Measurement time reduction using a regressive Discrete Fourier-Transform technique

One of the most common techniques for evaluating (optical) measurement data is by means of a fourier analysis. It is well known that for periodic and band-limited sequences the Discrete Fourier Transform (DFT) returns the true Fourier coefficients when exactly I period (or a multiple) is processed. Leakage will occur when less than I period is considered. This gives rise to non-negligible errors, which can be resolved by using a Regressive Discrete Fourier Transform (RDFT), introduced by J.R.F. Arruda on spatial domain signal for the purpose of data compression. In the method introduced in this article, the measured signal is a time domain sequence, which is represented by a model using sines and cosines where the frequency is fixed within a narrow band signal. The coefficients of those sines and cosines are then estimated on a global scale by means of a frequency domain system identification technique. An important advantage of this particular technique is that one does not have to measure a full period of the signal. Therefore one can drastically shorten the measuring time itself, by measuring only a portion of the signal period. This is a key benefit for in-line quality control when using for example a laser scanning vibrometer, which can have upwards of 1000 spatial measurement locations. In this paper the regressive fourier method will be applied in particular to the reduction of measurement time for laser scanning vibrometer measurements. The proposed technique will be validated on both simulations and experiments of varying complexity.