Manuel / Description of the calculation ?

[Olivier]

Hello,

Is there somewhere a detailed description of the mathematical calculations used in Spectroid? I would like to understand all the "Audio" parameters in detail.

Context: I struggle to capture the frequency when I pinch the timing belt of my car... It should be around 90 Hz according to the car manual, but the pinch noise is really crappy. I think that I could improve the acquisition if I understood the "Audio" parameters better.

Best regards,

Olivier

[Murray atuptown]

I have used Spectroid to measure long toothed urethane belts on a machine, but I did not know what the frequency was supposed to be. I later also bought a Chinese belt tensionometer that measures and displays frequency, as well as displaying tension if you know and enter the parameters for the specific belt. That part never made any sense to me. The manual seemed to have an error in the formula described, so I just noted the (single) frequency it displays.

On the machine, the belt is quite resonant and 'rings' for some time. Spectroid captures the spectrum. The tensionometer is apparently programmed to ignore the overtones and display the fundamental. It has fixed capture parameters and comes with its own microphone.

For Spectroid, I tried both a phone mic, and an outboard preamp with cardioid percussion mic, thinking it had better low frequency response. Because Spectroid shows a variety of components and not one frequency, I spent some time studying the frequencies detected. This was experimentally/empirically helpful because  I did not know what capture settings, sample rate, etc. were relevant. Same question as you, but different perspective.

I noted some of the frequencies had ratiometric relationships, but some numbers were not present. I don't remember exactly what I did, but I compared the ratios of the detected frequencies. I remembered the machine had three long belts, 2 identical and one shorter. I wondered if I was detecting 'sympathetic vibration' in some cases because there were 'outlier' frequencies that didn't make sense, or double peaks for two slightly different belt tensions.

The lowest frequency Spectroid detected began to appear like the 2nd harmonic and not the fundamental. If I 'interpolated' (divided by two) I got a frequency that was very close to what the tensionometer displayed. One of the belts I was trying to measure produced a lowest frequency of about 66 Hz. I had decided that 33 Hz made sense for the frequency ratios of most of the frequencies visible. That was close to what frequency the tensionometer displayed, leading me to conclude the tensionometer is programmed to determine the fundamental and ignore the overtones. I think harmonics by definition are integer multiples (1,2,3,4,5,6,7, etc. x fundamental). Overtones I believe have 'geometric' ratios like 2:1, 3:2, 4:3, 5:4 and so on.

Then I began to contemplate why Spectroid didn't detect the fundamental. The tensionometer had difficulty at times. The acoustic amplitude might not have been ideal where I tried measuring it.  For a vehicle, there are probably not a lot of places to measure.

I did not think 33 Hz was too low for the phone or the microphones I used. Eventually I observed that experimenting with different parameters in the Spectroid menu affected the response time. Intuitively, I expected certain settings to provide better or best accuracy and detection. 

What I actually saw revealed I didn't understand what the settings actually did or meant. For example, high sample rate and high everything else seemed to take a long time to acquire. The low frequency end of the spectral display took several seconds or longer to even appear on the frequency axis. Once the software determined it had enough data to validate the lower frequency range, the frequency axis updated with lower frequency range that was not there initially. This didn't matter whether I was plucking the belt or not.

Eventually I found some settings contrary to my intuition that gave me a frequency range I wanted to view, and what I thought 'looked' like a reasonable waveform, vs. the other settings that produced strange waveforms. By 'reasonable', I told myself the 'Gaussian' or bell curve-like spectral peak looked like what I have seen on old-school analog spectrum analyzers. A spectral peak with angular shape seemed to suggest (to my ignorant self) that I had selected poor settings.

For both of our applications, it seems the lowest frequency fundamental is all we care about. My machine also has short toothed belts right at the machine's drive motors. They were not of concern to me and a 'pocket' tension gauge seemed like a more practical method if I ever needed that number, and far less costly than the electronic gauge approach the tensionometer used. I made some phone calls to industrial machine motion control service companies and found most of them used mechanical gauges or compared audible tones to another specimen (like a 2nd car or machine). The one person who even knew what I was asking about using told me those were not common in industry because a quality one was over US$1000, so almost no one but universities and laboratories use them. The Gates model was indeed too costly for me to consider, and the inexpensive one I bought was about $150. Oddly, the best price was in England (I am in USA), so I bought it from a British seller.

Finally, the tensionometer had a calibration mode that generated an audible tone for its own microphone.

If you have a musical instrument or other app that can generate the frequency near what you expect to measure, you could experiment with the Spectroid settings for the quickest response that produces repeatable and expected measurements. 

I imagine a short span of automotive belt might have a rather short period of oscillation due to the damping of the thick rubber (and any composite strands of strengthening material that may be part of its composition).  

Maybe the app author here can sweep aside what I wrote that is not relevant and comment on settings that might support belt frequency measurement.

Good luck to you. This was a distracting science experiment for me. Even the person who designed the machine I was measuring didn't care what the frequency was. I was surprised, even stunned. He just had an idea in his head what it sounded like and tried to tell me over the phone 'it sounds like 'bong'...SO helpful (???).

Murray

[Carl Reinke]

Audio source:  Pick "Unprocessed" if you have that option; otherwise, "Default".

Sampling rate:  The maximum frequency on the plot will be half of the sampling rate.  Lowering the sampling rate results in finer frequency resolution, but you lose higher frequencies.  Pick the lowest sampling rate that meets your needs.

FFT size:  A greater the number of bins results in finer frequency resolution but worse time resolution (i.e. slower to respond).  A greater number of bins requires more processing power (and therefore higher battery consumption).

Decimations:  A greater the number of decimations also results in finer frequency resolution but only at the low end of the spectrum.  Each additional decimation adds another frequency band at the low end of the spectrum that has finer frequency resolution than the last but also worse time resolution.  A greater number of decimations requires more processing power.

Window function:  Picking a window function is something of an art.  The Window Function article[1] on Wikipedia may be of some help.  Every window function has tradeoffs.  Rectangular might be a good choice if you don't need amplitude accuracy and don't mind the very wide "skirt".  Flat top has the worst frequency resolution but the best amplitude accuracy (but given that the microphone is uncalibrated, amplitude accuracy is always questionable).

Transform interval:  This controls how often the plot updates (and also how quickly the waterfall scrolls).  A lower interval (higher frequency) results in the plot updating more often but requires more processing power.  Due to a limitation in the software design, you will likely find that choosing a lower interval past a certain point does not increase the update rate.

Exponential smoothing factor:  A lower value makes the plot respond more quickly, but the spectrum will be more noisy.

[1] https://en.wikipedia.org/wiki/Window_function

--Carl