User`s manual

18 WAVELET ANALYSIS
18.1 INTRODUCTION
The Wavelet Analysis tool allows to post-process impulse responses and to create
color plots of the energy of the signal versus time and frequency. The tool is similar
to the ETF analysis described in chapter 12, but since it is based on wavelet
transform instead of Fourier Transform, does not suffer from the fixed time-
frequency resolution.
The ETF analysis is based on Short Time Fourier Transform (STFT). The idea behind
STFT is to show the temporal evolution of the signal by means of the division of the
signal itself into short sections and then Fourier Transform every section. In this
way the joint time-frequency evolution of the signal is highlighted. But at the same
time the process lead to a fixed time and frequency resolution, due to the fact that
time resolution is linked to section duration and frequency resolution is linked to
FFT size.
The Wavelet Analysis tool implemented in CLIO uses a kernel of modified complex
Morlet wavelets and can be interpreted as a constant Q analysis. Time resolution is
high at high frequencies and frequency resolution is not too rough at low
frequencies. This kind of analysis it is particularly suited for the inspection of
wideband non stationary signals as the impulse responses of loudspeakers and
rooms.
As a result of the Wavelet Analysis post-processing tool a matrix of coefficients is
calculated. The magnitude squared of the coefficients is directly proportional to the
energy of the signal in a domain located around a certain time and frequency. The
magnitude squared of the Wavelet coefficients is depicted into a color plot called
Scalogram:
Figure 18.1 - Wavelet Analysis panel
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