Design Filter Banks for every 100 Hz
A windowed FFT with a length that corresponds to 2/100ths of a second will give you overlapping filters each with roughly 100 Hz bandwidth.  Just use every other FFT result bin if you want 100 Hz filter spacing.  The window shape (Von Hann, Nutall, etc.) will allow some tuning of the filter shape, but the main passband lobe of a windowed FFT will be about twice the FFT bin spacing in width.

An unwindowed FFT creates filters with too much stop band ripple to usually be considered useful.

You can also zero-pad and/or use an FFT a higher integer multiple of 0.01S in length to get better control over the windowing (a proportionately wider or narrower Gaussian window, for instance) and the window's frequency response.

The number of samples needed will be the FFT length in samples, or the sample rate multiplied by the FFT's length in time.