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Least Squares Model for Human Hearing, Examples / Problem Solving - Coggle…
Least Squares Model for Human Hearing
Definition & introduction
how do we ACTUALLY hear?
4- The movements of these hairs activate nerve cells that send signals along various neural pathways to the brain, where the signals are interpreted as sound.
3- The cochlea contains thousands of minute hairs that oscillate with the fluid.
2- 3 tiny bones pass on the vibrations of the eardrum to a fluid within the cochlea.
1- Sound waves enter the outer ear causing eardrum to vibrate.
Ear
Ear is one of the most important organ because it gather the sound for we to hear and to maintain the balance of our body. There are 3 main components in our ear which is :
middle ear
inner ear
outer ear
anatomy of an ear
Least square method/model
The least square method is the process of finding the best-fitting curve or line of best fit for a set of data points by reducing the sum of the squares of the offsets (residual part) of the points from the curve. This method of fitting equations which approximates the curves to given raw data is the least squares.
Application & Problem Statement
problem statement
how do sound frequency sends signal to the brain?
what is the effect of the air pressure to the sound waves
what are the factor affected the frequencies of the sound waves?
How does a least square model relate with human hearing?
applied industry
audiology and otology
hearing aid transducer
hearing and technology
telephone
microphone
speaker
Theorem & Objective
theorem
THEOREM 1
(due to the technical problem, please press the link to see the slide theorem and skip to the page 7)
THEOREM 2
(due to the technical problem, please press the link to see the slide theorem and skip to the page 8)
objective
used in a model for human hearing, when energy consideration is what drives the use of the least squares approximation method.
Proof
Elementary type of sound wave for auditory system is sinusoidal variation in the air pressure and can be described by a function of time,
To be perceived as sound, sinusoidal waves must have frequencies within a certain range.
ear is a linear system,
Find the trigonometric polynomial of order 3 that is the least square approximation to the function
over the integral [ 0, 2π ].
solution
That minimizes the mean square error and has coefficients,
Then we compute,
Hence, the least squares trigonometric polynomial of order 3 is
Examples / Problem Solving
