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

Waves are mathematically represented using cosine and sine functions.

$y = A*sin(2{\pi}ft)$

Two main characteristics of a wave are 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) 

Frequency is the number of times a wave repeats itself. Frequency is measured in cycles per second.
Time taken by a wave to complete one cycle is  period of the wave.

$T = \frac{1}{f}$

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.



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