, and an antenna 14.

  Although not shown in the figure, it may be configured that an up converter and a down converter are inserted after the output of the DAC 4 and before the input of the ADC 11, but here, the drawing is complicated. The description is omitted to avoid it.

  Here, the high-frequency amplifier R is connected to a mobile phone base station (not shown) by ROF (Radio Over Fiber) or the like, and used as a relay station that relays between mobile phone terminals (not shown). The operation is explained as an example. The pre-stage circuit 1 separates the digitized input signal from the base station into I and Q channels and outputs them to the DPD 2.

  The DPD 2 is a predistortion compensation circuit that preliminarily corrects distortion generated in the power amplifier 8 or the like, and is a test signal generation circuit for measuring the distortion amount and a compensation component thereof in order to set the compensation amount internally. A predistortion generation function and a compensation control function for controlling these predistortion compensation processes are provided.

  In the embodiment of the present invention, the test signal generated from the white noise is used instead of the modulation test signal (training signal) similar to the transmission radio wave for generating the test signal, thereby facilitating circuit miniaturization and compensation control. Yes. The signal to which the predistortion signal is added by the DPD 2 is passed through the DAC 11 to remove unnecessary high frequency components by the LPF 5, then the required modulation is performed by the MOD 6, spurious is removed by the filter 7 a, and the signal is passed through the coupler 9 and the switch 13 It is transmitted from the antenna 14.

  The DPD 2 performs calibration (calibration) immediately after the high-frequency amplifier R is switched on or when a predetermined command is input. In the calibration mode, a test signal obtained by amplifying white noise generated in the DPD 2 instead of the input signal is switched to the terminal unit 10 and consumed instead of being output to the antenna by the switch 13.

  During this calibration, a part of the output signal is input from the coupler 9 to the DPD 2 and compared with white noise (test signal) by taking a difference. The predistortion signal is adjusted so that no distortion is assumed for each of Ich and Qch.

FIG. 2 is a functional block diagram for explaining the internal operation of the DPD 2.
In FIG. 2, the DPD 2 generates and outputs a test signal in a predetermined band described later from white noise, a switch 20 that switches between I and Q signals from the preceding circuit 1 and an internal test signal. A white noise generator (WNGen) 21, a predistortion signal generator (PGen) 24 that generates and outputs a predistortion signal, and controls the PGen24 to control the predistortion signal. A signal is input to one input terminal in each of the control processing unit (Cont) 22, Ich, and Qch for controlling the switch 20 and the switch 13 to be switched, and controlling the calibration and predistortion processing procedure, and the other input terminal. Two synthesizers 23 that receive predistortion signals and combine them to generate a predistortion compensation signal and output it to the DAC 4, and some output signals from the coupler 9 are QDEM 3. And a comparison unit 25 for inputting the test signal from the WN Gen 21 to the input terminal of the other I and Qch group and inputting the test signal from the WN Gen 21 to the Cont 22. ing.

  As the synthesizer 23, for example, a multiplier is often used. As a result, bias addition by addition, multiplication and division with a predistortion signal with respect to an input signal, and nonlinear input-to-output characteristics are performed. , A predistortion compensation signal that cancels (compensates) the distortion characteristics of the subsequent amplifier is output.

  The Cont 22 includes a database PB that stores therein data for outputting from the PGen 24 a predistortion signal that eliminates the difference corresponding to the difference between the input of the test signal and the test signal. Note that a delay unit (DL) 26 for matching the timing with the signal from the QDEM 3 is inserted into the input system of the test signal from the WN Gen 21 of the comparison unit 25. These components are connected to each other by a bus line or the like, and the above signals and information are input / output.

FIG. 3 is a conceptual diagram of channel allocation for each mobile phone operator. FIG. 4 is a conceptual diagram illustrating the relationship between channel allocation and test signal bandwidth in this embodiment.
In FIG. 3, one telecommunications carrier is granted a business license in the band BMHz, and further operates in a plurality of bands (channels) of n in the center frequencies fc1, fc2, and fcn and in the band bMHz. It has been broken. The band B0 MHz means a total band in the case where a guard band is provided for other adjacent uses or other operators. As for the width of the band, B ≧ B0 is normally set.

  Between the mobile phone terminal and the base station (or repeater), wireless communication is performed by selecting any one of the plurality of bands described above for each wireless link facing each other. For example, a high-frequency amplifier used in a transmitter on the base station side must operate below a predetermined distortion characteristic over the entire band BMHz. Therefore, self-calibration (calibration) is performed at the time of startup or the like, and pre-distortion is performed. Set the amount.

  There is a method of performing calibration for each band or for all bands at once. If the former, the modulation signal having band b is the band currently in operation in band B. A test signal is output to be calibrated, and if it is the latter, a test signal (training signal) in band B is used.

  FIG. 4 shows the concept of distortion correction when calibration is performed in the band P1 having fc1 as the center frequency. In this case, even if calibration is performed in the band P1, the distortion component d2 generated when transmission is performed in the band P2 having fc2 as the center frequency is out of the calibration range, so that sufficient compensation is not performed. As a result, calibration must be performed for each applicable band. As a practical matter, calibration cannot be performed each time a link is set in each band, and even if it is performed at startup, band switching control becomes troublesome. Since a large filter is required, the circuit scale required for the calibration process increases.

  However, a repeater used in the ROF system is required to reduce the size and power consumption of the apparatus, so that calibration must be performed with a circuit as small as possible.

  In the calibration used in the high-frequency amplifier according to the embodiment of the present invention, a test signal using a white noise component having a band of 1/3 or more of the band B allocated to the operator can be used for one calibration. The circuit configuration is simple and easy to control.

  In other words, since the high-frequency amplifier has a center frequency of fc0 and is a transmitter that transmits radio waves in the bandwidth B, the calibration in the band B may be simply performed.

FIG. 5 is an image diagram for explaining the relationship between distortion generated in an amplifier and an ideal test signal.
FIG. 5A shows a square-wave input signal wave So in the band W that is input to the high-frequency amplifier. FIG. 5B is an image diagram of an output signal waveform Sp output from a high-frequency amplifier with an ideal waveform signal distorted, and FIG. 5C is an example of an actual measurement using a spectrum analyzer. If the high-frequency amplifier performs distortion-free operation with a sufficient frequency band, the input / output waveforms match, but if not, distortion components appear on both sides of the original signal output.

  In FIG. 5 (b), mutual distortions between single-frequency carriers, for example, third-order and fifth-order distortions appear as distortion components d, but for an input signal in a band W created from white noise, The distortion component envelope E as indicated by the dotted line or the envelope curve shown in FIG.

  Therefore, in the calibration for predistortion compensation according to the embodiment of the present invention, the gain deviation information and distortion over the band B are processed once when the bandwidth W of the test signal (training signal) is narrower than the bandwidth B. Estimated by performing calibration.

  Assuming that the distortion component to be corrected is output from the amplifier to about three times the test signal bandwidth, the bandwidth W of the square wave test signal (training signal) is not made the same as the bandwidth B, but more than 1/3. In this case, it is considered that the distortion over the band B may be examined by one calibration. In other words, even if distortion components up to the third order distortion are handled, if the flat portion of the test signal is set to 1/3 of the allocation band B, it is considered that information related to distortion correction can be acquired.

  In this embodiment, a test signal that is 1/3 or more of the band B at the center frequency of the assigned frequency band is input to the high frequency amplifier, and compared with the output signal of the high frequency amplifier, the amount of distortion is measured, and An approximate distortion correction amount is produced.

  FIG. 6 is a diagram for explaining the frequency band of the test signal in the embodiment of the present invention.

  In FIG. 6, the center frequency of the band B is fc0. B / 3 (W) is a test signal frequency band (hereinafter referred to as a test signal band) having a flat characteristic near the center of the test signal (for example, a predetermined flat characteristic such as 1 dB or 3 dB). is there.

  The attenuation characteristics of both shoulders of the low frequency and high frequency (fL, fU) of the test signal are arbitrary, but at the frequency boundary (fuc, flc), it is attenuated to a level lower than the upper limit value of the predetermined spurious. A bandpass filter for the test signal is set.

  Next, a method for generating a test signal will be described. If the test signal having the ideal cutoff frequency characteristic is used, a distortion component having a frequency other than the test signal band of the test signal band W can be obtained from the output of the high-frequency amplifier. However, in order to measure the distortion component in the band B even if it is in the out-of-band W, the distortion component also appears larger when the test signal has the transmission input component in the out-of-band W, and calibration is easy. .

  Originally, the flat area may be equal to or close to the band B, but in this case, the cutoff characteristic of the test signal output filter that outputs the test signal from the white signal of WN Gen21 is required to be very steep. In addition, since the digital filter and the high-level processing are also performed, WN Gen 21 is complicated, which is not preferable.

  On the other hand, a WN Gen21 filter (not shown) has a flat cutoff region of about B / 3, and has a gentle cutoff characteristic from the low and high frequencies fL and fU of the test signal toward the frequency boundaries fuc and flc, for example, 6 dB. The characteristics are as in / oct. By doing so, not only can the filter be simplified, but also a transmission component for measuring distortion can be obtained as a test signal.

  As a result, a test signal having the sloped portion of FIG. 6 is generated, which is useful for distortion compensation to each band in the band B. The comparison unit 25 compares the test signal from the WN Gen 21 with the transmitter output via the QDEM 3 and outputs a compensation difference for applying predistortion to the Cont 22.

  To repeat, the band is set to B / 3, calibration is completed at the center frequency fc0, and the test signal is generated with a gentle characteristic of the filter, so that it is replaced with the actual frequency band of fc1 or fcn. Even with this, it is possible to minimize the impact.

  Further, in the pre-distortion method in which the base band is synthesized, an image at the aliasing frequency is generated in the Ich and Qch signals, but it is possible to take image countermeasures by performing correction in the above band.

  If it is a high-frequency amplifier installed in the base station, there is no problem even if the circuit scale of the final stage power amplifier or DPD2 is somewhat large, but high-frequency amplifiers for relay applications such as ROF are proposing low power consumption and miniaturization. It is. For repeater applications such as ROF, fine calibration with a test signal that is modulated in the same way as the relay operation band in the band B complicates the apparatus and processing procedure. However, predistortion compensation using the test signal generation of this embodiment Thus, a small high-frequency amplifier can be used.

FIG. 7 is a functional block diagram for explaining an operation processing procedure of the DPD 2. FIG. 8 is a flowchart of a control procedure executed by the Cont 22 of the DPD 2.
2 and 8, Cont 22 starts an initial process when the power is turned on, enters a calibration mode, stops PGen 24, and waits (step s1). Select the cal contact of the switch 20, input a test signal from the WNGGen 21 to the synthesizer 23, and switch the switch 13 of FIG. 1 to be connected to the terminator 10 (step s2), then start the WNGGen 21 The test signal is output (step s3).

  The WNGGen 21 includes an NGen 21a2 that generates white noise and a BPF 21b that receives the output and sets a frequency band B / 3 at the center frequency fc0 in FIG. For example, the NGen 21a is a white noise generator using a PN sequence random code generator having a predetermined number of stages, and the band pass filter (BPF) 21b, which is composed of a digital filter, can be easily set in various settings by the Cont 22. Since it is realizable, it is preferable. As described above, the BPF 21 has a gentle cutoff characteristic such as a cutoff frequency fU, fL to 6 dB / oct as shown in FIG. 4, but this inclination characteristic is appropriately set according to the conditions of the metering. Is.

  Note that NGen 21a may be a white noise generator using a diode, and BPF 21b may be a digital converter that outputs a signal generated by an analog filter using a passive element.

  The comparison unit 25 receives the test signal from the WNGGen 21 via the delay unit (DL) 26 and the output signal amplified by the power amplifier 8 via the synthesizer 23, DAC 4, etc. via the coupler 9, ADC 11, etc. Are entered. The DL 26 is a delay unit that is inserted so that the input timing of the test signal from the WNGGen 21 that is input to the comparator 25 and the feedback signal that is input via the ADC 11, that is, the delay time of the feedback signal matches.

  The comparison unit 25 obtains a differential output for each Ich and Qch obtained by orthogonal demodulation of the test signal from the WNGGen 21 and the feedback signal from the ADC 11 by the QDEM 3, and outputs the difference output to the Cont 22 (step s4). Here, the comparison unit 25 has, for example, an internal FFT, and outputs a difference output for amplitude and phase corresponding to the frequency.

  The internal memory (not shown) of Cont 22 stores and accumulates the frequency-to-phase shift and frequency-to-amplitude distortion characteristics of the pattern in which the difference appears as a database PB (LUT: also referred to as a lookup table). Has been.

  In addition, in the database PB of the pattern of how the difference appears, a predistortion signal that is previously compared with the ideal state and measured or theoretically analyzed to compensate for the difference is associated with an identification number or the like. And memorized.

  The Cont 22 refers to the database PB and extracts a pattern having a high correlation with the difference output pattern from the patterns stored in the database PB (step s5).

  The Cont 22 receives the identification number of the predistortion signal that reduces this difference with respect to the pattern extracted from the database PB, or the identification number that is a candidate for the predistortion signal close to the pattern, via the bus line B. It outputs to PGen24 (step s6).

  In the PGen 24, a predistortion signal pattern output corresponding to the identification number of the predistortion signal or generation data of the predistortion signal is stored in an internal memory (not shown), and according to the input control signal, the predistortion signal is stored. Is output to the synthesizer 23 (step s7).

  The Ich and Qch synthesizers 23 synthesize the predistortion signal from the Ich and Qch PGen 24 and the test signal from the WN Gen 21, respectively, and output it to the power amplifier 8 via the DAC 4 (step s8). .) Switch from calibration mode to operation mode. In the operation mode, the contact of the switch 20 selects op, and the switch 13 selects the connection destination to the antenna 14 (step s9).

  Note that switching to the operation mode is performed when the comparison unit 25 after selecting the switch connection destination refers to the difference and the database PB, and when the difference that gives additional predistortion is minimized so as to compensate for the shortage, You may make it carry out from the time of becoming the difference below. Then, when the operation mode is entered, the comparison unit 25 stops operating.

  On the other hand, as a modification, when the operation mode is set in step 8 above, the comparison unit 25 is continuously operated, the input signal and the transmission signal are compared, and the compensation difference is output to the Cont 22. A general feedback control for outputting a predistortion signal to PGen 24 may be performed with reference to the difference compensation database PB (LUT) in the mode.

  The combination of the configuration of the high-frequency amplifier and the processing procedure at the beginning of the DPD 2 may be changed without departing from the gist of the above.

  As described above, since the predistortion compensation according to the embodiment of the present invention does not perform complicated distortion correction processing, it is possible to provide a small-sized and low power consumption high frequency amplifier.

1 Pre-stage circuit 2 Digital predistortion circuit (DPD)
20 Switch 21 White noise generator (WNGen)
22 Control processing part (Cont)
23 Synthesizer 24 Predistortion signal generator (PGen)
25 Comparator 3 Quadrature Demodulator (QDEM)
4 Digital-to-analog converter (DAC)
5 LPF
6 Modulator (MOD)
7a, 7b Filter 8 Power amplifier 9 Coupler 10 Termination unit 11 Analog / digital conversion unit (ADC)
12 Amplifier 13 Switch 14 Antenna PB Database

Claims (5)

In a high-frequency amplifier that amplifies by performing predistortion compensation on an input signal transmitted in a predetermined frequency band within a maximum allowable frequency band by measuring and calibrating the distortion characteristics of the self with the test signal,
A synthesis means for generating a predistortion compensation signal obtained by synthesizing the input signal and the predistortion signal and outputting the predistortion signal to the amplifying unit;
An amplification unit that amplifies and outputs a predistortion compensation signal input from the synthesis unit;
Test signal output means for generating white noise and outputting the generated white noise as a test signal in a center frequency of the maximum frequency band and a test signal band within the maximum frequency band;
Comparing means for inputting the test signal input from the test signal output means and the output signal of the amplifying unit to which the test signal is input, and for outputting information on the difference between both inputs to the control means;
When performing the calibration, input the test signal to be output to the amplification unit, refer to the information of the difference input from the comparison means, and a database storing a predistortion signal for eliminating the difference, Control for outputting the predistortion signal that eliminates the input difference and outputting the predistortion signal to the predistortion signal generating means for calibration Control means for performing control to switch to input,
A high frequency amplifier comprising: a predistortion signal generating means for inputting the control information and generating the predistortion signal for generating the predistortion compensation signal to the synthesizing means. The test signal output means includes
2. A filter for inputting the output white noise and outputting the white noise as the test signal having a flat peak portion over a band of 1/3 or more at the center frequency of the maximum frequency band. The high-frequency amplifier described. The filter is
3. The high-frequency amplifier according to claim 2, wherein the test signal is output after being gently attenuated from each shoulder portion of the peak portion to an allowable output limit at each boundary allowable frequency in the maximum frequency band. A test signal output means, a comparison means, a predistortion signal generation means, a control means, a synthesizing means, and an amplifying unit are provided for transmitting in a predetermined frequency band within the permitted maximum frequency band, In a predistortion compensation method for a high-frequency amplifier, the amplification unit amplifies a predistortion signal in which a predistortion signal is synthesized with respect to an input signal to be transmitted.
The test signal output means outputs the white noise to be generated as a test signal having a flat peak portion over a band of 1/3 or more at the center frequency of the maximum frequency band,
The comparison means inputs a test signal from the test signal output means and a signal obtained by amplifying the test signal, and outputs information on the difference between both inputs to the control means,
The control means to which the difference information is input is:
When performing the calibration, the test signal to be output is input to the amplifying unit, the difference information input from the comparison unit, and a database storing a predistortion signal for eliminating the difference, Control for outputting and calibrating the control information for outputting the predistortion signal for eliminating the difference to be inputted to the predistortion signal generating means, and after the calibration is completed, the amplifier unit inputs the predistortion compensation signal. Control to switch,
The predistortion signal generating means outputs the predistortion signal to be combined with the transmitted input signal in accordance with the input control information to the combining means,
The synthesizing unit to which the predistortion signal is input generates the predistortion compensation signal by synthesizing the transmitted input signal and the predistortion signal, and outputs the predistortion signal to the amplifier. Predistortion compensation method for high frequency amplifier. The test signal is
5. The predistortion compensation method for a high-frequency amplifier according to claim 4, wherein the attenuation is gently attenuated from each shoulder portion of the peak portion to an allowable output at each boundary allowable frequency of the maximum frequency band.

Images