# What is the difference between Spectrogram and Scalogram?

Could someone please explain the difference between the two?

Spectrogram:

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

Scalogram:

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

• One represents a spectrum and the other a wavelet transform... do you understand the difference between those? – 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.