interactivederivativeinfo.txt

Interactive smoothing for your own data, with sliders to control derivative order, smooth width, a

Interactive Derivative for time-series signals.

Interactive differentiation for time-series signals, with sliders 
that allow you to adjust the derivative order, smooth width, and 
scale expansion continuously while observing the effect on your 
signal dynamically. Run InteractiveDerivativeTest to see how it 
works.  Details are in the text file InteractiveDerivativeInfo.txt. 
Typical applications of differentiation in measurement are described
in http://www.wam.umd.edu/~toh/spectrum/Differentiation.html
 Tom O'Haver, [e-mail], July 2006.  
 Slider function by Matthew Jones.


InteractiveDerivative

Interactive smoothing for your own data, with sliders to control 
derivative order, smooth width, and scale expansion.  To use it, 
place your signal in the global variables "x" and "signal" and then
execute this m-file. The smoothed derivative is placed in global 
variable "derivative". The actual differentiation is performed by the 
function  InteractiveDerivativeRedraw, which is called when the sliders
are moved. If you wish, you can change the maximum range of the smooth 
width slider (MaxSmoothwidth in line 14) and the maximum range of the 
derivative order slider (MaxDerivativeOrder in line 15). You can also
change the smoothing function by replacing "fastsbmooth" in
InteractiveDerivativeRedraw with any other smoothing function.


InteractiveDerivativeTest

Test of InteractiveDerivative. Generates a synthetic
signal assigned to "signal", then calls InteractiveDerivative.


DerivativeDemo

Demonstration of the application of differentiation to
the detection of peaks superimposed on a strong, variable 
background. Generates a signal peak, adds random noise and 
a variable background, then differentiates and smooths it, and 
measures the signal range and signal-to-noise ratio (SNR). 
Interactive sliders allow you to control the following variables:
Amp: The amplitude (peak height) of the signal peak.  
     Default range: 0-3
Back1: The amplitude of the background. 
       Default range: 0 to 20
Back2: The position of the background. 
       Default range: -800 to +800
Noise: Random white noise added to the signal.  
        Default range: 0 - 0.5
Order: Derivative order. Default range: 0-4
Scale: Scale expansion of the y-axis. 
        Default range: 0.1 - 10.
Smooth: Width of the smoothing function, in data points. 
        Default range: 0 - 100
Resample: Applies different random noise samples, to demonstrate 
          the low-frequency noise that remains after smoothing. 

function SmoothY=fastbsmooth(Y,smoothwidth)
 Smooths vector Y by unweighted sliding-average (boxcar)
 smooth of width = smoothwidth. Works well with signals up  to 
 100,000 points in length and smooth widths of 1000 points or more.
 Faster than convolution-based smooths for large smooth widths.

function d=deriv(a)
First derivative of a signal using 2-point central difference.