How to extract specific frequencies in Discrete Fourier Transform. I'm collecting accelerometer data and interested in extracting frequencies from 1-10 Hz. I'm aware of how to do the FFT but not sure how to extract these frequencies 1Hz, 3Hz and 10Hz. Any pointers?

Just take the inner product of your data with a complex exponential at the frequency of interest. If $g$ is your data, then just substitute for $f$ the value of the frequency you want (e.g., 1, 3, 10, ...):

$$ \int_{-\infty}^{+\infty} g(t) e^{ -j2\pi f t } dt $$

Or if discrete:

$$ \sum_{n=0}^{N-1} g[n] e^{-j2\pi n \frac{f}{f_s} }, $$

where $f_s$ is the sampling frequency and $N$ is the number of samples you have.

The DFT (which is what the FFT calculates) implements the above but only over a subset of the frequencies. You could also interpolate the output of the FFT, but it's unnecessary and probably easier to just calculate it directly.