Amplitude Estimating Using a Windowed DFT Let's say we want to estimate the amplitude A of a mono-frequent signal using a windowed DFT. The frequency of the signal is unknown, and the frequency resolution of the DFT is limited, thus it cannot be expected that there is a DFT bin that matches this frequency directly. Therefore, A is estimated from the amplitude of the next closest DFT bin. Now the question is,

should the frequency response of the window exhibit a narrow or a wide mainlobe to obtain a good estimate, and why?
I have several blog articles that solve this problem exactly in a theoretical sense, and quite accurately in an implementattion.

3. DFT Pure Tone Frequency Formulas


Exact Frequency Formula for a Pure Real Tone in a DFT
Two Bin Exact Frequency Formulas for a Pure Real Tone in a DFT
Improved Three Bin Exact Frequency Formula for a Pure Real Tone in a DFT
A Two Bin Exact Frequency Formula for a Pure Complex Tone in a DFT
Three Bin Exact Frequency Formulas for a Pure Complex Tone in a DFT


4. DFT Phase and Amplitude


Phase and Amplitude Calculation for a Pure Real Tone in a DFT: Method 1
Phase and Amplitude Calculation for a Pure Complex Tone in a DFT
Phase and Amplitude Calculation for a Pure Complex Tone in a DFT using Multiple Bins


The rest of the articles are pretty good too. ;-)

I posted one this morning:


Angle Addition Formulas from Euler's Formula