Method for ascertaining the harmonic components of an analog electrical signal at a fundamental frequency which changes over time

A method includes ascertaining harmonic components of a periodic analog signal at a fundamental frequency which changes over time. The signal is digitized and fast Fourier transformed. A target signal is produced by modulating the signal using a first carrier frequency to form two frequency sidebands, the first carrier frequency being greater than the fundamental frequency of the signal. One of the two frequency sidebands of the modulated signal is filtered. The filtered frequency sideband is modulated using a second carrier frequency forming two frequency sidebands. The second carrier frequency is greater than the fundamental frequency of the signal. The difference between the second and first carrier frequencies is the same as the difference between the fundamental frequency and the target fundamental frequency. One of these two frequency sidebands is output as the target signal to calculate the fast Fourier transformation.

PRIORITY STATEMENT

The present application hereby claims priority under 35 U.S.C. §119 on German patent application number DE 10 2007 056 605.2 filed Nov. 22, 2007, the entire contents of which is hereby incorporated herein by reference.

FIELD

Embodiments of the invention generally relates to a method for ascertaining the harmonic components of an analog electrical signal at a fundamental frequency which changes over time.

BACKGROUND

Methods for ascertaining the harmonic components of analog electrical signals are known. In this case, the analog signal is sampled and digitized at a sampling frequency, for example, so as then to use fast Fourier transformation FFT to calculate the Fourier transformation for the signal. This requires a fixed number of samples to be ascertained per period of time. For this reason, a fundamental frequency changing over time requires the sampling frequency to be continually tracked. In addition, the sampling system needs to be in tune with the maximum sampling frequency.

SUMMARY

In at least one embodiment of the invention, tracking the sampling frequency is avoided.

The solution of at least one embodiment provides for the analog signal at a fundamental frequency which changes over time to be taken as a basis for producing an analog target signal at a target fundamental frequency which is constant over time, the analog target signal then being digitized at the target fundamental frequency as the sampling frequency and being used instead of said analog signal to perform the fast Fourier transformation to ascertain the harmonic components of the analog signal, wherein the target signal is produced by modulating the analog signal using a first carrier frequency to form two frequency sidebands, the first carrier frequency being chosen to be greater, particularly several orders of magnitude greater, than the fundamental frequency of the analog signal, then filtering one of the two frequency sidebands out of the modulated analog signal, then modulating the filtered-out frequency sideband (as SSB signal) using a second carrier frequency to form two frequency sidebands again, the second carrier frequency being greater, particularly several orders of magnitude greater, than the fundamental frequency of the analog signal, and the difference between the second and first carrier frequencies respectively being the same as the discrepancy between the fundamental frequency and the target fundamental frequency, and outputting one of these two frequency sidebands as the analog target, signal which is to be produced. In this way, a fluctuating fundamental frequency is transformed into a target fundamental frequency which is constant over time. The sampling frequency is chosen to be equal to the target fundamental frequency, so that per period it is possible to perform sampling with a constant even number of samples.

DETAILED DESCRIPTION OF THE EXAMPLE EMBODIMENTS

The single FIGURE shows a schematic illustration of the method for ascertaining the harmonic components of an analog electrical input signal ES at the fundamental frequency fgein. In this case, the fundamental frequency fgein of the input signal ES fluctuates in the example embodiment between 45 and 60 Hz and is approximately 50 Hz on average. The harmonic components are ascertained by means of fast Fourier transformation (FFT) in a known manner using an output signal AS which is to be produced (target signal ZS, which has a constant fundamental frequency fgaus (target fundamental frequency fzg) of 55 Hz.

The input signal ES is at the frequency fein, which besides the fundamental frequency fgein respectively comprises the frequencies of the “harmonics”, which are an integer multiple of the fundamental frequency fgein. The entire frequency spectrum FSE, including the fundamental frequency fgein, is shown schematically in the FIGURE.

In addition, a (first) oscillator TO (carrier oscillator) is provided which uses a crystal Q to produce a (first) signal (carrier signal) at a fixed frequency of 1 MHz, the (first) modulation frequency (carrier frequency) fHF1. The input signal ES is mixed with the (first) signal in a modulator M (is modulated with the carrier signal). Besides a carrier at the carrier frequency fHF1of 1 MHz, the mixed signal at the frequency fZF has two sidebands SB1, SB2, as shown schematically in the FIGURE. The fundamental frequency of the sidebands SB1, SB2is 1 MHz−fgein or 1 MHz+fgein (that is to say for fgein=50 Hz 1 MHz−50 Hz or 1 MHz+50 Hz).

The (first) modulation frequency fHF1differs from the fundamental frequency fgein of the analog signal ES by more than 4 orders of magnitude; it must be at least greater than the fundamental frequency fgein, where possible several orders of magnitude, as in this case in the exemplary embodiment.

A steep-edged crystal filter QF is used to filter out one of the two frequency sidebands (in this case the frequency sideband SB1) and the carrier at the carrier frequency fHF1, so that downstream of the crystal filter QF there is now only the frequency sideband SB2as an “SSB” (Single Side Band) signal, which effectively lacks the reference to the fundamental frequency fgein as a result of the absence of the carrier. (For an SSB signal which has been produced beforehand by modulation with a carrier at a frequency of 1 MHz, an offset in the SSB signal of 1 MHz is also referred to.)

The SSB signal is modulated (mixed) with a (second) modulation frequency fHF2of a (second) oscillator BFO (Beat Frequency Oscillator) using a (second) modulator M2(often also called product detector), which produces a low-frequency output signal AS with a frequency spectrum FSA for a fundamental frequency fgaus.

Regulation of the (second) oscillator BFO by means of a controller C is used to set the modulation frequency fHF2in each case such that the output signal AS is at a fixed fundamental frequency fgaus. The controller C calculates the required controlled variable from the output signal AS (e.g. by means of signal analysis).

The possibility of obtaining an output signal AS at a fixed fundamental frequency fgaus is obtained by virtue of the fundamental frequency fgaus respectively changing, after the (second) modulation, with the interval between the (second) modulation frequency fHF2and the SSB signal (sideband).

In other words, the regulation ensures that the difference from the second and the first modulation frequency (carrier frequency) fHF1, fHF2is respectively the same as the discrepancy between the fundamental frequency fgein and the fundamental frequency fgaus.

This method is thus used to transform the fluctuating fundamental frequency fgein into a constant fundamental frequency fgaus.

In the example embodiment in this case, the modulation frequency fHF2is respectively tracked (regulated) such that the fundamental frequency fgaus of the mixed frequency faus is constantly 55 Hz in each case.

The output of the output signal AS at the constant fundamental frequency fgaus of 55 Hz means that one of the two frequency sidebands delivers the analog target signal ZS to be produced at a constant target fundamental frequency fzg.

This target signal ZS is digitized at the constant target fundamental frequency fzg as the sampling frequency and is used to calculate the fast Fourier transformation. This is then used to calculate the harmonic components of the target signal ZS, which correspond to those of the input signal ES.