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Signal processing question: First derivative vs tangetial slope?

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Hi everyone,

 

I have a question regarding a strain signal processing...

 

Do the terms the "first derivative" and "tangential slope" basically refer to the exact same property; that is change in strain (y) relative to the change in time (x) at a specific point in time...

 

I have determined the rate of strain development by calulating the first derivatives all data points within signal segement of interest and obtained the mean dx/dt value for analysis... Is this the same as "mean tangential slope"? Or they the different?... My basic understanding this that they are one and the same... Could someone please confirm or correct this?

 

Any feedback greatly appreciated.

 

Regards,

Jack

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Accepted by topic author jcannon

The tangential slope of a curved line is the slope of the line tangent to the curve at a particular point.  This can be calculated by taking the first derivative of the function and evaluating at the point.  Yes, for all practical purposes, "first derivative" and "tangential slope" refer to the same property.

 

I would assume that the mean tangential slope could be calculated by taking the mean of the evaluated derivatives.  Some quick googling bears this out.  But I am a physicist, not a DSP guy, so my opinion may not be correct.

 

You may also want to look at how you calculate your derivative.  The default LabVIEW method is a simple two-point calculation which is very susceptible to noise.  If you have a new enough version of LabVIEW, there are functions included which will calculate Savitzky-Golay coefficients which you then use with the convolution filter to determine the derivatives at each point. The Savitzky-Golay method essentially calculates a least-squares fit to a polynomial at each point and takes the derivative of the polynomial.  This reduces noise considerably.  Note that Savitzky-Golay coefficients can be used to generate almost any derivative order, provided you use enough points for the convolution.  The default is a zero order, or smoothing filter.  If your version of LabVIEW is not new enough to contain the Savitzky-Golay coefficient generator, you can do it yourself fairly easily.  A quick internet search for "Savitzky-Golay coefficients" should give you the formulae.

 

However, since you are taking the mean of a bunch of points, whether you do this or not will depend upon how much noise your data contains, how many points make up your mean, and how much resolution/accuracy you need.

 

Let us know if you have further questions.

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Hi DFGray,

 

Thanks for the reply.... I have vis for the filters you suggested and will chase them up... I will also crunch my data a few different ways and see how the numbers compare using the different aproaches.

 

Thanks again.

 

Regards,

Jack

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