# System of Equations with Sinc

• Nov 12th 2012, 06:53 AM
fobos3
System of Equations with Sinc
I have the following system:
$\displaystyle A\frac{\sin (B(f_1 - f_0))}{B(f_1 - f_0)} = X_1$
$\displaystyle A\frac{\sin (B(f_2 - f_0))}{B(f_2 - f_0)} = X_2$
where the unknowns are $\displaystyle A$ and $\displaystyle f_0$.

Can you solve such a system analytically? I can reduce it to k*sinc(...) = sinc(...) but what do I do from there?
• Nov 12th 2012, 08:06 PM
chiro
Re: System of Equations with Sinc
Hey fobos3.

Can you show us what you have tried?
• Nov 13th 2012, 01:33 PM
fobos3
Re: System of Equations with Sinc
I tried solving for A in the two equations and then equating the result. This gives you something like:
$\displaystyle k\times sinc(B(f_1-f_0)) = sinc(B(f_2-f_0))$
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.