JP2692723B2 - Carrier frequency difference measurement method - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for obtaining a carrier frequency difference between frequency-modulated waves at the time of modulation in a frequency-modulation synchronous broadcasting system. Here, the carrier frequency difference is
It is assumed that the frequency difference equivalently occurs due to the time variation of the difference in the carrier initial phase between the first carrier wave and the second carrier wave.

[0002]

2. Description of the Related Art To measure the frequency difference between two signals, 2
Use a frequency counter on the platform to find the difference, or use a phase detector. In order to measure the carrier frequency difference between the two synchronized frequency modulated waves, it is possible to similarly use two frequency counters or a phase detector. In this case, since the frequency-modulated wave changes the instantaneous frequency with the modulation, it is necessary to measure and average the frequency over a long time period in which the modulated signal can be regarded as a stationary process.

[0003]

SUMMARY OF THE INVENTION It is an object of the present invention to measure the carrier frequency difference between two synchronized frequency modulated waves in the shortest possible measuring time. It also aims to measure the carrier frequency difference in a dynamic state during modulation.

[0004]

In order to achieve the above object, in the carrier frequency difference measuring method of the present invention, the first carrier and the second carrier are time-synchronized with the same modulation signal and frequency-modulated, respectively. 1 frequency-modulated wave and second frequency-modulated wave, the second frequency-modulated wave is delayed by the time τ with respect to the first frequency-modulated wave, and the two frequency-modulated waves are added together to generate an interference wave. The time series H _i of the short-time spectrum of the generated interference wave H _i (i =
0, 1, 2,. . ) Is obtained, and the time change of the feature points such as the minimum point and the maximum point in the time series H _i is tracked, and the spectrum frequency f _i of the feature point at time i and the spectrum at time k when time Δt elapses from time i. detecting a frequency f _k, the first carrier and the frequency difference generated equivalently due to the time variation of the difference of the carrier initial phase of the second carrier _{τ (f k -f i) /} Δt, i It is determined by ≠ k.

When obtaining the carrier frequency difference from the time change of the minimum point which is one of the characteristic points of the spectrum envelope pattern of the interference wave, it is necessary to consider the time required to obtain the short time spectrum. There are generally three methods for obtaining a short-time spectrum.

The first is a filter bank method in which a large number of narrow band filters are prepared, required band components are extracted and detected to obtain a spectrum.

The second is an FFT method in which a waveform in a short time section is spectrally analyzed by FFT.

A third method is a frequency sweep type spectrum analysis method for sweeping the tuning frequency of a single narrow band filter to obtain a spectrum.

[0009]

Operation: When there are two frequency-modulated waves that are synchronized, the first
Frequency modulated wave x ₁ (t) and second frequency modulated wave x
₂ (t) is generally represented by Equations 1 and 2. The following signals are handled by a symbolic method using complex numbers.

[0010]

(Equation 1)

[0011]

(Equation 2)

Where a _n , n = 1, 2 are amplitudes, f _c is a carrier initial setting frequency, Δf _n (t), n = 1, 2 is a carrier initial setting frequency deviation, and η _n (t), n = Reference numerals 1 and 2 are carrier initial phases. μ (t) is the frequency shift due to the modulated signal g (t) and is given by equation 3.

[0013]

(Equation 3)

Where D is the maximum frequency shift. Δμ _n
(T), n = 1, 2 are deviations of the frequency shift due to the modulation and are given by the equation 4.

[0015]

(Equation 4)

Here, ΔD _n , n = 1, 2 is the deviation of the maximum frequency deviation and changes with time. The carrier initial setting frequency deviation of two ideally synchronized frequency modulated waves is Δf ₁ = Δf ₂ = 0 regardless of time. Further, the frequency shift deviation due to the modulation is Δμ ₁ (t) = Δμ ₂ (t) = 0. Furthermore, the carrier initial phase is dη ₁ (t) / dt = dη
₂ (t) / dt = 0 and η ₁ (t) = η
₂ (t).

One method of achieving frequency synchronization in actual synchronous broadcasting is to generate a carrier initial setting frequency by phase-locking to a common signal source outside two frequency modulators, for example, a clock of a modulation signal. is there. in this case,
Equivalent frequency deviations occur in each term of the carrier initial setting frequency, frequency deviation due to modulation, and carrier initial phase.

Phase fluctuations are added in the PLL circuit which generates the carrier default frequency. Moreover, the phase fluctuation generated outside the PLL circuit cannot be absorbed. These phase fluctuations can be considered by incorporating them in the carrier initial phase.

The deviation of the frequency shift due to the modulation may be regarded as 0 in the situation where synchronization is taken. When the frequency modulation is actually performed by using the digital signal processing technique, the frequency deviation does not occur due to the modulation. The jitter or drift of the generated phase may be considered by incorporating it in the carrier initial phase.

Considering these situations, equations 1 and 2 become equations 5 and 6, respectively. In Equation 5 and Equation 6, φ _n (t), n =
Reference numerals 1 and 2 are new carrier initial phases.

[0021]

(Equation 5)

[0022]

(Equation 6)

However, here, the carrier initial phase φ ₁ (t)
And φ ₂ (t) are given by Equations 7 and 8 and include various equivalent frequency deviations.

[0024]

(Equation 7)

[0025]

(Equation 8)

The operation of adding a delay time to one of two synchronized frequency modulated waves and adding them together will be described. The short-time spectrum P (ω, i) at time i in the first frequency-modulated wave that has been synchronously modulated is given by Equations 9 and 10 by the Fourier transform of x ₁ (t). However, ω has an angular frequency of 2πf.

[0027]

(Equation 9)

[0028]

(Equation 10)

Assuming that the carrier initial phase has such a change that it can be regarded as constant from time t _i -ΔT to t _i + ΔT, equation 10 is represented by equation 11.

[0030]

[Equation 11]

Here, φ ₁ (i) is the carrier initial phase at time i, and F (ω, i) is given by equation 12.

[0032]

(Equation 12)

Similarly, the short-time spectrum Q (ω, i) of x ₂ (t) at time i is given by equation 13.

[0034]

(Equation 13)

The spectrum S (ω, i) of the wave i obtained by adding the frequency modulated wave 1 and the frequency modulated wave 2 after delaying them by the delay time τ is given by equation (14).

[0036]

[Equation 14]

Substituting equations 11 and 13 into equation 14, equation 1
Get 5.

[0038]

(Equation 15)

When Equation 15 is rearranged, Equation 16 is obtained.

[0040]

(Equation 16)

Equation 16 Difference of initial phase of carrier on right side φ
₂ (i) −φ ₁ (i) is given again by Equation 17.

[0042]

[Equation 17]

Substituting equation 17 into equation 16, equation 18 is obtained.

[0044]

(Equation 18)

Here, Z (ω, i) is given by equation 19.

[0046]

[Equation 19]

The absolute value A (ω, i) of S (ω, i) gives the spectral amplitude and is given by equation 20.

[0048]

(Equation 20)

Here, sqr {} means a square root, and * means to take a conjugate. By substituting the equation 18 into the equation 20 and applying the equation 19, the equation 21 is obtained.

[0050]

(Equation 21)

Where | F (ω, i) | is the spectral amplitude of the frequency modulated wave. r = a ₂ / a ₁ . Also θ
(I) is expressed by Equation 22.

[0052]

(Equation 22)

A (ω, i) in the equation 21 has a maximum value when θ (i) is an integral multiple of 2π and a minimum value when it is an odd multiple of π. A minimum point also occurs at a position separated by a frequency ± 1 / τ with respect to the spectrum frequency of one minimum point. This is because the phases of the two frequency-modulated waves are opposite to each other at those frequencies. That is, the adjacent minimum points differ in phase by 2π. This is brought about by giving a delay time τ.

On the other hand, the minimum point of the ripple on the frequency axis of the spectrum envelope moves left and right due to the carrier initial phase difference φ (i). If it moves exactly by one ripple cycle, it means that a phase change of 2π has occurred.

Let f _i be the frequency of one minimum point of A (ω, i) at time _i, and at time k, the minimum point is frequency f _k.
, The frequency change Δf of the minimum point between
Is given by Equation 23.

[0056]

(Equation 23)

Considering that the frequency width 1 / τ corresponds to the phase 2π, the phase difference change Δφ of the carrier generated during the time Δt is given by the equation 24.

[0058]

(Equation 24)

Since this Δφ occurs during the time Δt, the phase difference change dφ per unit time is given by equation 25.

[0060]

(Equation 25)

By dividing this change in phase difference by 2π, the frequency difference is obtained as shown in equation 26.

[0062]

(Equation 26)

This frequency difference df is the carrier frequency difference derived from the time change of the difference between the two carrier initial phases.

The operation of obtaining the envelope of the spectrum of the interference wave will be described. Short-time spectrum S (ω,
The amplitude A (ω, i) of i) is multiplied by the spectrum amplitude | F (ω, i) | of the frequency-modulated wave itself as shown in Expression 21. This frequency-modulated wave spectrum amplitude is complex and has many maximum and minimum values. By obtaining the envelope of A (ω, i), the influence of | F (ω, i) | can be eliminated, and the characteristic point of the spectrum amplitude peculiar to the interference,
For example, it becomes easy to detect the minimum point.

Among the above-mentioned methods for obtaining the short-time spectrum, the first and second methods obtain the respective components of the spectrum at the same time, so that the change of the characteristic points with time is different from that of the short-time spectrum. It can be obtained only from the series.

On the other hand, in the third method, the frequency axis of one short-time spectrum is a function of time in order to sweep the frequency. By using this, the phase change can be known from the frequencies of several feature points in one spectral envelope, and thus the carrier frequency difference can be obtained.

[0067]

1 is a block diagram of an embodiment for measuring the carrier frequency difference of two frequency modulators synchronized by the method of the present invention. 10 is a modulation signal generator, 21 is a frequency modulator that outputs frequency modulated wave 1, 22 is a frequency modulator that outputs frequency modulated wave 2, 23 is a delay circuit, 30
Is an adder circuit, 40 is a spectrum analyzer, and 50 is a signal processing computer.

The modulation signal output from the modulation signal generator 10 is, for example, a 1 kHz sine wave. If necessary, it may be converted into a stereo composite signal by a stereo modulator, but monaural modulation will be considered here for simplification of description. The carrier wave initial setting frequency of the frequency modulator 21 is 79
MHz, the carrier frequency of the frequency modulator 22 is set to 7
It is set to 9 MHz + 1 Hz. Their maximum frequency shift is 75 kHz. The output of the frequency modulator 22 is delayed by, for example, 20 μs in the delay circuit 23, added to the output of the frequency modulator 21 in the addition circuit 30, and added to the spectrum analyzer 40, and the spectrum data is taken into the signal processing computer 50.

FIG. 2 shows spectra (S1) and (S2) at intervals of 0.1 second obtained by the spectrum analyzer 40 and their envelopes (E1) and (E2). The horizontal axis is the relative frequency, and the vertical axis is the relative intensity of the spectrum. The sweep speed of the spectrum analyzer at this time is 200 kHz / 10
0 ms, the analysis bandwidth is 3 kHz.

In (S1) and (S2) of FIG. 2, there is a comb-shaped small-cycle ripple in addition to the large-cycle intensity change due to the delay time. The large period intensity change is due to the delay time, and the small period ripple is due to the modulation. In order to eliminate the small period ripple, it is necessary to find the envelope of the spectrum, but here the moving average and the analytic signal method are used together.

Attention is paid to the minimum points a, b and c and A, B and C which are characteristic points in (E1) and (E2) of FIG. One minimum point b of the envelope (E1) has moved to B of the envelope (E2) 0.1 seconds later. Calculating the carrier frequency difference using Expression 26 shows +1 Hz correctly.

Since the frequency sweep type spectrum analysis is used here, if the sweep speed is low with respect to the frequency change of the characteristic points, the frequencies of the minimum points a, b and c in FIG. 2 (E1) or (E2). The carrier frequency difference is also obtained from the frequency intervals of A, B, and C. If the sweep speed is fast, the sweep speed may be negligible.

If the carrier frequency difference between the two frequency-modulated waves is constant, the minimum point moves in one direction and disappears outside the spectrum range. In such a case, it is advisable to move to the tracking of another local minimum before one local minimum disappears outside the band.

The occupied bandwidth of the current FM broadcasting is 150 kHz
This frequency width corresponds to a ripple period with a delay time of about 6.7 μs. The delay time suitable for measurement depends on the sweep speed and the carrier frequency difference or the amount of phase fluctuation.

[0075]

As described above, according to the method of the present invention, the carrier frequency difference can be shortened in a short time by the time change of the interference short-time spectrum pattern of two frequency-modulated waves that are synchronously modulated, and the modulated state can be obtained. Can be measured at.

The method of the present invention is not limited to the measurement of the carrier frequency difference between frequency-modulated waves. If the spectrum change due to the modulation and the spectrum change due to the delay interference can be separated, it is possible to obtain the difference between the frequency-modulated waves. Carrier frequency difference measurement is possible.

[Brief description of the drawings]

FIG. 1 is a block diagram for explaining the method of the present invention.

FIG. 2 is a short-time spectrum and its envelope for explaining the method of the present invention.

[Explanation of symbols]

 10 modulation signal generator 21 frequency modulator 22 frequency modulator 23 delay circuit 30 adder circuit 40 spectrum analyzer 50 signal processing computer a spectrum minimum point b spectrum minimum point c spectrum minimum point A spectrum minimum point B spectrum Local minimum point of C spectrum

Claims (2)

(57) [Claims] 1. A carrier frequency difference measuring method for measuring a carrier frequency difference between synchronized frequency-modulated waves, wherein the first carrier and the second carrier are time-synchronized with the same signal and frequency-modulated, respectively. Wave and the second frequency modulated wave, the second frequency modulated wave is delayed by the time τ with respect to the first frequency modulated wave, and the two frequency modulated waves are added to generate an interference wave. Time series Hi of the envelope of the short-time spectrum of the interference wave
(I = 0,1,2, ...) Is obtained, and the time change of the feature points such as the minimum point and the maximum point in the time series Hi is tracked, and the spectrum frequency fi at the time i of the feature point and the time i are calculated. The spectrum frequency fk at time k after the lapse of time Δt is detected, and the frequency difference equivalently caused by the time variation of the carrier initial phase difference between the first carrier and the second carrier is calculated by τ.
A method of measuring a carrier frequency difference, which is obtained by (fk-fi) / Δt, i ≠ k. 2. The synchronized frequency modulation according to claim 1, wherein the time series of the spectrum obtained by using a frequency sweep type spectrum analyzer is used to obtain the envelope of the short time spectrum. A method of measuring the frequency difference between signals.