Amplitude and Phase inaccuracies due to the Round-Off noise of FFT processors

This report proposes to discuss the Fourier domain analysis performances of a RESPER probe. A uniform ADC, which is characterized by a sensible phase inaccuracy depending on frequency, is connected to a Fast Fourier Transform (FFT) processor, that is especially affected by a round-off amplitude noise linked to both the FFT register length and samples number. If the register length is equal to 32 bits, then the round-off noise is entirely negligible, else, once bits are reduced to 16, a technique of compensation must occur. In fact, oversampling can be employed within a short time window, reaching a compromise between the needs of limiting the phase inaccuracy due to ADC and not raising too much the number of averaged FFT values sufficient to bound the round-off. Finally, the appendix presents an outline of somewhat lengthy demonstrations needed to calculate the amplitude and especially phase inaccuracies due to the round-off noise of FFT processors