I have a pretty simple question which i should have been able to answer. Just wanted to check if people here have a better solution to it.
I am trying to establish that FFT as a frequency estimator (imagine a single sinusoid + AWGN model) is unbiased. I guess we can agree that the answer to that depends on the number of grid points on the frequency axis or put in a different way it depends on how many zeros you pad to your signal. And no matter what, you will always be limited by your grid resolution. There are many papers out there which sort of interpolate using samples around the detected peak to refine the estimate and that pretty much is unbiased. This question can then be extended to other sort of correlation based estimators such as range estimation for a radar wavefrom etc.
I have a similar setting that i am working on, skipping the details for brevity but the signal model and algorithm are essentially what i described above. I plotted the resulting errors and they do come out to be unbiased. I was just wondering if i can somehow prove mathematically that the estimator is indeed unbiased. The reason i want to do that is because i eventually want to compare with the CRB.
If any papers/lectures or ideas come to mind, do share them. Thanks.