Frequency Domain

Energy characterization and applications for spectral decomposition

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.

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.

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

Advanced pitch-detection algorithms analyze the frequency spectrum to identify the fundamental frequency of a signal, enabling applications such as dominant-frequency tracking.