Cochlear Implants - Revision history

Lof: /* Types of mapping functions */

2024-08-19T11:01:59Z

Types of mapping functions

← Older revision		Revision as of 11:01, 19 August 2024
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	In the Normalized Logarithmic Scaling Function (NLSF) C is a scaling parameter that determines the curvature of the Y function.		In the Normalized Logarithmic Scaling Function (NLSF) C is a scaling parameter that determines the curvature of the Y function.
	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K ~~(Signal)~~ + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K X + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping function. In practice high values for C are used, in which case the NLSF is very close to the logarithmic mapping type.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping function. In practice high values for C are used, in which case the NLSF is very close to the logarithmic mapping type.
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	In case of the Power Law Function:		In case of the Power Law Function:
	*For small values of alpha (0<alpha<<1) the Power Law Function can be very close to the Logarithmic Function.		*For small values of alpha (0<alpha<<1) the Power Law Function can be very close to the Logarithmic Function.
	*For alpha is one the function becomes linear.		For alpha is one the function becomes a linear function I = K X + C1.
	*In the limit of alpha is zero it simplifies to ~~Y(X)~~ = 1.		*In the limit of alpha is zero it simplifies to a constant value: I = K + C1. Which again is not useful.

	Sometimes different constants are used below and above the kneepoint.		Sometimes different constants are used below and above the kneepoint.

Lof: /* Types of mapping functions */

2024-08-19T10:59:02Z

Types of mapping functions

← Older revision		Revision as of 10:59, 19 August 2024
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	In case of the Power Law Function:		In case of the Power Law Function:
	*For small values of alpha (0<alpha<<1) the Power Law Function can be very close to the Logarithmic Function.		*For small values of alpha (0<alpha<<1) the Power Law Function can be very close to the Logarithmic Function.
			*For alpha is one the function becomes linear.
			*In the limit of alpha is zero it simplifies to Y(X) = 1.

	Sometimes different constants are used below and above the kneepoint.		Sometimes different constants are used below and above the kneepoint.

Lof: /* Types of mapping functions */

2024-08-19T10:49:18Z

Types of mapping functions

← Older revision		Revision as of 10:49, 19 August 2024
Line 81:		Line 81:

	In case of the Power Law Function:		In case of the Power Law Function:
	*For small values of alpha (0<alpha<<1) the Power Law ~~function~~ can be very close to the Logarithmic Function.		*For small values of alpha (0<alpha<<1) the Power Law Function can be very close to the Logarithmic Function.

	Sometimes different constants are used below and above the kneepoint.		Sometimes different constants are used below and above the kneepoint.

Lof: /* Types of mapping functions */

2024-08-19T10:48:51Z

Types of mapping functions

← Older revision		Revision as of 10:48, 19 August 2024
Line 81:		Line 81:

	In case of the Power Law Function:		In case of the Power Law Function:
	*For ~~certain~~ values of alpha the Power Law function can be very close to the Logarithmic Function.		*For small values of alpha (0<alpha<<1) the Power Law function can be very close to the Logarithmic Function.

	Sometimes different constants are used below and above the kneepoint.		Sometimes different constants are used below and above the kneepoint.

Lof: /* Types of mapping functions */

2024-08-19T10:45:46Z

Types of mapping functions

← Older revision		Revision as of 10:45, 19 August 2024
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	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping function. In practice C ~~= 500 is~~ used ~~as a default~~, in which case the NLSF is very close to the logarithmic mapping type.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping function. In practice high values for C are used, in which case the NLSF is very close to the logarithmic mapping type.

	In case of the Power Law Function:		In case of the Power Law Function:

Lof: /* Types of mapping functions */

2024-08-19T10:45:15Z

Types of mapping functions

← Older revision		Revision as of 10:45, 19 August 2024
Line 78:		Line 78:
	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic mapping type.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping function. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic mapping type.

	In case of the Power Law Function:		In case of the Power Law Function:

Lof: /* Types of mapping functions */

2024-08-19T10:44:52Z

Types of mapping functions

← Older revision		Revision as of 10:44, 19 August 2024
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	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just ~~the~~ logarithmic ~~Map law~~. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic mapping type.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just a logarithmic mapping. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic mapping type.

	In case of the Power Law Function:		In case of the Power Law Function:

Lof: /* Types of mapping functions */

2024-08-19T10:44:00Z

Types of mapping functions

← Older revision		Revision as of 10:44, 19 August 2024
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	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just the logarithmic Map law. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic ~~Map Law~~.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just the logarithmic Map law. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic mapping type.

	In case of the Power Law Function:		In case of the Power Law Function:

Lof: /* Types of mapping functions */

2024-08-19T10:43:36Z

Types of mapping functions

← Older revision		Revision as of 10:43, 19 August 2024
Line 78:		Line 78:
	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get ~~I =~~ I = K * log(Signal) + C1 which is just the logarithmic Map law. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic Map Law.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = K * log(Signal) + C1 which is just the logarithmic Map law. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic Map Law.

	In case of the Power Law Function:		In case of the Power Law Function:

Lof: /* Types of mapping functions */

2024-08-19T10:42:54Z

Types of mapping functions

← Older revision		Revision as of 10:42, 19 August 2024
Line 78:		Line 78:
	In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.		In the limit of C is zero it simplifies into a linear relationship: Y(X) = X and thus I = K (Signal) + C1.
	*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.		*In the limit of C is infinite it simplifies into Y(X) = 1 and thus I = K + C1 which is constant and not very useful.
	When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 in C1 and ln(C) in K we get I = I = K log(Signal) + C1 which is just the logarithmic Map law. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic Map Law.		When C is large but finite it simplifies into Y(X) = 1 + log(Signal)/log(C) and by absorbing 1 K in C1 and ln(C) in K we get I = I = K * log(Signal) + C1 which is just the logarithmic Map law. In practice C = 500 is used as a default, in which case the NLSF is very close to the logarithmic Map Law.

	In case of the Power Law Function:		In case of the Power Law Function: