System of Equations with Sinc

**fobos3** · November 12th 2012, 06:53 AM

I have the following system:
$A\frac{\sin (B(f_1 - f_0))}{B(f_1 - f_0)} = X_1$
$A\frac{\sin (B(f_2 - f_0))}{B(f_2 - f_0)} = X_2$
where the unknowns are $A$ and $f_0$ .

Can you solve such a system analytically? I can reduce it to k*sinc(...) = sinc(...) but what do I do from there?

**chiro** · November 12th 2012, 08:06 PM

Hey fobos3.

Can you show us what you have tried?

**fobos3** · November 13th 2012, 01:33 PM

I tried solving for A in the two equations and then equating the result. This gives you something like:
$k\times sinc(B(f_1-f_0)) = sinc(B(f_2-f_0))$
I also tried expressing the two equations in exponential form but couldn't figure out how to solve it. I am not sure if it is possible to solve the system analytically.

P.S.
This is not a homework problem and it is related to calculating the frequency and amplitude of a sine wave using two recursive DFTs.

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