JP2005055412A - Fast-fourier transform type frequency analyzer - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To speedily obtain a wide-band spectrum identical to a sweep type frequency analyzer at one measurement in wide-band spectrum measurement by FFT (fast-fourier transformation) processing, without combining a plurality of results. <P>SOLUTION: A local oscillator emits a sweep signal, of which the frequency increases or decreases in a uniform rate at a certain time intervals in place of the local oscillation signal by a fixed frequency. An FFT calculating circuit is constituted to cancel the sweep signal, and for extracting only the frequency components in a base-band signal, and it preliminarily operates, by multiplying the product of a sweep compensation signal and a window function to the base-band signal and executes FFT processing. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to an FFT type frequency analysis apparatus.

  At present, in the commercially available FFT type frequency analyzer, the spectrum obtained is limited by the Nyquist frequency of the A / D converter, the passable frequency of the band pass filter, and the like. To obtain a wider spectrum, step up the analog frequency down converter and connect the results together. Therefore, you must wait until the analog circuit stabilizes every time you step up. Furthermore, if the step-up frequency is not operated correctly, a discontinuous region is generated at the frequency joint.

  In addition, the result of the FFT processing is superimposed on the characteristics of the band-pass filter provided in the middle and appears as a form of multiplication on the spectrum. In the worst case, the result is a ripple on the spectrum. End up.

  Even in the measurement of a broadband spectrum by FFT processing, it is possible to obtain a broadband spectrum equivalent to that of the sweep-type frequency analysis device at a high speed by one measurement without synthesizing a plurality of results.

The invention according to claim 1 is a down-converter unit comprising a local oscillator, a mixer circuit, and a band pass filter for limiting the frequency band of the input RF signal, an A / D converter, a quadrature detection circuit, a low A signal processing unit comprising a pass filter and an FFT operation circuit, a so-called DSP unit;
The local oscillator generates a sweep signal whose frequency is increased or decreased at a uniform rate every fixed time, instead of a local oscillation signal with a fixed frequency,
The mixer circuit extracts a sum or difference between a sweep signal and an input RF signal arbitrarily band-limited as an IF signal,
The quadrature detection circuit and the low-pass filter separate the extracted IF signal into a complex signal composed of a real part and an imaginary part, and extract only a difference component in the complex signal to convert it into a baseband signal To do,
After the FFT operation circuit performs the window function processing operation to multiply the base band signal by the product of the sweep compensation signal and the window function in order to cancel the sweep signal and extract only the frequency component in the base band signal , Configured to perform FFT processing.

  When the present invention is compared with a conventional FFT type frequency analyzer, it is possible to measure a spectrum in a wide band in principle without limitation by one sweep. By performing the spectrum extraction process in a single sweep, the waiting time for the local oscillator step-up, that is, the loss time of data acquisition is eliminated, and the continuity of measurement is obtained.

式１３中のｋは通常、約２．０であって、この式１３の結果と式１２の結果は、

であれば、掃引式のものより高速な測定が実現できる。
例えば、Ａ／Ｄ変換器に１００ＭＨｚ程度の処理能力を有するものを使用すれば、平坦帯域幅（Ｆｌｔ）は３０ＭＨｚ程度まで拡張可能となり、従来の掃引式との速度比は、

となり、Ｒｂｗを１０ＭＨｚ、Ｆｌｔを２０ＭＨｚとすると、（２／３）１０＾６＝６６万６千倍の高速化が実現する。同様にＲｂｗが１ｋＨｚとしても、２万倍の高速化が実現する。In addition, compared with a conventional sweep type frequency analyzer, the speed does not slow down even if the resolution of the spectrum is increased.
In general, the sweep speed of the sweep type frequency analyzer depends on the resolution of the spectrum, which is obtained by the following equation.

In Equation 13, k is usually about 2.0, and the result of Equation 13 and the result of Equation 12 are

If so, it is possible to realize a measurement faster than the sweep type.
For example, if an A / D converter having a processing capability of about 100 MHz is used, the flat bandwidth (Flt) can be expanded to about 30 MHz, and the speed ratio with the conventional sweep type is

Assuming that Rbw is 10 MHz and Flt is 20 MHz, (2/3) 10 ^ 6 = 666,000 times higher speed is realized. Similarly, even if Rbw is 1 kHz, a speed increase of 20,000 times is realized.

  In addition, since the signal processing unit in the latter half is replaced with digital signal processing, the resolution selectivity is accurate, adjustment during manufacturing is not required, there is no secular change in signal processing characteristics, and the main causes of level errors are The log amplifier becomes unnecessary.

  By using the IF signal to which the sweep signal is added, which is taken out from the conventional sweep type frequency analysis device, it becomes an external speed increasing device of the conventional sweep type frequency analysis device.

  The band-limited input RF signal is added to the sweep signal emitted from the local oscillator in the mixer circuit, and the extracted sum or difference is converted into an IF signal by a quadrature detection circuit and a low-pass filter. Is separated into a complex signal, and only the difference component in the complex signal is extracted and converted into a baseband signal. In the FFT operation circuit, the sweep signal included in the baseband signal is canceled and only the frequency component is obtained. In order to extract the signal, a window function processing operation for multiplying the product of the sweep compensation signal and the window function by the base band signal is performed, and then an FFT process is executed.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
FIG. 1 is a block circuit diagram of a conventional FFT type frequency analysis apparatus. FIG. 1A is a diagram in which an input RF signal is directly frequency-converted by an analog frequency down converter 1-1 to a frequency capable of A / D conversion in advance. . Further, the band is limited by the band pass filter 1-6 to prevent aliasing that may occur during A / D conversion in the A / D converter 1-2.

  The A / D converted signal is subjected to quadrature detection by the quadrature detection circuit 1-7 in the signal processing unit 1-3, and is converted into a complex signal limited to a desired band by the subsequent digital filter 1-8. By performing FFT processing on the signal, a spectrum within a range limited to a desired frequency is obtained.

  FIG. 1b is substantially the same as FIG. 1a, except that quadrature detection followed by a low pass filter is implemented with an analog circuit.

  The drawbacks of these conventional systems are that the spectrum obtained is limited by the Nyquist frequency of the A / D converter, the passable frequency of the band pass filter, and the like. To obtain a wider spectrum, step up the analog frequency down converter and connect the results together. Therefore, you must wait until the analog circuit stabilizes every time you step up. Furthermore, if the step-up frequency is not operated correctly, a discontinuous region is generated at the frequency joint.

  The result of the FFT processing is superimposed on the characteristics of the band pass filter provided in the middle, and appears in the form of multiplication on the spectrum, and in the worst case, it becomes a ripple on the spectrum. .

In either method, the input RF signal is converted into an IF signal (intermediate signal) by an analog down converter. The IF signal has a pass band and a center frequency ω _IF determined by a band pass filter.

Ｉ，Ｑ： ベースバンド信号
ω： 搬送波周波数
Ａ（ｔ）： 振幅の時間推移
θ（ｔ）： 位相の時間推移
ダウン・コンバータによる周波数の移動は局部発振器の周波数をω_１とすると次式によって表される。

（Ｉ，Ｑ、Ａ（ｔ）、θ（ｔ）にはなんら変化はない。）
下記文献に記載されている証明によって、式（５）が導かれる。
長野 昌生著「ディジタル無線通信における信号処理の基礎」（インターフェース誌２００２年９月号） A general system of band-limited signals is expressed by the following equation.

I, Q: baseband signals omega: carrier frequency A (t): time course of the amplitude θ (t): Table When the movement of the frequency with time transition down converter phases to the frequency of the local oscillator and omega ₁ by: Is done.

(I, Q, A (t), θ (t) are not changed at all.)
The proof described in the following document leads to equation (5).
Masao Nagano, “Signal Processing Basics in Digital Wireless Communication” (Interface Magazine, September 2002)

  The input RF signal converted into the IF signal as described above is converted into a digital signal by the A / D converter.

ｆ_ＩＦにｃｏｓ（ω_ＩＦｔ）を掛けたものを実数部、ｓｉｎ（ω_ＩＦｔ）を掛けたものを虚数部とした複素数を求めると、下式と等価になる。

三角関数の加法定理により、周波数における和の成分ｅｘｐ［−ｊ２ωＩＦｔ］と差の成分ｅｘｐ［０］が現れ、差の成分だけをロー・パス・フィルタ（ＬＰＦ）によって濾過して抽出すると次式のごとき複素信号の実数成分Ｉと虚数成分Ｑが得られる。

The digital signal is quadrature detection processing in the digital down converter is converted into decorated with the baseband signal f _B. That is, it is obtained by the following calculation with the intermediate frequency set to 0 Hz.

A complex number obtained by multiplying f _IF by cos (ω _IF t) as a real part and multiplying by sin (ω _IF t) as an imaginary part is equivalent to the following expression.

According to the addition theorem of the trigonometric function, the sum component exp [−j2ωIFt] and the difference component exp [0] appear in the frequency, and when only the difference component is filtered and extracted by the low-pass filter (LPF), Thus, the real component I and the imaginary component Q of the complex signal are obtained.

σ：掃引速度
Ｆｌｔ：平坦帯域幅（後述）
Ｇｔ：定数で通常は２〜３程度
Ｒｂｗ：分解能帯域幅で通常は３ｄＢ
換言すれば、信号経路上のバンド・パス・フィルタ（ＢＰＦ）やロー・パス・フィルタ（ＬＰＦ）のうち、最も通過帯域の狭いフィルタの範囲内に限定される。The spectrum is obtained by performing complex FFT processing on the I + jQ signal obtained by the above calculation. The effective spectrum obtained by one FFT of this method is determined by the following equation.

σ: sweep speed Flt: flat bandwidth (described later)
Gt: Constant, usually about 2 to 3 Rbw: Resolution bandwidth, usually 3 dB
In other words, the filter is limited to the narrowest passband of the band pass filter (BPF) and the low pass filter (LPF) on the signal path.

  The steps described above are general and include parts common to the present invention. In the present invention, however, in the local oscillator 3-2 in FIG. 3 in which the down converter 2-1 in FIG. A sweep signal is oscillated like an analyzer.

The frequency repeats increasing or decreasing at a uniform rate between the start frequency ω _START and the stop frequency ω _STOP at regular time intervals.
Here, assuming that the frequency of the local oscillation signal l (t) increases from ω _START to ω _STOP during time St seconds, assuming that l (t) = Re [exp [jθ ₁ (t)], the frequency ω _{Since 1} (t) is the time derivative of the phase,

  When the time exceeds St, the same frequency is repeatedly increased with t = 0. (In fact, there is very little blanking time between the above run and the next run.)

If ω _STOP −ω _START / St in Equation 6 is replaced with σ, ω ₁ = ω _START + σt can be expressed. If σ is called a sweep speed and integrated, the phase becomes l (t).

When the down converter is operated with the signal of Equation 9, the IF signal is as follows.

ただしこれは、ω_ＩＦ＝ω_０＋σＳｔ／２がバンド・パス・フィルタ３−３の通過域内の場合であって、それから外れた周波数の場合はレベルが下がる。それは中間周波数、ω_ＩＦ＝ω_０＋σＳｔのバンド・パス・フィルタ３−３の特性関数Ｂ（ω）となり上式は

For the sake of simplicity, if the time that the local oscillator 3-2 sweeps is −St / 2 <t <St / 2, then ω _IF = ω ₀ −σSt / at time t = St / 2, 0, and St / 2, respectively. 2, ω _IF = ω ₀ , ω _1F = ω ₀ + σSt / 2, the frequency of the intermediate signal spreads back and forth around ω _IF = ω ₀ , and the IF signal is expressed by the following equation.

However, this is the case where ω _IF = ω ₀ + σSt / 2 is within the pass band of the band pass filter 3-3, and the level is lowered when the frequency is out of the range. It becomes the characteristic function B (ω) of the band pass filter 3-3 with an intermediate frequency, ω _IF = ω ₀ + σSt, and the above equation is

となる。When the quadrature detection processing is performed on the IF signal by Expression 10 in the quadrature detection circuit 4-4 in the down-converter unit 4-3 shown in FIG. 4, the term of ω ₀ is eliminated from the IF signal by expansion of the following expression.

It becomes.

By performing window function processing by multiplying Expression 11 obtained as described above by a window function having a phase component exp [−jσt ² ] in the window function processing unit 4-8 in the FFT operation circuit 4-7. , I + jQ can be obtained as a spectrum affected by the window function. The window function in this case is obtained by multiplying a normal window function w (t) by a complex component exp [−jσt ² ] for compensating the sweep signal.

ここで、バンド・パス・フィルタの特性によるＢ（ω（ｔ））は、ｗ（ｔ）と一体と考え

となり、これをＦＦＴ演算回路４−９においてＦＦＴ処理すれば、Ｉ＋ｊＱのスペクトラムと窓関数の周波数ドメインでの畳み込みが得られる。

ｗ（ｔ）の時間幅をＢ（ω（ｔ））の影響はほとんど出ないが、逆にｗ（ｔ）の時間幅がＢ（ω（ｔ））よりも大きい場合はＢ（ω（ｔ））の影響が支配的になる。Multiplying equation 11 by the window function above,

Here, B (ω (t)) due to the characteristics of the band pass filter is considered to be integral with w (t).

If this is subjected to FFT processing in the FFT operation circuit 4-9, convolution in the frequency domain of the spectrum of I + jQ and the window function can be obtained.

The time width of w (t) is hardly affected by B (ω (t)). Conversely, when the time width of w (t) is larger than B (ω (t)), B (ω (t) )) Influence becomes dominant.

上式においてΔｔが小さい（負）場合、すなわち窓関数を乗ずるタイミングが前の場合には周波数は実際よりも高く見え、Δｔが大きい（正）場合、すなわち窓関数を乗ずるタイミングが遅い場合には、周波数が実際よりも低くみえる。すなわち、窓関数を掛ける時間をずらせば、得られるスペクトラムは式１２だけシフトして観測される。
また、Δｔ^２の項は位相のみの差異であり得られるスペクトル成分の結果には影響しない。If exp [jσt ^2] time has deviated Δt in complex component exp [-jσt ^2] an IF signal of the window function in said would frequency by the following equation moves 2Shigumaderutati.

In the above equation, when Δt is small (negative), that is, when the timing to multiply the window function is before, the frequency appears higher than the actual frequency, and when Δt is large (positive), that is, when the timing to multiply the window function is late. The frequency looks lower than it actually is. That is, if the time for multiplying the window function is shifted, the obtained spectrum is observed with a shift of Equation 12.
Also, the term Δt ² is a phase only difference and does not affect the resulting spectral component result.

  When the sweep width of one time, that is, the interval between the START frequency and the STOP frequency is expanded, the spectrum is obtained by multiplying the window function w (t) at an appropriate time interval and executing the FFT process each time. A broadband spectrum can be obtained at high speed. In addition, the down-converter's local oscillator only needs to generate a single sweep signal, enabling continuous frequency analysis in a short time.

As shown in FIG. 5, the resolution of the spectrum is proportional to the time width of the window function, and the time length depends on Gt / Rbw (Gt: constant is usually about 2 to 3, Rbw: resolution bandwidth is usually 3 dB). As required, the larger the Gt, the better the dynamic range. During this time, the number of sweeps by the local oscillator of the down converter is within the range that can be handled as a signal, which is the pass of the narrowest filter bandwidth in the path until the baseband I and Q signals are obtained. Band, where it is assumed that the passband is considered to be flat: Flt, the maximum sweep rate σ _max is determined by:

  By arbitrarily moving the timing and interval for applying the window function, the number of spectrum points obtained can be arbitrarily changed, and the same data can be changed.

It is a circuit block diagram of a conventional frequency analysis apparatus. It is a circuit block diagram of the frequency analyzer by this invention. It is an enlarged view of the down converter part of FIG. FIG. 3 is an enlarged view of a signal processing unit in FIG. 2. It is a figure which shows the relationship between filter response time and the frequency width which can be swept.

Explanation of symbols

1-1 Analog Frequency Down Converter 1-2 A / D Converter 1-3 Signal Processing Unit 1-4 Mixer 1-5 Local Oscillator 1-6 Band Pass Filter 1-7 Quadrature Detection Circuit 1-8 Low pass filter 2-1 Down converter 2-2 A / D converter 2-3 (digital) signal processing unit 2-4 Interface 3-1 Mixer 3-2 Local oscillator 3-3 Band pass Filter 4-1 A / D converter 4-2 Local oscillator 4-3 (digital) signal processor 4-4 Quadrature detection circuit 4-5 Numerically controlled oscillator (NCO)
4-6 Low Pass Filter 4-7 FFT Operation Circuit 4-8 Window Function Processing Unit 4-9 FFT Processing Unit Flt Flat Bandwidth

Claims (1)

A local oscillator,
A mixer circuit;
A quadrature detection circuit and a low pass filter;
An FFT operation circuit,
The local oscillator generates a sweep signal whose frequency is increased or decreased at a uniform rate every fixed time, instead of a local oscillation signal with a fixed frequency,
The mixer circuit extracts a sum or difference between a sweep signal and an input RF signal arbitrarily band-limited as an IF signal,
The quadrature detection circuit and the low-pass filter separate the extracted IF signal into a complex signal composed of a real part and an imaginary part, and extract only a difference component in the complex signal to convert it into a baseband signal To do,
After the FFT operation circuit performs the window function processing operation to multiply the base band signal by the product of the sweep compensation signal and the window function in order to cancel the sweep signal and extract only the frequency component in the base band signal An FFT type frequency analysis apparatus that performs FFT processing.

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