Vibration and exploring the Fast Fourier Transform with CAD

[Frances IoM]

On Frances IoM Said:

there’s nothing special about sinusoids (tho convenient) – any pair of mutually orthogonal (ie the intergral of the product of the two is zero) and their harmonics can be used as the basis of a transform

Do you mean the cyclotomic FFT over a finite field or the number theoretic transforms such as Mersenne and Fermat?

Julie

[ZephyrinParticipant @zephyrin]

this is a quite interesting thread…

I use regularly the free software “Audacity “, where a FFT function is implemented, and when recording the soundtrack of my model engines running, it appears that this function gives sometime a simple way to measure the speed of the model

[SillyOldDufferModerator @sillyoldduffer]

Been horribly interrupted and unwell too, so will take a while to absorb this.   My fog is slowly clearing.

Just as a quicky, Julie explained Windows, thanks.  The difference can be shown fairly easily with GRC, though not why one is better than another!   I’m obliged to Julie for the word ‘filter’.  Like all tools there are ifs and buts. Here’s the same data with different Windows applied:

BLACKMAN

HAMMING

HANN

BLACKMAN-HARRIS

RECTANGULAR

KAISER

FLATTOP

Now, which of these is ‘best’.  Depends on what the display is needed for I think.   For example, FLATTOP tends to merge two peaks, that I want to stand out individually.  KAISER eliminates the noisy skirts.  RECTANGULAR sharpens the peaks.  To my eyeball, BLACKMAN and BLACKMAN-HARRIS look suitable for vibration analysis.

With my software engineer hat on, the real tool will be implemented by me using an FFT library.  Therefore, I should look for one that supports all the Windowing methods, and allow the user to select the one he likes!

Also, some of the other display options might be useful, such as constellation:

and waterfall:

Apart from the visual display, I shall probably have to write code that extracts peaks for statistical purposes.  Which Window is used for that needs more thought.  I have to read the posts again and take notes.  Much to this!

Thanks Again,

Dave

 

 

 

 

[Zephyrin]

On Zephyrin Said:

this is a quite interesting thread…

I use regularly the free software “Audacity “, where a FFT function is implemented, and when recording the soundtrack of my model engines running, it appears that this function gives sometime a simple way to measure the speed of the model

Yay, like it. Thanks for the report, hadn’t thought of that. Must look for the RPM of my lathe in an audio sample.  And the lead-screw…

Dave

[Nigel Graham 2]

On Nigel Graham 2 Said:

….“weed the raspberry patch…” Organic computers?

Sadly not, but I am finally getting a decent crop of raspberries.

I must be the only person alive who has never used a Raspberry Pi! Although I vaguely knew Jack Lang. He was a cofounder of the company I mentioned above (Topexpress); albeit at the time I joined it was being reorganised and Jack Lang had moved on and invested in another company. Called Perihelion if I remember correctly, which was involved parallel computing – remember the Transputer? Jack Lang lived in the same village as me, albeit on the outskirts.

The mention of sonar by Nigel is interesting. Topexpress was involved in sonar, both theory and experimental. It is a difficult area from the perspective of signal processing. The velocities being measured are significant compared to the speed of sound in water so Doppler shift is more than just a linear frequency shift. To make things more complicated the speed of sound varies with water temperature and salinity.

My only involvement with sonar was being asked to design some 8-pole filters with arbitrary pole/zero locations in the complex w-plane, which is the complex conjugate of the more familiar s-plane. I found a paper in the IEE journals that described a second order filter block with arbitrary pole and zero positions. Once I’d worked out that the mathematics in the paper was wrong I derived my own (correct) transfer function. I won’t bore everyone with the filter design, but I did get them working according to the theory.

Julie

 

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