Difference between spectrogram and scalogram

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 𝜌(𝑡) with two parameters 𝑝 and 𝑞.

So the signal is analyzed through the form:

𝑅𝑠(𝑝,𝑞)=∫𝑠(𝑡)$𝜌{\ast }_{𝑝,𝑞}$(𝑡)𝑑

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

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

Why they have those properties is another story.

https://dsp.stackexchange.com/questions/53310/what-is-the-difference-between-spectrogram-and-scalogram#:~:text=With the spectrogram%2C ρ is,a factor proportional to q.

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