tags: mus-407 spectrum timbre sound
Fourier Theorem
The Fourier theorem states that any periodic [waveform] can be expressed as a sum of sinusoidal vibrations ([sine waves]).
Every period wave consists of:
- a [fundamental] [frequency]
- the fundamental is the lowest frequency that is present in a complex vibration
- if the fundamental is the only frequency present in the waveform, we are dealing with a [sine wave]
- some number of [overtones]
All these sine waves are collectively called [partial]s
- A fundamental is a partial
- An overtone is a partial
- A fundamental is not an overtone
The Fourier theorem also has an [inverse theorem], which is often used within applications of both theorems for modifying wave and signal data.
In Sound
The Fourier Theorem can be applied to [sound waves] to pick out specific frequencies present in a [spectrum].
Any sound comprised of a periodic waveform can be expressed as a sum of [sine waves]