Bin-centres - Background

Background

When performing FFT-based spectral measurements, traditionally a window function has been used to reduce the effects of discontinuities at the ends of the FFT buffer, but these result in spectral leakage. When generating a single frequency test signal for FFT analysis, it is possible to create the frequency such that it aligns perfectly within an FFT bin-centre frequency. These frequencies are multiples of the frequency resolution of the FFT, given by the sample rate divided by the number of sample points. This results in no spectral leakage and all the power from the signal is present in only one FFT bin. Viewed in the time domain, a sine wave will fit in the centre of an FFT bin if it has a complete number of cycles within the length of the sample buffer. Such signals can be analysed without an FFT window function provided the system is synchronous (i.e., the signal generation and analysis are using the same clock source.) It follows that a stimulus can be constructed of many sine waves (as many as there are FFT bins) and the signal can still be analysed without an FFT window function. This is called multitone analysis. The amplitude and phase of these sine components can be freely adjusted in order to construct a signal with a particular frequency response characteristic.