1
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`RS1034
`Rohde & Schwarz Gmbh & Co., KG vs. Tektronix, Inc.
`IPR2018-00643
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`US. Patent
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`US 6,631,341 132
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`US. Patent
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`Oct. 7, 2003
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`Sheet 2 0f5
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`US 6,631,341 B2
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`I4
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`DISPLAY
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`SECTION
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`DATA
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`STORAGE
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`SECTION
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`DATA
`ACQUISITION
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`MANAGEMENT
`SECTION
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`CONDITION
`CONVERTING
`SECTION
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`SIGNAL
`I
`PROCESSING
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`US. Patent
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`Oct. 7, 2003
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`Sheet 3 0f5
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`US 6,631,341 132
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`SET AND COMPUTE CONDITIONS
`AT SETTING INPUT SECTION
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`CONTROL DATA STORAGE
`SECTION AT DATA ACQUISITION
`MANAGEMENT SECTION
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`START CORRESPONDING DATA
`ACQUISITION AT DATA
`STORAGE SECTION
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`TERMINATE CORRESPONDING
`DATA ACQUISITION AT DATA
`STORAGE SECTION
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`GENERATE INFORMATION
`REQUIRED FOR DATA GENERATING
`SECTION AT PROCESSING
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`CONDITION CONVERTING SECTION
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`GENERATE DATA BY
`RE-SAMPLING IT AT DATA
`GENERATING SECTION
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`GENERATE DISPLAY DATA AT
`DISPLAY CONTROL SECTION
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`FIG.IC
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`DISPLAY DATA AT
`DISPLAY SECTION
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`4
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`US. Patent
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`Oct. 7, 2003
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`Sheet 4 0f5
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`US 6,631,341 B2
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`US. Patent
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`US 6,631,341 B2
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`1
`SIGNAL ANALYZING APPARATUS
`
`CROSS-REFERENCE TO RELATED
`APPLICATIONS
`
`This application is based upon and claims the benefit of
`priority from the prior Japanese Patent Application No.
`2000-47888, filed Feb. 24, 2000,
`the entire contents of
`which are incorporated herein by reference.
`BACKGROUND OF THE INVENTION
`
`The present invention relates to a signal analyzing appa-
`ratus for measuring frequency characteristics of a signal
`employed for a mobile communication system such as
`automobile telephone or portable telephone, and displaying
`a waveform of the signal, thereby analyzing the signal.
`A signal employed for a mobile communication system
`such as automobile telephone or portable telephone, for
`example, is modulated by a variety of systems.
`In addition, a TDMA (Time Division Multiple Access)
`system is employed as a communication system in order to
`efficiently use a communication line.
`A frequency of a carrier wave for carrying a signal
`employed in such a mobile communication system ranges
`some hundreds MHZ to some GHz, which is very high.
`In general, a signal analyzing apparatus such as spectrum
`analyzer is employed for precisely measuring a variety of
`frequency components included in such a signal.
`FIG. 3 is a block diagram depicting a general configura-
`tion of a conventional signal analyzing apparatus used for
`measuring frequency characteristics of a measured signal
`with its high frequency.
`In a signal analyzing apparatus 21 shown in FIG. 3, a
`measured signal with its high frequency inputted via an
`input terminal 22 is adjusted to a predetermined, normalized
`level by an attenuator (ATT) (not shown).
`Then, the level adjusted, measured signal with its high
`frequency is mixed with a local oscillation signal from a
`local oscillator 24 by means of a signal mixer 23, and the
`mixed signal is converted into an intermediate frequency
`signal having its intermediate frequency.
`Here, the oscillation frequency of the local oscillator can
`be swept (frequency swept) over the range of predetermined
`frequencies by means of a sweep control section (not
`shown).
`In this manner, a frequency of the intermediate frequency
`signal outputted from the signal mixer 23 also changes in
`synchronization with a sweep operation.
`Then, the intermediate frequency signal with its reduced
`frequency is inputted to a resolution bandwidth (hereinafter,
`referred to as RBW) filter 25, an undesired frequency
`component is eliminated by means of the RBW filter 25, and
`only a required intermediate frequency signal is selected.
`A bandwidth (RBW) at a time when a peak level at the
`passage center frequency of the frequency characteristics of
`this RBW filter 25 drops by 3 dB indicates a frequency
`resolution in this signal analyzing apparatus.
`Asignal from the RBW filter 25 is gain adjusted by means
`of an amplifier (not shown), and a switching section 26 is
`switched to a LOG converter 27 side. In this state, a signal
`logarithm converted by means of a LOG converter 27 to be
`compressed is detected by means of a waveform detector
`(DET) 28.
`In contrast, when the switching section 26 is switched to
`the RBW filter 25 side, the signal from the RBW filter 25 is
`detected by means of a waveform detector (DET) 28.
`
`2
`The signal detected by this waveform detector 28 within
`a sweeping period indicates the size of a time series wave-
`form at the swept frequency.
`The thus outputted signal by the waveform detector 28 is
`inputted to an anti-aliasing filter 29.
`The anti-aliasing filter 29 used here is composed of a filter
`for eliminating a high frequency component
`(noise
`component) of a frequency spectrum waveform finally dis-
`played at a display section 34 provided at a panel of an
`apparatus main body.
`The signal from this anti-aliasing filter 29 is converted
`into digital data by means of a next A/D converter 30, and
`the converted digital data is stored in a data storage section
`31.
`
`Predetermined processing is applied to the digital data
`stored in this data storage section 31 by means of a signal
`processing section 33.
`Then, the frequency spectrum waveform obtained by this
`processing is displayed in a frequency domain (frequency on
`horizontal axis and amplitude on vertical axis) on a display
`screen of the display section 34.
`In the meantime, in the signal analyzing apparatus 21 of
`such type, a signal employed in a mobile communication
`system such as automobile telephone or portable telephone,
`the signal being inputted as a measured signal is a burst
`shaped signal whose level changes with an elapse of time.
`In the field of such mobile communication system, there
`is a demand to measure such burst shaped signal in detail by
`tracking a time.
`The signal analyzing apparatus 21 shown in FIG. 3 is
`provided with a function for performing time span sweeping
`such that a frequency of the local oscillator 24 is fixed so as
`to measure a time change of a signal bandwidth-restricted by
`the RBW filter 25 within a normalized bandwidth, thereby
`displaying the result of the time span sweeping while time
`and amplitude are defined on the horizontal and vertical
`axes, respectively, on the display screen of the display
`section 34.
`
`By this time span sweeping, in the case where a burst
`shaped measured signal is measured in detail by tacking a
`time, there have been conventionally employed a method of
`measuring the signal by changing a sampling rate of an A/D
`converter and a method of decimating unwanted data after
`sampling has been performed at a sufficiently high speed by
`employing an A/D converter that operates at a high speed.
`However, in the method of changing the sampling rate of
`the A/D converter, it has been necessary to reacquire data
`every time the sampling rate is changed.
`Moreover, in the case where the sampling rate is changed,
`thereby causing operation at a high speed, there has been a
`problem that a sufficient dynamic range cannot be obtained.
`In the method of decimating unwanted data after sampling
`has been performed at a sufficiently high speed by using the
`A/D converter that operates at a high speed,
`it has been
`necessary to use a sampling rate of the lowest common
`multiple for the resolution of data per one time domain to be
`acquired.
`For example, in the case where 1 Msec is required as a time
`span, assuming that 500 items of data are provided, a
`resolution of 2 nsec per one item of data is obtained. Thus,
`the sampling rate of the A/D converter is set to a frequency
`of 500 MHz.
`
`Similarly, the sampling rate of the A/D converter at a
`resolution of 5 nsec is set to a frequency of 200 MHz.
`In order to meet resolutions of both of the above 2 nsec
`
`and 5 nsec, it is required that the A/D converter operates
`when the sampling rate of the converter is set to a frequency
`of 1 GHz.
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`US 6,631,341 B2
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`Therefore, with the above described method, the sampling
`rate of the A/D converter could not be changed freely.
`Even if the sampling rate can be changed, in the case of
`a high speed operation, there has been a problem that a
`sufficient dynamic range cannot be obtained.
`In addition,
`there has been a problem that a memory
`requires its capacity corresponding to the maximum opera-
`tion.
`
`Namely, in the case where the sampling rate is changed,
`thereby causing high speed operation, it is required to use an
`A/D converter that corresponds to the highest speed opera-
`tion. In the A/D converter that corresponds to high speed
`operation, there has been a problem that a sufficient con-
`version bit cannot be allocated, processing must be done at
`the same conversion bit even during a low speed sampling,
`and there is a limitation to a dynamic range according to the
`conversion bit, thus making it impossible to obtain a suffi-
`cient dynamic range.
`In the meantime, in the signal analyzing apparatus 21
`shown in FIG. 3, a signal bandwidth-limited by the RBW
`filter 25, the signal passing through the waveform detector
`28, is a base band signal having a bandwidth of the RBW
`filter 25.
`The inventors found that the bandwidth of the RBW filter
`
`25 is sampling at a sampling rate that can be reproduced, and
`then, arbitrary time data is generated by means of
`re-sampling using a digital signal processing technique,
`whereby detailed time analysis can be performed without
`changing the sampling rate, and reached the present inven-
`tion based on the findings.
`BRIEF SUMMARY OF THE INVENTION
`
`The present invention has been made in order to solve the
`foregoing problems. It is an object of the present invention
`to provide a signal analyzing apparatus capable of perform-
`ing detailed time analysis by reproducing arbitrary time data
`without increasing a sampling rate of an A/D converter, and
`capable of obtaining a sufficient dynamic range.
`In order to achieve the foregoing object, according to a
`first aspect of the present invention, there is provided a
`signal analyzing apparatus comprising:
`a resolution bandwidth (hereinafter, referred to as RBW)
`filter 5 in which a bandwidth is set so as to selectively
`pass a frequency component of only a desired signal
`bandwidth, of the measured signal
`frequency-
`converted into a normalized intermediate frequency
`signal;
`a waveform detector 8 for detecting a signal passing
`through the RBW filter;
`an analog/digital (hereinafter, referred to as A/D) con-
`verter 10 for sampling the signal detected by the
`waveform detector at a predetermined sampling rate at
`which a Nyquist frequency is within the frequency
`bandwidth of the RBW filter, thereby converting the
`sampled signal into digital data;
`a data storage section 11 for storing digital data converted
`by the A/D converter;
`a signal processing section 13 for re-sampling the digital
`data stored in the data storage section so as to enable to
`reproduce a bandwidth of the signal detected by the
`waveform detector, thereby generating arbitrary time
`data; and
`a display section 34 for displaying the arbitrary time data
`generated by the signal processing section while time
`and amplitude are defined on horizontal and vertical
`axes, respectively, on a display screen.
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`in order to achieve the foregoing object,
`In addition,
`according to a second aspect of the present invention, there
`is provided a signal analyzing apparatus according to the
`first aspect, wherein re-sampling at the signal processing
`section is performed by using at
`least one of line
`interpolation, spline function interpolation and sampling
`function interpolation.
`Further, in order to achieve the foregoing object, accord-
`ing to a third aspect of the present
`invention,
`there is
`provided a signal analyzing apparatus according to the
`second aspect, wherein re-sampling at the signal processing
`section is performed by using the sampling function
`interpolation, and a passing bandwidth of the sampling
`function interpolation is limited by a window function.
`Furthermore,
`in order to achieve the foregoing object,
`according to a fourth aspect of the present invention, there
`is provided a signal analyzing apparatus according to the
`first aspect, wherein an anti-aliasing filter 9 set in a passing
`bandwidth encompassing the maximum bandwidth of the
`RBW filter is provided between the RBW filter and the A/D
`converter.
`
`Still furthermore, in order to achieve the foregoing object,
`according to a fifth aspect of the present invention, there is
`provided a signal analyzing apparatus according to the first
`aspect, wherein the signal processing section comprises:
`data acquisition management means for, in interpolating
`data between the existing data, guaranteeing acquisi-
`tion of interpolation data before and after generation
`data used for interpolation, and then, associating a data
`acquisition timing from the data storage section with an
`address of the data storage section;
`processing condition converting means for determining a
`condition corresponding to a data generation resolution
`(time span) indicating how many address in the data
`storage section is required for one item of data, and
`determining a condition corresponding to a data acqui-
`sition timing indicating what is the number of data
`generated in the data storage section or indicating the
`number of address from which the data in the data
`
`storage section must be used;
`data generating means for using a re-sampling function
`(or interpolation function and decimation),
`thereby
`generating data between the existing sampling data
`stored in the data storage section by means of
`re-sampling; and
`display control means for controlling a display section so
`as to display a level variation of the measured signal
`based on data generated by the data generating means
`based on the data stored in the data storage section
`while time and amplitude are defined on horizontal and
`vertical axes, respectively, on the display screen of the
`display section.
`Additional objects and advantages of the invention will be
`set forth in the description which follows, and in part will be
`obvious from the description, or may be learned by practice
`of the invention. The objects and advantages of the invention
`may be realized and obtained by means of the instrumen-
`talities and combinations particularly pointed out hereinaf-
`ter.
`
`BRIEF DESCRIPTION OF THE SEVERAL
`VIEWS OF THE DRAWING
`
`The accompanying drawings, which are incorporated in
`and constitute a part of the specification, illustrate presently
`preferred embodiments of the invention, and together with
`the general description given above and the detailed descrip-
`
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`US 6,631,341 B2
`
`5
`tion of the preferred embodiments given below, serve to
`explain the principles of the invention.
`FIG. 1A is a block diagram depicting a general configu-
`ration of a signal analyzing apparatus according to one
`embodiment of the present invention;
`FIG. 1B is a functional block diagram depicting an
`internal configuration of a signal processing section shown
`in FIG. 1A;
`FIG. 1C is a flow chart illustrating an operation of each
`portion of the signal processing section shown in FIG. 1B;
`FIG. 1D is a view illustrating a re-sampling operation
`caused by the signal processing section shown in FIG. 1B;
`FIG. 2A to FIG. 2D are views showing a signal bandwidth
`a
`to
`at each of points “ ”
`“d”; and
`FIG. 3 is a block diagram depicting a general configura-
`tion of a generally known conventional signal analyzing
`apparatus.
`
`DETAILED DESCRIPTION OF THE
`INVENTION
`
`Reference will now be made in detail to the presently
`preferred embodiments of the invention as illustrated in the
`accompanying drawings, in which like reference numerals
`designate like or corresponding parts.
`Hereinafter, a signal analyzing apparatus according to one
`embodiment of the present invention will be described with
`reference to the accompanying drawings.
`FIG. 1A is a schematic block diagram depicting a signal
`analyzing apparatus 1 according to one embodiment of the
`present invention.
`FIG. 1B is a functional block diagram depicting an
`internal configuration of a signal processing section shown
`in FIG. 1A.
`
`FIG. 1C is a flow chart illustrating an operation of each
`portion of the signal processing section shown in FIG. 1B.
`FIG. 1D is a timing waveform chart
`illustrating a
`re-sampling operation caused by the signal processing appa-
`ratus shown in FIG. 1B.
`
`First, a configuration of a signal analyzing apparatus
`according to the present embodiment will be described in
`accordance with the signal processing procedures.
`An operation during frequency sweeping in the signal
`analyzing apparatus according to the present embodiment is
`executed in the same manner as that in the prior art described
`by referring to FIG. 3. A description of the above operation
`is omitted here.
`
`The signal processing procedures described hereinafter is
`executed by time span sweeping for fixing a frequency of a
`first local oscillator, and measuring a time change of a signal
`bandwidth limited to a normalized bandwidth by means of
`a RBW filter.
`
`That is, the signal level of a measured analog signal with
`its high frequency (for example, some hundreds KHz to
`some GHZ) inputted via an input terminal 2 is adjusted to a
`normalized level by means of an attenuator (ATT) (not
`shown).
`Then, the measured signal with its level adjusted high
`frequency is mixed with the local oscillation signal from a
`local oscillator 4 by means of a signal mixer 3, whereby the
`mixed signal
`is converted as an intermediate frequency
`signal reduced to a predetermined intermediate frequency.
`In this manner, the intermediate frequency signal with its
`reduced frequency is inputted to an RBW filter 5 at the next
`stage configured of an analog band pass filter.
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`This RBW filter 5 is such that its bandwidth (RBW:
`bandwidth H at a time when a peak level at the passing
`center frequency IF shown in FIG. 2A falls by 3 dB) can be
`variably set to 30 KHz, 10 KHz, 3 KHz, 1 KHz or 300 Hz,
`for example.
`Then, this RBW filter 5 eliminates an unwanted frequency
`component of an intermediate frequency signal
`inputted
`from the signal mixer 3, thereby passing only the interme-
`diate frequency signal of the frequency component in the
`bandwidth (RBW) variably set as described above.
`In this manner, the signal passing through the RBW filter
`5 is gain adjusted by means of an amplifier (not shown), and
`then, a contact point (not shown) of a switching section 6 is
`switched to the LOG converter (LOG) 7 side. In this state,
`the signal is logarithm converted by means of this LOG
`converter 7 to be compressed, and then, detected by a
`waveform detector (DET) 8.
`In contrast, while the contact point (not shown) of the
`switching section 6 is switched to the RBW filter 5 side, the
`signal passing through the RBW filter 5 is detected intact by
`means of the waveform detector (DET) 8.
`At the switching section 6,
`in the case where data is
`acquired over a wide dynamic range, a contact point (not
`shown) is switched to the LOG converter 7 side. In the case
`where linear data is acquired, a contact point (not shown) is
`switched to the RBW filter 5 side.
`
`The thus detected signal by the waveform detector 8 is
`inputted to an anti-aliasing filter 9 at a next stage, as a base
`band signal having its bandwidth characteristics of the RBW
`filter 5, as shown in FIG. 2B.
`This anti-aliasing filter 9, as shown in FIG. 2C, has its
`passing bandwidth that encompasses frequency characteris-
`tics of the maximum bandwidth of the RBW filter 5 variably
`set as described above, and, for example, eliminates a noise
`component caused by a sampling frequency inputted to an
`A/D converter 10 at a next stage.
`The signal from this anti-aliasing filter 9 is serially
`converted into digital data at a sampling frequency “fs” by
`means of the A/D converter 10 at a next stage.
`The digital data from this A/D converter 10 is stored in a
`data storage section 11 at a next stage.
`Then, re-sampling processing is applied to data stored in
`the data storage section 11 by means of a signal processing
`section 13 based on input information of a setting input
`section 12 described below.
`
`Then, arbitrary time data is generated by re-sampling
`processing of the signal processing section 13, and the data
`is displayed on the display screen of a display section 14
`according to a time domain in which time and amplitude are
`defined on horizontal and vertical axes, respectively.
`The setting input section 12 consists of a man-machine
`interface for determining measurement conditions (data gen-
`eration resolution, data acquisition timing and measurement
`start timing).
`This setting input section 12 sets and inputs to the signal
`processing section 13 a variety of parameters such as data
`generation quantity, data generation resolution and data
`acquisition start time.
`Among them, the data generation quantity is generally
`fixed on the display screen of the display section 14.
`In addition, the data generation resolution is varied by a
`value such as time span.
`Further, the data acquisition start time is determined by
`the apparatus or is determined by the user using a trigger
`function or the like.
`
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`

`US 6,631,341 B2
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`7
`These parameters are processed by means of the signal
`processing section 13 so as to be converted into an address
`of the data storage section 11 in which sampling data is
`stored.
`
`Then, the signal processing section 13 is composed of, for
`example, a microprocessor unit (MPU), a digital signal
`processor (DSP), and a central processor unit (CPU) and the
`like.
`
`As shown in FIG. 1B, this signal processing section 13
`internally comprises a data acquisition management section
`131, a processing condition converting section 132, a data
`generating section 133, and a display control section 134.
`The data acquisition management section 131 guarantees
`acquisition of interpolation data before and after generation
`data used for interpolation when data between the existing
`data is interpolated as re-sampling processing, and associ-
`ates a data acquisition timing from the data storage section
`11 with an address of the data acquisition section 11.
`In addition, a processing condition converting section 132
`introduces a condition corresponding to a data acquisition
`resolution (time span) in which how many addresses of the
`data storage section 11 require one item of data.
`Further, a data generating section 133 uses a re-sampling
`function (or interpolation function and decimation), and
`creates data between the existing sampling data stored in the
`data storage section 11 by re-sampling.
`That is, the data generating section 133 performs convo-
`lution computation between filter data and sampling data
`caused by a re-sampling function, thereby generating inter-
`polation data.
`Linear interpolation, a spline function and a sampling
`function (sinx/x), for example, are employed to generate
`data re-sampled at the data generating section 133.
`Actually, when data is generated by performing
`re-sampling at the data generating section 133, a sampling
`function with its small error and good signal reproduction
`may be preferably employed.
`In addition, in the case where re-sampling is performed by
`employing a sampling function, a passing bandwidth can be
`restricted by employing a rectangular wave window, a
`Hanning window,
`a Hamming window,
`a Blackman
`window, a Kaiser window or a Blackman Harris window.
`In an example shown in FIG. 2D, a characteristic sinx/x
`with a finite length using a window function is denoted by
`a broken line.
`
`In the case where a rectangular wave window is used as
`a window function, a side robe is superimposed on a main
`robe (basic wave) as a ripple.
`Therefore,
`in order to suppress the ripple, a window
`function such as a Hanning window, Hamming window,
`Blackman window, Kaiser window, or Blackman Harris
`window which have a small maximum value of attenuation
`
`quantity of the side robe as compared with a rectangular
`wave window may be preferably employed.
`Further, at the display control section 134, since a value
`of data stored in the data storage section 11 is merely a read
`value of the A/D converter 10, a conversion to a significant
`value is simultaneously performed.
`That is, the display control section 134 controls a display
`section 14 so that a level change of the measured signal
`signal-processed by a signal processing section 13 based on
`data stored in the data storage section 11 is displayed on the
`display screen of a display section 14 by defining time and
`amplitude on horizontal and vertical axes of the display
`section 14, for example.
`
`10
`
`15
`
`20
`
`25
`
`30
`
`35
`
`40
`
`45
`
`50
`
`55
`
`60
`
`65
`
`8
`Now, an outline of processing executed at a data acqui-
`sition management section 131, processing condition con-
`verting section 132, data generating section 133, and display
`control section 134 of the signal processing section 13, will
`be described with reference to a flow chart shown in FIG.
`1C.
`
`First, assume that the following measurement conditions
`are set and computed by the setting input section 12 (step
`S1).
`Sampling rate: 10 MHZ (100 ns resolution)
`Data generation quantity: 501 (0 to 500 points)
`Data generation resolution: Time span 0.125 msec
`Resolution=250 milliseconds/data interval
`Data acquisition start time: (from data) of 2025 nsec after
`data acquisition start time
`Based on the above measurement conditions, 501 items of
`data are generated by 2.5 items by re-sampling them from
`the 20.25-th address of the data storage section 11 using the
`data stored in the data storage section 11 (steps S2, S3, S4
`and S5).
`the data acquisition management section 131
`That is,
`controls a data storage section 11, as described above (step
`S2 .
`Next, the data storage section 11 starts acquisition of the
`corresponding data (step S2), and terminates acquisition
`after the corresponding data has been acquired (step S3).
`Then,
`the processing condition converting section 132
`generates information required for processing at the data
`generating section 133, as described above (step S3).
`Next, the data generating section 133 generates data by
`re-sampling processing (step S4).
`Then, the display control section 134 generates display
`data (step S5), and displays the display data on the display
`section 14 (step S6).
`The re-sampling used here denotes that a sampling rate of
`the A/D converter 10 and/or a data acquisition time are/is
`changed by combining interpolation or decimation with each
`other.
`
`In principle, in this re-sampling, data is generated at a
`sufficiently high sampling rate by using an interpolation
`function, and data is generated at a desired sampling rate and
`timing by decimation.
`As an example, a case in which data shifted by a 1/4 clock
`of 4 MHZ is obtained from data generated at a sampling rate
`of 10 MHZ, will be described with reference to FIG. 1D.
`In the case of considering interpolation, assuming that
`data is generated at the lowest common multiple of 10 MHZ
`and 4 MHZ, the data can be converted into data generated at
`10 MHZ to 4 MHZ. Thus, one item of 20 MHZ data may be
`acquired by 5 items.
`In this case, however, a timing of data to be obtained is
`shifted by a 1A: clock, and thus, data corresponding to 40
`MHZ is generated in accordance with the procedures below.
`First, as shown in FIG. 1D, three items of data (a1, a2, a3),
`(b1, b2, b3), (c1, c2, c3), (d1, d2, d3), (e1, e2, e3), (f1, f2,
`f3), (g1, g2, g3), (h1, h2, h3) are interpolated among data A0,
`A2, A3, A4, A5, A6, A7, A8 .
`.
`. by a 14 internal, (x4
`interpolation).
`In this way, 40 MHZ data A0, a1, a2, a3, A1, b1, b2, b3,
`A2, c1, c2, c3, A3, d1, d2, d3, A4, e1, e2, e3, A5, f1, 2, f3,
`A6, g1, g2, g3, A7, h1, h2, h3, A8 are generated.
`Next, when data A0 is defined as a start point (0th), 4
`MHZ data shifted by a 1A: clock is obtained. Thus, the next
`first data al of data A0 is defined as a new start point (% clock
`shift).
`Then, a new data array (corresponding to 4 MHZ) from
`which one item of data a1, c3, f1, h3, is removed per by 10
`items is generated (1/5 decimation).
`
`10
`
`10
`
`

`

`US 6,631,341 B2
`
`9
`In this manner, re-sampling completes, and the 4 MHZ
`data shifted by a 1A: clock is generated from the data
`generated at a sampling rate of 10 MHZ.
`In the meantime, as described above, in both of interpo-
`lation and decimation, if a signal component is ignored, an
`error can occur.
`
`In general, a low pass filter is used in order to apply
`limitation to a finally required frequency bandwidth.
`Interpolation and decimation are defined as sampling
`actions, and the same filter characteristics may be used.
`The same filter characteristics used here denotes that
`decimation is defined as simple decimation if a filter is
`applied during interpolation.
`In operation under the above described measurement
`conditions, it is found that only 0.25-th (a1), 2.75-th (c3),
`5 .25-th (f1), 7.75-th (h3) data, of 4 MHZ are required.
`Namely, the other items of data (A0, a2, a3, A1, b1, b2,
`b3,A2, c1, c2, A3, d1, d2, d3, A4, e1, e2, e3, A5, f2, f3, A6,
`g1, g2, g3, A7, h1, h2, A8 .
`.
`. ) and the like are discarded
`even if they are generated.
`Only required timing data is generated by using a
`re-sampling function (or
`interpolation function and
`decimation).
`In the case arbitrary data is generated by a re-sampling
`function (or interpolation and decimation), new data is
`generated based on the preceding and succeeding data. Thus,
`redundant data is required before and after the above data.
`In this manner, in a signal analyzing apparatus according
`to the present embodiment, there can be provided a signal
`analyzing apparatus (spectrum analyzer) in which a sam-
`pling rate of the A/D converter 10 is fixed according to the
`frequency characteristics (bandwidth) of the RBW filter 5
`instead of time analysis and/or decomposition to be
`obtained, the apparatus being provided with a time span
`sweeping function.
`In particular, data is generated by re-sampling using a
`sampling function (sinx/x) with its finite length so that
`characteristics up to the vicinity of a Nyquist frequency of
`fs/2 (sampling frequency: fs) can be reproduced.
`In this manner, when the maximum bandwidth of the
`RBW filter 5 is determined, there is no need to change a
`sampling rate of the A/D converter 10. Thus, as in a
`conventional case, the time change of a measured signal can
`be recognized in detail without increasing the sampling rate
`of the A/D converter.
`A sampling function sinx/x function will be described in
`more detail.
`
`.
`
`.
`
`When the sampling function=fs, the sampling time T=1/
`fs, x=t><(a'c/T) is obtained, where “t” indicates a time of data
`to be acquired.
`Therefore, the sampling data exists in a value of t=n><T, n=
`.
`, —1, 0, 1 .
`.
`. (integer).
`Re-sampling denotes that data is generated when t=1.5,
`for example.
`The sampling function (sinx/x) is efficient in that the
`sampling function is a LPF (low pass filter) of the Nyquist
`frequency (=sampling frequency/2) (basically using an infi-
`nite number of samples).
`The use of the sampling function is equivalent to acqui-
`sition of data of desired time by applying an analog filter.
`Further, in comparing one interpolation caused by the
`sampling function and the other interpolation, a signal is
`digitally produced from certain data irrespective of fre-
`quency characteristics (i.e., by ignoring analog signal based
`frequency characteristics).
`Spline function interpolation is better than linear interpo-
`lation in quality, and however, such spline interpolation does
`not still consider frequency characteristics.
`
`10
`Namely, a sampling function is used for the purpose of
`reproduction considering frequency characteristics, and
`thus, precision is improved (reproduced more precisely
`considering signal characteristics).
`In the meantime, the signal analyzing apparatus according
`to the present embodiment can be used to analyze an optical
`signal th