I record a sample of 2000 data points, with a sampling rate of 40khz, so freq. resolution is 20hz. I multiplied the chunk of data with a Hanning window prior to doing the FFT.
I recorded a 1khz test tone, and the result of FFT showed a peak at 1khz, as it should. But the magnitudes at 980hz and 1020hz is also significantly higher than the rest, although not as high as the magnitude at 1khz (about 50%).
Is this really bad? Did I apply the Hanning window wrong or is this unavoidable? Will using finer frequency resolution help?