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.