# Frequency Domain

Another way to study sound is by examining how amplitude changes relative to frequency, producing graphs where the horizontal axis is expressed in **hertz** *(Hz)* allowing interpretation.

These representations correspond to the *frequency* domain.&#x20;

The relationship between the time domain and the frequency domain is grounded in **Fourier** decomposition, which states that waves can be described as the sum or superposition of multiple sinusoidal waves, each contributing a specific frequency, amplitude, and phase.

The more sinusoids are combined, the more accurate the approximation of the original wave becomes. To uncover the sinusoidal components of a signal, a *Fourier* *transform* is applied, with the Fast Fourier Transform *(FFT)* being the most common method.&#x20;

This algorithm allows us to **decompose** a waveform, identify its frequencies and amplitudes, and represent them as a spectrum in the *frequency* domain.

{% hint style="info" %}
Advanced **pitch-detection** algorithms analyze the *frequency spectrum* to identify the fundamental frequency of a signal, enabling applications such as dominant-frequency tracking.
{% endhint %}


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