Waveshape vs spectrum

[uneumann]

Recent threads got me to thinking about how we relate wave-shapes and spectra. There are classic symmetric and asymmetric wave-shapes that we associate with harmonic content. It led me to an interesting experiment (IMHO) that I think may be of general interest. A summary is below... a more complete version will appear on my website shortly.

There are three experiments - all use the same signals - a fundamental, a 2nd harmonic, and a 3rd harmonic. Mixing them in fixed proportions, but with varied phase produce three results that have very varied wave-shape, but exactly the same harmonic content. Since we don't hear phase shift directly, this demonstrates that a given waveform has a single spectrum - however a given spectrum can be produced by widely variable wave-shapes, depending on the phases of the harmonic components.

This is nothing new to many, I suspect - I'm only bring it up since the experiment is simple and kind of cool in that it offer some basic insights into what you can reliably read into wave-shapes (or not). Even though I was aware of the theory, I had not demonstrated it to myself so clearly. These SPICE screen shots sort of explain themselves, I hope. Maybe others can offer some comments or insights or suggestions for similar experiments.






More about this will appear at stringsandfrets shortly...

[Malcolm Irving]

Although we (apparently) cannot hear the difference between two continuous tones with the same amplitude spectrum but differing phase spectrums, it can make a big difference to the ‘crest factor’ of the time waveform.
The following article illustrates this, especially an extreme example shown in Fig. 8 and Fig. 9.
Waveforms and Spectra - or - Amplitude and Phase
The big change in crest factor would obviously affect how much the waveform might be clipped by a distorting stage.
In guitar amps, I think the main circuit which influences phase shifts of different frequencies would be the tone stack. The thing about changing the crest factor could be significant when we are thinking about pre-tone-stack distortion v. post-tone-stack distortion.

[MarkusBass]

In LTSpice you can save the output of transient simulation to a wav file. I suggest to "record" the output of the simulations (at least 5 seconds) and check whether they can be distingushed audibly.

Mark

[uneumann]

In LTSpice you can save the output of transient simulation to a wav file. I suggest to "record" the output of the simulations (at least 5 seconds) and check whether they can be distingushed audibly.

Mark

Malcolm has pointed to audio clips through the link he provided. Thanks Malcolm. Figure 5 in that document includes a wave clip of 2nd harmonics with/without phase shift. I can't hear any difference. The link is here if you don't want to hunt for it ...
http://www.colinpykett.org.uk/Sine-4...hase0and90.mp3
The two tones are 440/880 Hz in the same proportions, but with different phase.
The article explains the issues clearly and provides even more examples. I wish I had seen it sooner.