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  1. Xref: sparky comp.org.ieee:596 sci.optics:1315 sci.engr:2392
  2. Path: sparky!uunet!dtix!darwin.sura.net!zaphod.mps.ohio-state.edu!magnus.acs.ohio-state.edu!usenet.ins.cwru.edu!wsu-cs!nova!seeta
  3. From: seeta@eng.wayne.edu (Seetamraju UdayaBhaskar Sarma)
  4. Newsgroups: comp.org.ieee,sci.optics,sci.engr
  5. Subject: ... help : Estimating width of Fourier Spectrum ...
  6. Message-ID: <1992Dec20.212958.10480@cs.wayne.edu>
  7. Date: 20 Dec 92 21:29:58 GMT
  8. Sender: usenet@cs.wayne.edu (Usenet News)
  9. Reply-To: seeta@eng.wayne.edu
  10. Followup-To: sci.engr
  11. Organization: College of Engineering, Wayne State University, Detroit Michigan, USA
  12. Lines: 64
  13.  
  14.  
  15. ((Is there a  `sci.engr.electricalEngg ?    followups to sci.engr))
  16.  
  17.  
  18. Could someone help me with the following problem :-
  19.  
  20. I handle two types of functions :-
  21.  
  22. 1.    One is in the form of a black-box ((i.e.,I give it input and
  23.         it gives me output : nothing else is known about the function)).
  24. 2.    The other is in the form of a  mathematical expression (single equation?)
  25.  
  26. How does one estimate the ``WIDTH'' of the fourier spectrum of the function
  27.          ====================
  28. given in either of the forms above...
  29.  
  30.  
  31. There is no direct way, and I havent found any literature on how to `converge
  32. successively using an algorithmic approach' ...
  33.  
  34. For example, the fourier spectrum can be :- (Left half of real axis)
  35.                                                                                        
  36.                                                                                        
  37.  x                                                                                      
  38.    x                                                                                    
  39.      x                                                                                  
  40.         x                                                                               
  41.            x                                                                            
  42.              x                                                 x x                        
  43.                x                                                                        
  44.                  x                                            x    x                      
  45.                   x                                                  x                   
  46.                     x                                                   x                
  47.                       x                                      x                           
  48.                         x                                                 x              
  49.                           x x x x x x                       x                            
  50.                                       x x x x x x          x                x            
  51.                                                   x x x   x                   x            
  52.                                                         x                        x xx       
  53. Peak @ 0                    30th          2nd peak
  54.                         harmonic
  55.  
  56. Lets say I sampled with the Nyquists rate of 15, then I would see half of what is above
  57. and there is a fifty percent chance that I (a human decision) will erroneusly conclude
  58. that the higher harmonics have progressively lesser spectral energy...
  59.  
  60. The above is rephrased version of the question ::  What must be the sampling
  61. rate to include about 95% of the TOTAL spectral energy :: How can one estimate 
  62. (The key word here is ESTIMATE)  what the highest frequency componenets are 
  63. BY LOOKING AT THE FUNCTION (the black box version is clearly a toughie)...???
  64.  
  65. An approximation is sufficient.
  66.  
  67. I have functions (man made though) that are in expression form, and whose spectrum
  68. is closely resembling the absolute value version of the SINC wave... but with a
  69. large separation between each peaks..
  70.  
  71. I am actually dealing with TIME_DELIMITED functions, which are converted
  72. INTO periodic functions, bringing sense to the 95% spectral energy requirement
  73. as now we have discrete harmonics (rather than a continuous range of freqs).
  74.  
  75.  
  76. Seetamraju Udaya Bhaskar Sarma
  77. (email : seetam @ ece7 . eng . wayne . edu)
  78.