Estimate the Amplitude and Phase of Sinusoids

Sinusoids play an important role in describing physical phenomena and thus are widely used in signal processing.  Check out our blog post on how to estimate the amplitude and phase when the frequencies of the sinusoids are known.  Find out why the DFT is not the best solution to this problem and how you can estimate the amplitude and phase of $K$ sinusoids provided you have $N\ge 2K$ samples.   This post formulates the estimation problem in matrix-vector form.  Matrix-vector formulations are extremely powerful tools in signal processing as they often lead to straightforward solutions and insight for complex problems.