Publication

Reduction of the MSE in R-times oversampled A/D conversion from O(1/R) to O(1/R^2)

Martin Vetterli
1994
Journal Articles

Abstract

In oversampled analog-to-digital conversion, the usual reconstruction method using lowpass filtering leads to a mean squared error (MSE) inversely proportional to the oversampling ratio R. The authors prove, under certain assumptions and with periodic analog input signals, that optimal reconstruction achieves an MSE with an oversampling ratio dependence order of at least O(1/R2). That is, an MSE slope of -6 dB per octave of oversampling is obtained, rather than the conventional -3 dB/octave slope of classical schemes

Official source

https://infoscience.epfl.ch/entities/publication/53ed7d6d-0ee6-4b56-aa4e-1f30082bef94

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Martin Vetterli
1994
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/53ed7d6d-0ee6-4b56-aa4e-1f30082bef94

About this result

Related concepts (32)

Oversampling

In signal processing, oversampling is the process of sampling a signal at a sampling frequency significantly higher than the Nyquist rate. Theoretically, a bandwidth-limited signal can be perfectly reconstructed if sampled at the Nyquist rate or above it. The Nyquist rate is defined as twice the bandwidth of the signal. Oversampling is capable of improving resolution and signal-to-noise ratio, and can be helpful in avoiding aliasing and phase distortion by relaxing anti-aliasing filter performance requirements.

Mean squared error

In statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.

Audio bit depth

In digital audio using pulse-code modulation (PCM), bit depth is the number of bits of information in each sample, and it directly corresponds to the resolution of each sample. Examples of bit depth include Compact Disc Digital Audio, which uses 16 bits per sample, and DVD-Audio and Blu-ray Disc which can support up to 24 bits per sample. In basic implementations, variations in bit depth primarily affect the noise level from quantization error—thus the signal-to-noise ratio (SNR) and dynamic range.

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