Quantization Error White Noise
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) quantization noise power formula and the difference between the original signal and the reconstructed signal
Quantization Error Formula
(red). The difference between the original signal and the reconstructed signal is the quantization error and, quantization of signals in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process of mapping a
Quantisation Error
large set of input values to a (countable) smaller set. Rounding and truncation are typical examples of quantization processes. Quantization is involved to some degree in nearly all digital signal processing, as the process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially all what is quantization lossy compression algorithms. The difference between an input value and its quantized value (such as round-off error) is referred to as quantization error. A device or algorithmic function that performs quantization is called a quantizer. An analog-to-digital converter is an example of a quantizer. Contents 1 Basic properties of quantization 2 Basic types of quantization 2.1 Analog-to-digital converter (ADC) 2.2 Rate–distortion optimization 3 Rounding example 4 Mid-riser and mid-tread uniform quantizers 5 Dead-zone quantizers 6 Granular distortion and overload distortion 7 The additive noise model for quantization error 8 Quantization error models 9 Quantization noise model 10 Rate–distortion quantizer design 11 Neglecting the entropy constraint: Lloyd–Max quantization 12 Uniform quantization and the 6 dB/bit approximation 13 Other fields 14 See also 15 Notes 16 References 17 External links Basic properties of quantization[edit] Because quantization is a many-to-few mapping, it is an inherently non-linear and irreversible process (i.e., because the same output value is shared by multipl
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Quantization Noise In Pcm
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Quantization Example
posting ads with us Signal Processing Questions Tags Users Badges Unanswered Ask Question _ Signal Processing Stack Exchange is a quantization step size formula question and answer site for practitioners of the art and science of signal, image and video processing. Join them; it only takes a minute: Sign up Here's how it works: Anybody can ask https://en.wikipedia.org/wiki/Quantization_(signal_processing) a question Anybody can answer The best answers are voted up and rise to the top How does the quantization error generate noise? up vote 9 down vote favorite 3 I'm learning about sampling and DSP on my own. I have a hard time to understand how the quantization error results in noise. I think I miss a fundamental understanding but can't tell what it is. So how http://dsp.stackexchange.com/questions/2897/how-does-the-quantization-error-generate-noise does the quantization error generate noise? noise sampling share|improve this question asked Jul 15 '12 at 19:29 Jan Deinhard 1485 It's more distortion than noise. It depends on the signal, and is not random. –endolith Jul 15 '12 at 20:48 endolith, I think what I don't understand is how the error results in frequencies. –Jan Deinhard Jul 15 '12 at 21:04 2 distortion always produces additional frequencies. if you distort a sine wave, it becomes a different repetitive waveform. any repetitive waveform other than a sine wave is made up of multiple frequencies. –endolith Jul 15 '12 at 22:58 1 As @endolith has mentioned, let us assume you have a very bad ADC, such that you give it a pure tone, but get a signal that looks like a sine but has big steps in it. (So now your signal looks like a staircase that is going up and down with the original sine.) Now, you know intuitively that a step is composed of many frequencies. This is how an ADC will add frequencies as you are asking. It is a non-linear operation btw. If it was linear, you could not make new f
BemroseOctober 18, 20062 Share 0 0 Quantization adds noise. Taking a nice continuous signal and expressing it as distinct integers will introduce a round-off error, which means you've added random fluctuations to the signal, whichisthe definiton of noise.Remember thatnoise is inevitable, sowe https://blogs.msdn.microsoft.com/audiofool/2006/10/18/always-dither-before-you-quantize/ just have to manage it (such as using enough bits per sample). The problem is that round-off errors aren't random- just ask any banker. Whether you round up or down can be strongly correlated with the signal - down at the peak of the continuouswave and up at the trough, for example. We have a word for signal-correlated noise, and that's distortion. Distortion is much quantization error more difficult for the ear to separate from signal, which makes it much worse, from an audio perspective. Fortunately, there's a solution. Ironically, it's to add more noise. Dithering is the technique of adding white noise to a continuous signal before quantizing it. This noise effectivelycancels the distortion introduced by rounding because the noise is no longer correlated to the signal. The noise floor of quantization error white the quantized signal is higher (reducing dynamic range), but it is white noise which is much easier on the ear than the distortion it's covering up. One common type of dithering is Triangular Probability Dithering (TPD). With TPD, yougeneratetwo random numbers x and y in the range [0,1] (uniformdistribution) for each sample. Add (x-y)/2 to the sample, and then round to the nearest integer. This is gives the quantized signal a white noise floor 3dB over the undithered sample, but clears any distortion artifacts due to rounding. Quantization noise is usually not considered a big problem in signals, because the solution is as simple as adding more bits to your samples. Remember that quantization noise is determined by the theoretical maximum dynamic range for your sample size. The quantization noise floor for 16-bit samples will be 96dB below the full-scale level. If you use TPD, your noise floor goes to 93dBbelow full scale. This is only a problem, though, if your input continuous signal has more than 93dB of dynamic range, and if it does, you just add enough bits to push the quantization noise below the noise of your original samples. The add-m