Quantization Error Signal Processing
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) quantization error formula and the difference between the original signal and the reconstructed
Quantization Error Definition
signal (red). The difference between the original signal and the reconstructed signal is the quantization error quantization error in pcm and, 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
Quantization Error In Analog To Digital Conversion
a 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 quantization error ppt all 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
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Quantization Error In Dsp
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Quantization Error Pdf
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. Join how to reduce quantization error them; it only takes a minute: Sign up Here's how it works: Anybody can ask a question Anybody can answer The best answers are voted up and rise to the top What is “Maximum Quantization Error”? up vote 2 https://en.wikipedia.org/wiki/Quantization_(signal_processing) down vote favorite 1 I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation. It is defined as: $$Q = \dfrac {\Delta x}{2^{N+1}}$$ where $N$ is the number of bits used for quantization in a analog to digital conversion, and $\Delta x$ is, in portuguese "Faixa de Excursão do Sinal", I don't know what would be the correct translation, but I bet http://dsp.stackexchange.com/questions/15925/what-is-maximum-quantization-error on something like "Signal Excursion Band". I know, its a strange name. Can someone help me with this? What is this $\Delta x$? Sorry for my bad english, it isnt my native language. adc quantization share|improve this question edited Apr 29 '14 at 17:07 jojek♦ 6,71041444 asked Apr 29 '14 at 15:19 Diedre 20115 Evidently you are learning the basics. Speaking as a retired EE; real designs are a lot more complicated. The answer below is idealized for discussion. While not wrong, there are large confounding terms in physical implementation. –rrogers Dec 30 '15 at 14:42 add a comment| 1 Answer 1 active oldest votes up vote 4 down vote accepted When you quantize a signal, you introduce and error which can be defined as $$q[n] = x_q[n]-x[n]$$ where $q[n]$ is the quantization error, $x[n]$ the original signal, and $x_q[n]$ of the quantized signal. The maximum quantization error is simply $max(\left | q \right |)$, the absolute maximum of this error function. Dx in this definition seems to be the range of the input signal so we could rewrite this as $$Q = \frac{max(x)-min(x)}{2^{N+1}}$$ Let's look at a quick example. Let's assume you have a signal that's uniformly distributed between -1 and +1 and you want to quantize this with 3 bits. You have a total 8 of quantizaton steps which would map to [-1 -.75 -.5 -25 0 .25 .5 .75]. The differenc
a discrete time signal quantized? Topics Digital Signal Processing × 545 Questions 29,227 Followers Follow Jun 10, 2014 Share Facebook Twitter LinkedIn Google+ 0 https://www.researchgate.net/post/What_exactly_is_the_process_of_Quantization / 0 All Answers (9) Parul Nilesh Shah · Vubites India Pvt. Ltd. I have briefly explained that in the answer to your other question. Please refer to that. https://www.researchgate.net/post/What_is_the_basic_difference_between_a_Digital_signal_and_a_Discrete_Time_signal Jun 10, 2014 Khalaf Al-sabaawi · University of Mosul Http://www.princeton.edu/~cuff/ele201/kulkarni_text/digitizn.pdf Jun 10, 2014 Mostafa Azadbakht · Sahand University of Technology For convert discrate signale to standard value(digital)... For example: in quantization error the 3 bit signal you must converted amplitued between 1/8-2/8(less 2/8) to [001]. Jun 10, 2014 Fernando Soares Schlindwein · University of Leicester Quantisation means choosing the closest value to your quantity from a limited set of values. Are we doing your homework for you? Did you try to read a (basic) book? Jun 13, 2014 Aparna Murthy Quantization quantization error in is done in order to assign weighted values for discretized signals. Just using N # of bits and mapping values is not enough , you will have to approximate and with that comes issues such as DNL/INL/Errs such as offset/gain.. Say if you have 100 discrete values, and if you do binary quantization you will be needing at least 7 bits again [2^7=128] that is 28 excess (straight forward)!!! Say , you decide on using all , so you can now use probability theory and assign values (fixed or adaptive) so on ...Swastik , read ADC/DAC design books . For eg: Jacob Baker - CMOS mixed signal circuit design. Jun 15, 2014 Swastik Mohapatra · SRM University @Fernando: Actually these things are going to be taught to me in my coming term...it's vacccation so i was doing a bit of study to easily understand the concepts when they are taught in my university...and yeah i did read “Discrete Time Signal Processing” by Alan V Oppenheim and Ronald W. Schafer but i did not get an intuitive understandin
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