RMS Level vs. Spectrum Level in FONIX Composite Signals
by Larry Revit, hearing scientist
Many Fonix reps and users have questions about why the levels on composite frequency response curves are generally lower than the "RMS" levels displayed near the graphs. So herein lies an explanation.
"RMS" (or "Root Mean Square") is a term referring to the overall level of a signal. "Spectrum level" refers to the level of each individual frequency component of a signal. With a pure-tone sweep, only one frequency is tested at a time: There is only one frequency component. With only one component, the overall, RMS level of the signal is the same as the spextrum level of the signal at each frequency. That's why there's little confusion with pure-tone tests.
But the Fonix 6500 composite signal is a combination of 80 pure tones of different frequencies (79 for the FP40), presented simultaneously. The overall RMS level is a combination of all the spectrum levels of the 80 frequencies put together.1 The overall (RMS) level, therefore, is greater than the (spectrum) level of each component. Spectrum levels are what appear on the curve of a frequency response graph. So the levels on a composite frequency response graph will be lower than the numerical RMS level in the readout to the right of the graph.
As an example, for flat-spectrum (unweighted) composite consisting of 80 pure tones, the spectrum level of each component is 19 dB down from the RMS level.2 The spectrum of the flat composite can be viewed by first "leveling" the sound chamber and then immediately observing a flat-weighted composite SPL ("POWER" or "OUTPUT") measurement, without moving the microphone from the calibration position in the chamber. {With the 6500 press[RESET], and then press [WEIGHT] twice; with the FP40, turn GAIN OFF with [F2] or [F3], and then select FLAT in the menu under COMPOSITE PARAMETERS.} An example is shown in graph "(A)". Note that the RMS SOURCE and OUT levels are essentially the same (because the microphone is at the calibration position), but the spectrum levels of the curve are 19 dB down from the RMS level.
The "speech weighted" composite signal combines a high-frequency filter with the flat-spectrum composite. This filter causes a downward slope above 900 Hz. The spectrum of the speech-weighted composite can be viewed by observing a leveled, "WEIGHTED" SPL ("POWER" or "OUTPUT") measurement, without moving the microphone form the calibration position in the chamber. {With the 6500 press [RESET], and then press [WEIGHT] once; with the FP40, select SPEECH in the menu under COMPOSITE PARAMETERS.} An example is shown in graph "(B)". Note that the RMS SOURCE and OUT levels are, again, essentially the same (because the microphone is still at the calibration position), but the spectrum levels (levels on the curve) vary between about -10 to -30 dB relative to the RMS level.
Graph "(B)" represents the spectrum of the signal that is presented whenever the speech weighting is enabled. Thus, when viewing a weighted SPL measurement, one can expect to see a downward slope (the slope of the test signal) superimposed on the frequency response of the instrument under test. The purpose of such a measurement would be to estimate the output of an instrument in response to a signal having the long-term, peak spectrum of speech.
On the other hand, when viewing a "WEIGHTED GAIN" measurement, the input spectrum is subtracted from the output spectrum before display. In this case, although the speech weighting is still part of the test signal, the frequency response is displayed with the speech weighting (downward slope) removed.
In summary, the "RMS" (or overall) level is a summation of all the frequency components of a composite signal. The levels at each frequency (or "spectrum levels") will be lower than the RMS level. The "WEIGHTED SPL" ("POWER" or "OUTPUT") test displays a composite frequency response of an instrument combined with the downward-sloping effects of speech weighting. The "WEIGHTED GAIN" test subtracts the speech weighting from the measured output (removes the downward slope) before displaying the results, and thus only the composite frequency response of the instrument is visible.
At present, the ANSI standards committee for hearing-aid testing is nearing completion of a new standard for broadband, speech-weighted tests (such as with the Fonix real-time composite). The Fonix composite signal is so useful, that as concerned professionals we must recognize that now is the time to become familiar the new ways of interpreting RMS and spectrum levels. (Call 800-547-8209 with questions. Ask for Larry.)
Footnotes
- Mathematically, RMS is the square root of the mean of the squares of the values of each component:
Where "X" equals the voltage (or pressure) of each component, and there are 80 components.
- For a flat-spectrum composite: Spectrum level =
RMS level - 10 log (No. of frequency components)
=RMS level - 10 log (80)
=RMS level - (19).