Noise shaping - Revision history

85.23.153.60: /* Limits & filter design restrictions */

2013-06-21T12:17:54Z

Limits & filter design restrictions

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	frequency axis cannot drop below 0dB.		frequency axis cannot drop below 0dB.

	The noise shaping application poses some restrictions on the ~~fiter~~		The noise shaping application poses some restrictions on the filter
	design. The first sample of the filter's impulse response always equals		design. The first sample of the filter's impulse response always equals
	one. Also, interesting filters for noise shaping are so-called		one. Also, interesting filters for noise shaping are so-called

2008-08-20T13:05:17Z

References

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	==References==		==References==
	* Lipshitz. P, Stanley and John Vanderkooy. "Why 1-bit Sigma-Delta Conversion is Unsuitable for High-Quality Applications". 110th Convention. <i>Audio Engineering Society</i> (May 2001). 2-4.		* Lipshitz. P, Stanley and John Vanderkooy. "Why 1-bit Sigma-Delta Conversion is Unsuitable for High-Quality Applications". 110th Convention. <i>Audio Engineering Society</i> (May 2001). 2-4.
	*

	[[Category:Signal Processing]]		[[Category:Signal Processing]]

2008-08-20T13:04:50Z

Notes

2008-08-20T13:04:33Z

Example filters

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	-H(z).		-H(z).

	= Example filters =		== Example filters ==

	The following two filters have been designed by Sebastian Gesemann		The following two filters have been designed by Sebastian Gesemann
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	including the noise transfer function's second order factorizations.		including the noise transfer function's second order factorizations.

	== Sampling rate of 44100 Hz, derived from LAME's ATH formula ==		=== Sampling rate of 44100 Hz, derived from LAME's ATH formula ===

	The noise transfer function is given by		The noise transfer function is given by
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	{1 +1.0587 z^{-1} +0.0676 z^{-2} -0.6054 z^{-3} -0.2738 z^{-4}}</math>		{1 +1.0587 z^{-1} +0.0676 z^{-2} -0.6054 z^{-3} -0.2738 z^{-4}}</math>

	== Sampling rate of 48000 Hz, derived from LAME's ATH formula ==		=== Sampling rate of 48000 Hz, derived from LAME's ATH formula ===

	The noise transfer function is given by		The noise transfer function is given by

2008-08-20T13:04:02Z

Noise Shaper Implementation

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	[http://ccrma.stanford.edu/~jos/filters/Direct_Form_I.html direct form I].		[http://ccrma.stanford.edu/~jos/filters/Direct_Form_I.html direct form I].

	= Noise Shaper Implementation =		== Noise Shaper Implementation ==

	Usually a filter's transfer function is called 'H'. In this article 'N'		Usually a filter's transfer function is called 'H'. In this article 'N'
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	'H' is introduced that has a special relation to 'N'.		'H' is introduced that has a special relation to 'N'.

	== Direct Form I ==		=== Direct Form I ===

	For convenience let us substitute the actual difference in the		For convenience let us substitute the actual difference in the
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	determined by the filter order.		determined by the filter order.

	== Decoupling filtering and quantization ==		=== Decoupling filtering and quantization ===

	[[Image:Noiseshaper3.png\|thumb\|right\|200px]]		[[Image:Noiseshaper3.png\|thumb\|right\|200px]]

2008-08-20T13:03:36Z

IIR filters

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	to a multiplication in the Z-domain.		to a multiplication in the Z-domain.

	== IIR filters ==		=== IIR filters ===

	IIR filters are a simple extension to the FIR case:		IIR filters are a simple extension to the FIR case:

2008-08-20T13:03:08Z

FIR filters

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	where 'N' is the transfer function and 'm' the filter's ''order''.		where 'N' is the transfer function and 'm' the filter's ''order''.

	== FIR filters ==		=== FIR filters ===

	In case a1=a2=a3=...=0 the filter's [http://en.wikipedia.org/wiki/Impulse_response impulse response] is finite which is		In case a1=a2=a3=...=0 the filter's [http://en.wikipedia.org/wiki/Impulse_response impulse response] is finite which is

2008-08-20T13:02:43Z

Digital filter reminder

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	covered by this article.		covered by this article.

	= Digital filter reminder =		== Digital filter reminder ==

	A common representation of digital filters is their ''transfer function''		A common representation of digital filters is their ''transfer function''

2008-08-20T13:02:29Z

Limits & filter design restrictions

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	frequencies above 100 kHz).		frequencies above 100 kHz).

	= Limits & filter design restrictions =		== Limits & filter design restrictions ==

	Noise Shaping without [[Dithering\|''dithered'']] quantization is also possible but		Noise Shaping without [[Dithering\|''dithered'']] quantization is also possible but

2008-08-20T13:02:15Z

Applications

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	that the overall noise becomes less perceivable.		that the overall noise becomes less perceivable.

	= Applications =		== Applications ==

	In the field of digital image processing a popular noise shaping		In the field of digital image processing a popular noise shaping