## Distortion Graph

The Distortion graph shows the measurement's fundamental (the linear part of its response), its harmonic distortion components up to the tenth harmonic and Total Harmonic Distortion (THD). The plots are derived from analysis of the impulse response. Impulse responses measured using logarithmic sweeps separate distortion from the linear part of the system response, the distortion components appear at negative times, behind the main impulse. Analysing the frequency content of these components allows plots of distortion harmonics to be generated.

The harmonic plots can only be generated for frequencies within the bandwidth of the measurement. For example, if a measurement is made to 20 kHz, the second harmonic plot can only be generated to 10 kHz, as the 2nd harmonic of 10k Hz is 20 kHz. Similarly the third harmonic plot can only be generated to 6.67 kHz (20/3). When opening measurements made before the Distortion graph was added to REW fewer harmonics may be available to display.

The lower frequency limit for distortion plots is 10 Hz or the measurement start frequency, whichever is higher. 10 Hz is the lower limit of the logarithmic part of the measurement sweep. Start frequencies lower than that use an initial linear swept portion (to avoid spending an excessive proportion of the sweep duration time at very low frequencies) which means that region cannot be used to generate distortion data.

Total Harmonic Distortion is generated from the available harmonics up to the tenth. At higher frequencies the THD plot will incorporate fewer harmonics, according to which are available.

The plots of the Fundamental (the linear part of the measurement) and the distortion harmonics do not include mic/meter or soundcard calibration corrections. This is to avoid the effect of the corrections generating a misleading view of distortion levels. For example, mic/meter and soundcard calibration corrections boost the lowest frequencies of measurements to counter the roll-off of the mic/meter and soundcard interfaces, but adding those corrections to a distortion plot would make distortion appear to rise at low frequencies, hence their omission.

The fundamental and harmonic plots are smoothed to 1/24 octave. This cannot be adjusted. The distortion data can be exported to a text file using File -> Export -> Distortion data as text.

### Distortion Controls

The control panel for the graph has these controls:

By default the plot shows the actual SPL levels of the fundamental and the harmonics. If Plot normalised to fundamental is selected the harmonics are divided by the fundamental to show their relative level and the fundamental appears as a flat line at 0 dB. The legend value for the fundamental will continue to show the actual SPL, the readings for the harmonics and THD will depend on the Distortion Figures setting. Normalising the plot will cause the distortion traces to rise at high frequencies if the response of the system being measured rolls off (as is usually the case). This is exaggerated if Use harmonic frequency as ref is selected (see next section). The boosting due to low fundamental level can be controlled by selecting Limit norm. to 30 dB below peak, this sets a lower limit on the fundamental that is 30 dB below the peak level of the fundamental - for example, if the peak of the fundamental were 95 dB the minimum level used for normalising would be 65 dB.

By default the harmonic and THD plots in normalised mode use the level at the fundamental for each frequency as their reference - for example, the distortion figures for each harmonic at 1 kHz will depend on the level of the fundamental at 1 kHz. If Use harmonic frequency as ref is selected the reference will be the frequency of the harmonic - for example, at 1 kHz the 2nd harmonic figure will depend on the level of the fundamental at 2 kHz, the 3rd harmonic will depend on the level of the fundamental at 3 kHz and so on. This follows a recommendation made by Steve F. Temme in "How to graph distortion measurements" presented at the 94th AES convention in March 1993. If the response of the system being measured is flat this makes no difference to the results, but when the response is not flat (as for most acoustic measurements) it can remove the influence of the loudspeaker's fundamental response from the distortion figures. As an example, suppose the loudspeaker response was flat apart from a 6 dB peak at 2 kHz. 2 kHz is the 2nd harmonic of 1 kHz, so the 2nd harmonic level shown at 1 kHz will be increased by 6 dB due to the boost in the fundamental when using the excitation frequency as the reference. Similarly the 3rd harmonic level at 667 Hz (2/3 kHz) will be boosted by 6 dB. If the harmonic frequency were used as the reference the distortion figures would not show this boost. Using the harmonic frequency as the reference also provides a more meaningful view of distortion at frequencies below the LF roll-off of the system as otherwise the distortion levels are boosted as the level of the fundamental drops. Note that this option will not affect the traces when the plot is not normalised, but will still affect the values in the legend if the distortion figures are set to read in percent or in dB relative to the fundamental.

The Distortion Figures control selects the units that are used for the harmonic distortion levels displayed on the graph legend. The choices are dB SPL, which shows the actual sound pressure level of each harmonic; dB Relative, which shows how many dB the harmonic is below the fundamental; and Percent, which shows the harmonic level as a percentage of the fundamental. The frequency at which the fundamental level is taken depends on the setting of Use harmonic frequency as ref (see above). When the plot is normalised and distortion figures are in percent the Y axis changes to show percent values.

The Highest Harmonic control allows the higher harmonics to be hidden if they are not of interest. For example, if Highest Harmonic were set to 3 only the second and third harmonic traces would appear on the graph and in the graph legend.

### Distortion Examples

Here is a distortion plot generated from a loopback measurement of a soundcard, produced at a high sweep level (-4 dBFS, which resulted in 2 dB of headroom at the gain settings used). The readings in the legend are with the cursor at 1 kHz.

The THD trace has been omitted, as it overlays the 2nd harmonic trace (in red) which is the dominant component, 0.07%. The 3rd harmonic (in orange) is much lower at around 0.01%, whilst the higher harmonics are largely within the noise floor.

This is the impulse response for that measurement, the distortion peaks are to the left of the main peak. The first peak to the left is the 2nd harmonic, the next is the third harmonic and so on.

The next plot is from a room measurement. The 2nd (red), 3rd (orange) and 4th (yellow) harmonic traces are shown, along with the THD (black). Higher harmonics were within the noise floor. The measurement shows a sharp rise in 3rd harmonic distortion at 94 Hz, and a dramatic rise in all distortion components from about 2 kHz upwards. Further measurements at differing signal levels established that this distortion was being introduce by the SPL meter used for the measurement.

This is the impulse response for the in-room measurement, the distortion peaks are clearly visible to the left of the main peak.

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