# Thread: System of Equations with Sinc

1. ## 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?

2. ## Re: System of Equations with Sinc

Hey fobos3.

Can you show us what you have tried?

3. ## 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.