From the mathematical point of view, the easiest way to determine the frequencies contained in a signal is to convert the signal in the frequency domain through Fourier transforms. A simple way to implement the
Errors in fixed time counting techniques
Gate time matched to low velocity signals
Fourier transform in the hardware of a computer, i. e. in discrete form on a limited number of samples, is called the FFT (fast Fourier transform).
The signal from the photomultiplier is digitized in an A-D converter that will take samples whose number must be chosen according to the length of the signal: 8, 16, 32 or 64 with a sampling frequency corresponding to the selected bandwidth. The procedure is applied to all signals coming in; only those due to the passage of particles in the control volume must be selected, therefore the times of arrival and departure of the particle in the volume are recorded and the process of storage signals is started and ended.
A power spectrum is calculated by the equation:
k=-N, – N+ 1,…,N-1
where N (= number of samples) may have the values 8, 16, 32 or 64.
A post-processor estimates the Doppler frequency using a parabolic interpolation of the measured spectrum. Inspection of the spectrum is also carried out: the measure is discarded if a peak does not appear in the frequency spectrum. Doppler frequencies of the measures that are accepted are sent to the output buffer along with the times of arrival and residence of the particle in the control volume.
The FFT processors are very accurate. With them an experienced user can achieve results not available with other types of processors: signals with low SNR values or even completely immersed in noise can be handled; for this reason the FFT processors are the most suitable for research applications.