How can I improve peak detection in fast fourier tranform?

Question

Andrea Baricci 2013-1-29

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https://ww2.mathworks.cn/matlabcentral/answers/60247-how-can-i-improve-peak-detection-in-fast-fourier-tranform

Hello,

I recorded a sinusoidal signal and I want to figure out the amplitude and the phase of this signal. I do know the frequency. The signal length is 4096 and I have about 5 complete cycles in it plus one uncomplete cycle. By using FFT, I cannot get the impulse peak at the exact frequency, but it is distributed onto the adiacent frequencies.

Is there any procedure/function in Matlab able to give me the amplitude and the phase at a given frequency?

Thanks a lot