Could someone please explain the difference between the two?


A visual representation of the spectrum of a sound changing through time.


(signal processing) A visual representation of a wavelet transform, having axes for time, scale, and coefficient

  • 1
    $\begingroup$ One represents a spectrum and the other a wavelet transform... do you understand the difference between those? $\endgroup$ – MBaz Nov 14 '18 at 14:56

Both convert a 1D signal into a 2D complex map, aiming at unveiling transient features of the data. Both use a functional microscope: the signal $s(t)$ is analyzed through variations of a single template function $\rho(t)$ with two parameters $p$ and $q$.

So the signal is analyzed through the form:

$$R_s(p,q) = \int s(t) \rho^*_{p,q}(t) d\cdot$$

which is 2D (the differential increment $d\cdot$ can be specific).

  • With the spectrogram, $\rho$ is a fixed (non-zero sum) window, and $\rho_{p,q}$ is the same window, shifted by $p$, and modulated by a frequency proportional to $q$.

  • With the scalogram, $\rho$ is a fixed zero-mean function (a wavelet), and $\rho_{p,q}$ is the same wavelet, shifted by $p$, and dilated by a factor proportional to $q$.

Why they have those properties is another story.


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