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, 2018 at 14:56
  • $\begingroup$ Since wavelet transform can be used for different kinds of data, not only time-domain signals, we use the word "scale" for the inverse of the domain of our signal. If the signal is indeed in time domain, doesn't the scale become frequency? Since the transformation from signal to wavelet transform is essentially the same as from signal to windowed Fourier transform, the units of the scale do come out as frequency (Hz) for signal expressed in seconds. I would appreciate it if someone qualified my reasoning. $\endgroup$ Aug 28, 2023 at 22:58

1 Answer 1


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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