From: seeta@eng.wayne.edu (Seetamraju UdayaBhaskar Sarma)
Newsgroups: comp.org.ieee,sci.optics,sci.engr
Subject: ... help : Estimating width of Fourier Spectrum ...
Date: 20 Dec 92 21:29:58 GMT
Reply-To: seeta@eng.wayne.edu
Followup-To: sci.engr
Organization: College of Engineering, Wayne State University, Detroit Michigan, USA


((Is there a  `sci.engr.electricalEngg ?	followups to sci.engr))


Could someone help me with the following problem :-

I handle two types of functions :-

1.	One is in the form of a black-box ((i.e.,I give it input and
		it gives me output : nothing else is known about the function)).
2.	The other is in the form of a  mathematical expression (single equation?)

How does one estimate the ``WIDTH'' of the fourier spectrum of the function
	     ====================
given in either of the forms above...


There is no direct way, and I havent found any literature on how to `converge
successively using an algorithmic approach' ...

For example, the fourier spectrum can be :- (Left half of real axis)
                                                                                       
                                                                                       
 x                                                                                      
   x                                                                                    
     x                                                                                  
        x                                                                               
           x                                                                            
             x                                                 x x                        
               x                                                                        
                 x                                            x    x                      
                  x                                                  x                   
                    x                                                   x                
                      x                                      x                           
                        x                                                 x              
                          x x x x x x                       x                            
                                      x x x x x x          x                x            
                                                  x x x   x                   x            
                                                        x                        x xx       
Peak @ 0					30th		  2nd peak
						harmonic

Lets say I sampled with the Nyquists rate of 15, then I would see half of what is above
and there is a fifty percent chance that I (a human decision) will erroneusly conclude
that the higher harmonics have progressively lesser spectral energy...

The above is rephrased version of the question ::  What must be the sampling
rate to include about 95% of the TOTAL spectral energy :: How can one estimate 
(The key word here is ESTIMATE)  what the highest frequency componenets are 
BY LOOKING AT THE FUNCTION (the black box version is clearly a toughie)...???

An approximation is sufficient.

I have functions (man made though) that are in expression form, and whose spectrum
is closely resembling the absolute value version of the SINC wave... but with a
large separation between each peaks..

I am actually dealing with TIME_DELIMITED functions, which are converted
INTO periodic functions, bringing sense to the 95% spectral energy requirement
as now we have discrete harmonics (rather than a continuous range of freqs).


Seetamraju Udaya Bhaskar Sarma
(email : seetam @ ece7 . eng . wayne . edu)