Description of the Wavelet Transform Spectrum Analyzer (WTSA)

By using a low-cost commercially available evaluation board we have buit a spectrum analyzer working in real time in the frequency range 3x10-5 - 1.3x105 Hz. The Spectrum analyzer is built around a Digital Signal Processor running at 150 MHz. The wavelet decomposition of the signal allows to efficiently process nonstationary signals dominated by large amplitude events fairly well localized in time, thus providing the natural tool to analyze processes with 1/f α power spectrum. The wavelet transform spectrum analyzer represents a powerful alternative to traditional multi-tau correlators when dealing with non-stationary signals. In particular, when α>1 no information can be obtained by using conventional time-autocorrelation techniques



D. Brogioli and A. Vailati, Real-time wavelet-transform spectrum analyzer for the investigation of 1/f2 noise, Rev. Sci. Instrum. 74, 2583 (2003). e-print

Poster presented at the INFM meeting.


We used wavelet transform in order to evaluate the power spectrum of a signal, in real time, within the frequency range 3X10-5 - 1.3X105 Hz. We used a low-cost Digital Signal Processing board operating at 150MHz. The wavelet decomposition of the signal allows to efficiently process non-stationary signals dominated by large amplitude events fairly well localized in time, thus providing the natural tool to analyze processes characterized by a 1/f α power spectrum. The parallel architecture of the DSP allows the real-time processing of the wavelet transform of the signal sampled at 0.3MHz. The bandwidth is about 220dB, almost ten decades. The power spectrum of the scattered intensity is processed in real time from the mean square value of the wavelet coefficients within each frequency band.
The performances of the spectrum analyzer have been investigated by performing Dynamic Light Scattering experiments on colloidal suspensions and by comparing the measured spectra with the correlation functions data obtained with a traditional multi tau correlator. In order to asses the potentialities of the spectrum analyzer in the investigation of processes involving a wide range of timescales, we have performed measurements on a model system where fluctuations in the scattered intensities are generated by the number fluctuations in a dilute colloidal suspension illuminated by a wide beam. This system is characterized by a power-law spectrum with exponent -3/2 in the scattered intensity fluctuations. The spectrum analyzer allows to recover the power spectrum with a dynamic range spanning about 8 decades.
The paper describing the technique and the experiments we performed is available as e-print.