Understanding convolution is central to understanding filtering, the Discrete Fourier Transform, and other important DSP operations. In this tutorial, R. C. Kim explains convolution using a visual, intuitive, step-by-step method, and relates it to filtering and the DFT.
"FFTW is a C subroutine library for computing the discrete Fourier transform (DFT) in one or more dimensions, of arbitrary input size, and of both real and complex data (as well as of even/odd data, i.e. the discrete cosine/sine transforms or DCT/DST)."
How to interpolate the peak location of a DFT or FFT if the frequency of interest is between bins
by Matt Donadio
If the actual frequency of a signal does not fall on the center frequency of a DFT (FFT) bin, several bins near the actual frequency will appear to have a signal component. In that case, we can use the magnitudes of the nearby bins to determine the actual signal frequency.