Linear prediction - Revision history

Pepoluan: $-ify the expressions$

2006-09-02T07:53:44Z <math>-ify the expressions

← Older revision		Revision as of 07:53, 2 September 2006
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	<center><math>x'(n)=\sum_{i=1}^p a_i x(n-i)</math></center>		<center><math>x'(n)=\sum_{i=1}^p a_i x(n-i)</math></center>

	The trick with linear prediction is to choose the coefficients ~~(a(i))~~ in such a way that the difference between the estimated value (x'(n)) and the real value (x(n)) is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example x'(n)=x(n-1) or x'(n)=2x(n-1)-x(n-2), where the first assumes a function of the form y=a and the second assumes a function of the form y=ax+b)).		The trick with linear prediction is to choose the coefficients <math>a_i</math> in such a way that the difference between the estimated value <math>x'(n)</math> and the real value <math>x(n)</math> is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example <math>x'(n)=x(n-1)</math> or <math>x'(n)=2x(n-1)-x(n-2)</math>, where the first assumes a function of the form <math>y=a</math> and the second assumes a function of the form <math>y=ax+b</math>).


	[[Category:Technical]]		[[Category:Technical]]

Pepoluan at 07:51, 2 September 2006

2006-09-02T07:51:37Z

← Older revision		Revision as of 07:51, 2 September 2006
Line 4:		Line 4:

	The trick with linear prediction is to choose the coefficients (a(i)) in such a way that the difference between the estimated value (x'(n)) and the real value (x(n)) is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example x'(n)=x(n-1) or x'(n)=2x(n-1)-x(n-2), where the first assumes a function of the form y=a and the second assumes a function of the form y=ax+b)).		The trick with linear prediction is to choose the coefficients (a(i)) in such a way that the difference between the estimated value (x'(n)) and the real value (x(n)) is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example x'(n)=x(n-1) or x'(n)=2x(n-1)-x(n-2), where the first assumes a function of the form y=a and the second assumes a function of the form y=ax+b)).


			[[Category:Technical]]

Pepoluan: Replace inline PNG with something based

2006-09-01T22:16:20Z

Replace inline PNG with something <math></math> based

← Older revision		Revision as of 22:16, 1 September 2006
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	Linear prediction tries to estimate what the value a sample will have, based on previous samples. The general equation is:		Linear prediction tries to estimate what the value a sample will have, based on previous samples. The general equation is:
	~~[[Image:Linearprediction.png\|frame\|none\|~~x'(n)=~~sum(~~i=1:p~~:a(i)~~x(n-i)~~)]]~~
			<center><math>x'(n)=\sum_{i=1}^p a_i x(n-i)</math></center>

	The trick with linear prediction is to choose the coefficients (a(i)) in such a way that the difference between the estimated value (x'(n)) and the real value (x(n)) is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example x'(n)=x(n-1) or x'(n)=2x(n-1)-x(n-2), where the first assumes a function of the form y=a and the second assumes a function of the form y=ax+b)).		The trick with linear prediction is to choose the coefficients (a(i)) in such a way that the difference between the estimated value (x'(n)) and the real value (x(n)) is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example x'(n)=x(n-1) or x'(n)=2x(n-1)-x(n-2), where the first assumes a function of the form y=a and the second assumes a function of the form y=ax+b)).

Jan at 19:57, 25 March 2005

2005-03-25T19:57:44Z

New page

Linear prediction tries to estimate what the value a sample will have, based on previous samples. The general equation is:
[[Image:Linearprediction.png|frame|none|x'(n)=sum(i=1:p:a(i)x(n-i))]]

The trick with linear prediction is to choose the coefficients (a(i)) in such a way that the difference between the estimated value (x'(n)) and the real value (x(n)) is as small as possible. There are several ways of doing this, but one simple, commonly used (because of its simplicity, not its performance) method is to assume that the signal more or less follows an n-th order polynomial and simply use fixed coefficients (for example x'(n)=x(n-1) or x'(n)=2x(n-1)-x(n-2), where the first assumes a function of the form y=a and the second assumes a function of the form y=ax+b)).

Linear prediction - Revision history

Pepoluan: -ify the expressions

Pepoluan at 07:51, 2 September 2006

Pepoluan: Replace inline PNG with something based

Jan at 19:57, 25 March 2005

Pepoluan: $-ify the expressions$