Harmonic Number Scale for Frequency Analysis

[DickN]

A simple and useful tool would be a harmonic number scale which can be slid horizontally across the log frequency axis.

The tool would appear as a transparent ruler with tic marks and integers along its top edge. The leftmost tic would be
labeled '1', the next tic '2', etc. Aligning '1' on this tool with the fundamental frequency of a sound would result
in each harmonic which appears in the plot being aligned with the corresponding harmonic number shown on the tool.
Resizing the plot would, of course, have to resize the tool, and ideally not move it relative to the coordinate plane.

Use cases, in the presence of many unrelated frequency components in the display:
1: Determining a low frequency more accurately by finding high-order harmonics and dividing by the harmonic number.
2: Quickly identifying the most prominent harmonics of a noise to be filtered out.
3: Determining quickly whether a set of peaks is a harmonic series and finding its fundamental even when the fundamental doesn't show up in the plot.

All of these, of course, can be done without the tool but the tool would speed up the job considerably.

[kozikowski]

Past the engineering school debate that "1" is not the "first harmonic" at double the frequency....

This may be far easier than you think by setting Analyze > Plot Spectrum to linear instead of log. Harmonics appear as a straight comb left to right and it's a simple matter to settle your cursor over each one and read off the character.

Also, it's extraordinarily unlikely to have a sub-harmonic, so the lowest peak is always the largest with nothing below that.

Koz

[steve]

I like the idea, but as Koz wrote, the linear scale is very good for seeing harmonic series:

1000 Hz no-alias square wave

1000 Hz no-alias square wave.png (42.26 KiB) Viewed 5633 times

Currently the peak value close to the cursor is indicated in numbers below the graph. A "transparency overlay" as you describe that can indicate multiple peaks would perhaps still be useful, though I don't know if, or how well WxWidgets supports transparency overlays.

Also, it's extraordinarily unlikely to have a sub-harmonic,

Unfortunately that is not true in digital audio due to aliasing at the Nyquist frequency.

1000 Hz aliased square wave

1000 Hz aliased square wave.png (42.26 KiB) Viewed 5633 times

[kozikowski]

My bad.
Koz

[DickN]

Linear scale shows the comb nicely when the fundamental is > about 100 Hz. It is often the case that mechanical sources are below 100 Hz and the highest visible harmonic is below 1 KHz, and such a series is hard to pick out amidst other sound on the linear scale. It's also not unusual for the fundamental to not show up in the plot because either it's obscured by other noise or it just doesn't propagate to the mics or there's a low-cut filter in the mic channel taking it out. Knowing the fundamental helps a lot in identifying the source.

An alias is not a sub-harmonic, even though it might happen to coincide with f/n. As a harmonic-rich waveform increases in frequency, there's a set of aliases which increases and a set which decreases in frequency.
"1000 Hz Aliased squarewave" reminds me of a thread I started a long time ago and can't find now. I was pondering why all the aliases of a 10 KHz squarewave were at multiples of 100 Hz. I finally answered my own question and concluded experimentally that the Welch window yielded the most accurate relative amplitudes for the aliases. Makes a rather good buzzer sound, BTW.

[steve]

Yes, for low frequencies it would be very useful. What sort of sounds are you thinking of? The most common is probably "mains hum" (50 or 60 Hz) which is unlikely to be visible at all in linear view.

An alias is not a sub-harmonic

Yes and no - it is "below" the harmonics, hence "sub" harmonic, but not strictly "a sub-harmonic".
The lower alias frequencies occur through "folding" about the Nyquist frequency, so for example, with a sample rate of 10000 Hz, the Nyquist frequency is 5000 Hz a signal frequency of 8123 Hz will produce an alias frequency at 8123 - 5000 = 3123 Hz below the Nyquist frequency, which is an actual frequency of 1877 Hz. For a more complicated explanation: http://en.wikipedia.org/wiki/Aliasing#S ... _functions

[kozikowski]

...or it just doesn't propagate to the mics or there's a low-cut filter in the mic channel taking it out.

How would you know by a series of lumpy blue waves -- even if they did line up into orderly harmonics -- whether or not you already had the fundamental? You can have modulation effects where he fundamental isn't automatically to the left.

Koz

[kozikowski]

unlikely to be visible at all in linear view.

Unless, of course, you could drag and magnify Analyze Spectrum. Koz

[DickN]

You can have modulation effects where he fundamental isn't automatically to the left.Koz

[groan] I actually typed another paragraph into my last post but deleted it at the last minute because I deemed it off-topic. I saved it in notepad, so here it is:

The linear plot inspires another (related) request: A stretchable ruler with tics at adjustable regular intervals, which can be slid along the linear frequency axis independently of the stretching. This would be very useful for identifying sidebands of a modulated source. In my use case, they would be sidebands of the reed valves in an air conditioner modulated by the compressor frequency. The sidebands span about 1.5 KHz to 4.5 KHz with spacing of typically 58 Hz. If it were an RF spectrum it would be called "splatter". I use the difference of distant sidebands to accurately determine the compressor frequency, which enables me to accurately calculate the frequency of any other sideband in the set. This way I can quickly use Single Band Parametric to identify and prioritize sidebands that I can hear but not see, or can see only in the Spectrogram view. Generally, only a few frequencies are prominent at any one time, and I can prioritize which ones to notch out to minimize collateral damage. Unfortunately, I have to do this fairly often because as line voltage varies so does the compressor speed, which shifts the higher-order sidebands quite a lot. Also, as the wireless mic moves around, the set of prominent sidebands changes. I would use the ruler to pick a few prominent sidebands at the start of this process each time. I would think this is a common problem, and possibly one that is often not dealt with very well because of the time involved - especially if one doesn't understand the relationship to compressor speed and thus doesn't know how to use a few measurements to simplify the search.

Yes, for low frequencies it would be very useful. What sort of sounds are you thinking of? The most common is probably "mains hum" (50 or 60 Hz) which is unlikely to be visible at all in linear view.

I have a lot of LF noise from fans, including one box fan whose frequency is not at all stable. At one speed setting it varies from 67-72 Hz. 72 Hz is also a resonance in the pulpit. 57-58 Hz is the a/c compressor (sometimes I can see the 15th harmonic), 40 Hz is the fan in the a/c which also modulates the reed valve sound so I get ghosts around the sidebands.

Identifying a harmonic series in the presence of many unrelated peaks is also useful when I have to transcribe from cassette and correct the playback speed. In this case I can see the fundamental but don't have a precise frequency measurement. Identifying a set of harmonics yields a more accurate calculation of speed error. What I usually do now
is just find the last isolated peak at some octave from the fundamental, then check for other harmonic series of which it might also be a member. The more octaves between the harmonic and the fundamental, the more likely this is.

[Gale Andrews]

OK @Peter I will add these two FR's some time, so no need to put all this in PFR's.


Gale