I want to create a real-time sampler for woodwind instruments.
Because it is possible to slide from one note to another without stopping the sound I decided to do it as a synthesizer. I want to analyze the sample in the frequency domain (time-domain sample as the sum of sinus waves). This part can be heavy to compute, so I will only take the parts of the sound that are necessary for the sound (e.g. basic note and overtones).
When I do an FFT on a signal for testing that was originally created by a sum of 3 sinus waves, sometimes I get a sharp peak on some frequencies with the correct amplitude. On other frequencies however I get a more distributed peak. The maximum is correct but too low. When I look into more Spectral points around that peak and sum up the amplitudes of these, the sum is more than it should be by the original sine wave.
Can anyone explain me, how I can look at a frequency-band in the discrete frequency domain and estimate the amplitude and phase of a sine signal in that band?