[sdiy] Bezier? B-Spline?

[Richie Burnett]

It really comes down to your definition of "smoothed curve".  Basic linear 
interpolation would give you no discontinuities in y, but a discontinuity in 
the first derivative dy/dx at each point.  If you go to quadratic 
interpolation this can eliminate the discontinuities in the first 
derivative.  So the output of the interpolator will look like a smooth 
curve, but higher derivatives will still have discontinuities at the 
original input points.  You can then try higher order interpolating 
functions, FIR filters, Windowed-Sinc interpolation, etc. depending on the 
exact requirements of the application.

One other thing worth considering for smoothing a multi-point envelope is 
what will happen if the interpolating function momentarily exceeds some 
pre-defined limits of the input signal.  For example if the input signal is 
full scale at one point and then falls to zero for the next two points, then 
many interpolating functions will produce negative values for times in 
between the second and third sample instants.  Essentially the output signal 
has to ring negative slightly, otherwise there will be a gradient 
discontinuity if it suddenly changes slope when it reaches zero.  But is a 
negative output value what you really want out of an envelope generator? 
So, do you clip at 0% and 100% and accept some discontinuities and 
"non-smoothness" under some circumstances?  (A similar problem called 
"Inter-sample overs" can occur when digital audio is reconstructed from 
sample points too.)

-Richie,

-----Original Message----- 
From: Tim Ressel
Sent: Saturday, March 07, 2015 7:23 PM
To: Synth-diy Diy
Subject: [sdiy] Bezier? B-Spline?

Hi,

I have an application where I need to take segments of a multi-segment 
envelope generator and make them smoothed curves. Each segment is comprised 
of N samples. I want the smoothed curve to go through the end points of the 
segments. I was hoping a clever math dude can show me how to do this.

Thanks!

Tim Ressel
Circuit Abbey
503-750-9331
timr at circuitabbey.com
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