Real-Time Wavelet-transform spectrum analyzer for the investigation of 1/f^\alpha noise

摘要

A wavelet transform spectrum analyzer operating in real time within thefrequency range 3X10^(-5) - 1.3X10^5 Hz has been implemented on a low-costDigital Signal Processing board operating at 150MHz. The wavelet decompositionof the signal allows to efficiently process non-stationary signals dominated bylarge amplitude events fairly well localized in time, thus providing thenatural tool to analyze processes characterized by 1/f^alpha power spectrum.The parallel architecture of the DSP allows the real-time processing of thewavelet transform of the signal sampled at 0.3MHz. The bandwidth is about220dB, almost ten decades. The power spectrum of the scattered intensity isprocessed in real time from the mean square value of the wavelet coefficientswithin each frequency band. The performances of the spectrum analyzer have beeninvestigated by performing Dynamic Light Scattering experiments on colloidalsuspensions and by comparing the measured spectra with the correlationfunctions data obtained with a traditional multi tau correlator. In order toasses the potentialities of the spectrum analyzer in the investigation ofprocesses involving a wide range of timescales, we have performed measurementson a model system where fluctuations in the scattered intensities are generatedby the number fluctuations in a dilute colloidal suspension illuminated by awide beam. This system is characterized by a power-law spectrum with exponent-3/2 in the scattered intensity fluctuations. The spectrum analyzer allows torecover the power spectrum with a dynamic range spanning about 8 decades. Theadvantages of wavelet analysis versus correlation analysis in the investigationof processes characterized by a wide distribution of time scales andnon-stationary processes are briefly discussed.