Outline

Periodic signals

The Fourier transform

Applications of the Fourier transform

Periodic signals

Periodic signals

Two signals with different frequecies

Periodic signals

How can we find out the original frequencies?

The Fourier transform

Mathematical tool able to decompose the signal in its original frequencies

The Fourier transform

The Fourier transform

The Fourier transform

The Fourier transform

The Fourier transform

The Fourier transform

The Fourier transform

Plotting the result of the integral as we change the frequency

The Fourier transform

Sum of two frequencies

The Fourier transform

Decaying signal with frequency 3Hz

To recap

The Fourier transform is a mathematical tool

Takes a signal as input

Gives us the frequencies is made of as output

Applications in audio processing

Sound is change in air pressure

The A (La) note is a sine wave with frequency 440Hz

Talking or music is a sum of many different frequencies in the audible spectrum (20Hz - 20000Hz)

We can perform a Fourier transform on them!

Spectrogram

Thank you!

Questions?