Acoustic waves are complex waves which contains dissimilar waves at different frequencies and fourier analysis of sound waves helps to represent this complex wave as a sum of various sine waves of different frequencies.

San Jose State University

Acoustic waves can be mathematically represented using sine and cosine functions:

$$y = A \sin(2\pi ft)$$

Two key characteristics of an acoustic wave are its amplitude ($$A$$) and frequency ($$f$$).

Acoustic Waves

An on-going but a helpful book resource about NLP
https://web.stanford.edu/~jurafsky/slp3/

Speech and Language Processing (3rd ed. draft) 

The frequency of a sound wave is the number of cycles the wave completes per unit of time. It is typically measured in cycles per second, or Hertz (Hz).

Frequency of a Sound Wave

Amplitude measures the height a wave can reach in its span.

Amplitude of Sound Wave

Fourier Analysis of Acoustic Waves

The spectrum represents frequency and amplitude of each signal present in a waveform. The x axis represents the frequency and y axis represents the amplitude of component signals.

Cochlea, or inner ear computes the spectrum of sound waveforms in humans.



Spectrum of Acoustic Waveform

Spectrogram represents the changes in the complex waveform over the the time.

Each dark bar (or spectral peak) is called a formant, the formants are caused by the resonant cavities of the mouth.



Spectrogram of Acoustic Waveforms

The conversion from the analog representations (first air pressure and then analog electric signals in a microphone) into a digital signal.

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