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Deconvolution using a COS^2 response function.

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Andrey_L

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Hi All,

I'm new in signal processing. I'm not even sure I have given an appropriate title to my question. So, I describe my problem and hope someone will point me a direction to go.

I have a function: F(t)=a1cos2(wt+d1)+a2cos2(wt+d2)+...+ancos2(wt+dn).

The signal is measurend experimentally - descrete sampling.

How do I find/extract sets of ak and dk?

Any suggestions and advices are strongly appreciated.
 

It's impossible, because that sum is equal to:

SUM(ak cos²(wt+dk)) = 1/2 SUM(ak) + 1/2 cos(2wt) SUM(ak cos(2dk)) - 1/2 sin(2wt) SUM(ak sin(2dk))
= A + B cos(2wt) + C sin(2wt)


Remember: cos²(x) = (1 + cos(2x))/2 and cos(x+y) = cos(x)cos(y) - sin(x)sin(y)


EDIT: mistype in cos identity.
 
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Many thanks, Eduardo!

do you think it is possible in case COS^4 or even higher power?
 

Andrey_L said:
do you think it is possible in case COS^4 or even higher power?
Click to expand...

COS(x)^4 = (COS(4x) + 4COS(2x) + 3)/8
COS(x)^6 = (COS(6·x) + 6·COS(4·x) + 15·COS(2·x) + 10)/32
.......
COS(x)^(2n) = A+ SUM(ck COS(2k x)

It's the same "with harmonics"

The only way is with different frequencies or exponents for each component.
 
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