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| '''Bandwidth expansion''' is a technique for widening the [[Bandwidth (signal processing)|bandwidth]] or the [[resonances]] in an [[Linear predictive coding|LPC]] filter. This is done by moving all the [[Pole (complex analysis)|poles]] towards the origin by a constant factor <math>\gamma</math>. The bandwidth-expanded filter <math>A'(z)</math> can be easily derived from the original [[Digital filter|filter]] <math>A(z)</math> by:
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| :<math>A'(z) = A(z/\gamma)</math>
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| Let <math>A(z)</math> be expressed as:
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| :<math>A(z) = \sum_{k=0}^{N}a_kz^{-k}</math>
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| The bandwidth-expanded filter can be expressed as:
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| :<math>A'(z) = \sum_{k=0}^{N}a_k\gamma^kz^{-k}</math> | |
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| In other words, each [[Linear_prediction|coefficient]] <math>a_k</math> in the original filter is simply multiplied by <math>\gamma^k</math> in the bandwidth-expanded filter. The simplicity of this transformation makes it attractive, especially in [[CELP]] coding of speech, where it is often used for the perceptual noise [[Weighting filter|weighting]] and/or to stabilize the LPC analysis. However, when it comes to stabilizing the LPC analysis, [[lag windowing]] is often preferred to bandwidth expansion.
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| == References ==
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| P. Kabal, "Ill-Conditioning and Bandwidth Expansion in Linear Prediction of Speech", ''Proc. IEEE Int. Conf. Acoustics, Speech, Signal Processing'', pp. I-824-I-827, 2003.
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| [[Category:Signal processing]]
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Latest revision as of 11:23, 2 May 2014
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