Modulation (measuring systems)

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In measuring systems, modulation (also: leveling ) of measuring channels is the setting of the maximum expected amplitude ( peak value ) of the data stream to be measured .

Basics

Correct modulation is of elementary importance in order to obtain a meaningful measurement result . Overdriving a channel means that the signal is higher than the measuring system can process and leads to an incorrect measurement result. Understeering leads to a decrease in accuracy with the degree of understeering (higher quantization noise ), combined with a likewise decreasing dynamic range . Both types of incorrect modulation are to be avoided, but only the overmodulation leads to a result without any statement, while the undermodulated measurement still fulfills a more or less large utility value.

Explanations

  • The principle of leveling measurement channels is known in practice primarily from the audio sector: Even with simple sound recordings in mono or stereo , e.g. B. on magnetic tape or when digitizing at the line input of a sound card , must be controlled in order to achieve an acoustically satisfactory result.
  • With signal analytical measuring systems, theoretically any number of channels can be measured synchronously. In practice, the number of channels is limited by the finite resources of the measurement technology used, currently usually no more than 120 channels with sampling rates of typically 44100 Hz ( microphones ) or 11025 Hz ( accelerometers ). A channel number of this order of magnitude occurs, for example, in transfer path analyzes that are used in vehicle acoustics.

Effects of incorrect modulation

Override

In this case the modulation is set too low, the measuring channel is overdriven .

Step z. If, for example, the measurement signal has amplitudes of up to 1 Pa , at least 94 dB would have to be selected for correct control . At a modulation of 88 dB (this corresponds to 1–2 levels in a typical measuring system) the channel is overdriven by 6 dB.

Result: All amplitude values ​​that are 0.5 Pa or above (more precisely 0.50238 Pa or above) are set to 0.5 ( clipping ) (regardless of their actual value ), because the measuring system receives a measured variable that is not more can be represented, and therefore simply replaces it with the largest possible. In the data file, all '11111111'en are stored. This corresponds to a horizontal, constant signal, i.e. H. a DC signal. What would be correct, however, would be a measurement signal that results from the superposition (superposition) of the various frequencies (Fourier principle). In contrast, a constant signal (direct current) no longer contains any frequency information; the Campbell of a direct current signal corresponds to a solid color area. (Caution: The total level, which results from the calculation, does not necessarily have to deviate significantly - it only does so if the overload was very massive.)

Most of the time, the signal will not be overdriven for the entire measurement time, but only from time to time. In this case, a time signal is obtained which assumes a direct current curve at these time segments. So you get red stripes in the Campbell, which run through the entire frequency axis (if the frequency axis is drawn on the vertical axis, these are vertical stripes). In addition, the hard kinks in the signal curve at the transition point to overdrive and from overdrive result in artificially broadband (predominantly high-frequency) interferences that falsify the Campbell diagram in the area of ​​the FFT block length by every single one of these processes. In other words, frequencies are generated in the measurement signal (and displayed in the Campbell) that do not exist (see above). If the overmodulation occurs only briefly and “barely”, this is not visible in the level curve and cannot be clearly identified as overmodulation even in the Campbell. It is therefore imperative to ensure during the measurement that there is no overload.

Understeer

In this case the level has been set too high, e.g. B. to 100 dB (one level too high). We assume again that amplitude values ​​of up to 1 Pa occur in the measurement signal. The leveling, on the other hand, can record values ​​up to 2 Pa. That means 100000000 corresponds to 2 Pa, but only values ​​of <1 Pa occur. Result: The top bit of each data word (i.e. each stored amplitude value) always remains at "0"; it does not convey any information. This has two effects:

  • The smallest value still to be displayed (00000001) now corresponds to 2 ^ -6 Pa. However, this value is just 36.1 dB below the maximum occurring amplitude value (dynamic range). Although the word length in today's measuring systems is higher than 8 bits (at least 16 bits), in practice an under-modulation is usually in the range of −20 dB or even more. In practice, an “undermodulation” of 6 dB would rather be described as an extremely optimal modulation. You should always keep in mind that the measurement signal is a sum signal of different frequencies and that the individual frequency components can only be obtained from it through the FFT. Therefore, when evaluating whether an S / N distance is sufficient, the level of the narrow bands in the FFT should not be considered, but rather the level of the narrow bands in the FFT block in which this frequency has the lowest level.
  • The second problem arises from the fact that the higher level also results in higher quantization noise. It arises from the fact that with a digital representation of an analog variable (e.g. voltage coming from a microphone), only a finite number of different numerical values ​​can be “selected”. In other words, every measured time signal value must be rounded to a greater or lesser extent in the digital representation.
example
  • 8 bit word length again, level 142 dB. Then the top bit of the byte corresponds to 2 ^ 7 Pa and the bottom 1 Pa. d. H. binary 1 = decimal 1.
  • If the measuring system now measures a value of 1.51 Pa, only a value of 2.0 Pa can be stored due to the high level (binary 00000010), because the smallest representable value (and thus also the smallest difference) is now 1 Pa. The quantization error is therefore 0.49 Pa., Which corresponds to 2.44 dB. In relation to the narrowband level, this value is even higher, so that the information content of the measured signal tends to zero for high frequencies, since the useful signal disappears in the quantization noise.
  • If, on the other hand, the leveling is reduced to 100 dB, a value of 01100000 can be stored, which corresponds to 1.50. The quantization error is now only 0.058 dB