Least Squares Sinusoidal Parameter Estimation

Complex sinusoid in additive white noise:

$$x(n) \isdef {\cal A}e^{j\omega_0 n} + v(n)$$

where

• ${\cal A}= A e^{j\phi}$ is the complex amplitude of the sinusoid
• $v(n)$ is white noise

Given measurements of $x(n)$ , $n=0,1,2,\ldots,N-1$ , we wish to estimate the parameters $(A,\phi,\omega_0 )$ of this sinusoid.