[Scipy-tickets] [SciPy] #547: chirp - logarithmic cosine sweep - bad initial value and incorrect waveform

SciPy scipy-tickets@scipy....
Sun Nov 2 10:14:53 CST 2008


#547: chirp - logarithmic cosine sweep  - bad initial value and incorrect
waveform
--------------------------+-------------------------------------------------
 Reporter:  knorthover    |        Owner:  somebody
     Type:  defect        |       Status:  new     
 Priority:  normal        |    Milestone:  0.7.0   
Component:  scipy.signal  |      Version:          
 Severity:  major         |   Resolution:          
 Keywords:                |  
--------------------------+-------------------------------------------------
Comment (by Christian):

 Hi,

 The formula for a logarithmic chirp is given as fi = f0+10^(beta*t) where
 beta = log10(f1-f0)/t1. This has been obtained from

 http://www.ualberta.ca/dept/aict/bluejay/usr/local/matlab-6.5/help/toolbox/dspblks/chirp.html#873108

 To obtain the instantaneous frequency at t, fi needs to be integrated from
 0 to t.

 The integral of fi is (f0*t + (10^(beta*t))/(ln(10)*beta)) - (f0*0 +
 (10^(beta*0))/(ln(10)*beta)).

 This can be simplified to f0*t+(10^(beta*t) -1)/(ln(10)*beta).

 So adding the -1 will correct the error.

 Kind regards,
 Christian Christelis

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Ticket URL: <http://scipy.org/scipy/scipy/ticket/547#comment:1>
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