Quantization Error Formula
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal (yellow) and the difference between the original signal and the reconstructed signal (red). The difference between the original quantization error in pcm signal and the reconstructed signal is the quantization error and, in this simple quantization quantization error example scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process of mapping how to reduce quantization error 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
Quantization Error In A/d Converter
process of representing a signal in digital form ordinarily involves rounding. Quantization also forms the core of essentially 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 quantization level 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 multiple input values, it is impossible in general to recover the exact input value when given only the output value). The set of possible input values may be infinitely large, and may possibly be continuous and therefore uncountable (such as the set of all real numbers, or all real numbers within some limited range). The set of possible output values may be finite or countably infinite. The input and output sets involved in quantization can be defined in a rather general way. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input data.[1] Basic types of quantization[edit] 2-bit
Data Conversion Website Quantization Error and Signal - to - Noise Ratio calculations The signal to noise ratio of a quantized signal is 2+6*(no of bits), as shown in the following table. Resolution and Signal to Noise Ratio for signals what is quantization coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, dB 1
Quantization Step Size Formula
2 0.5 8 2 4 0.25 14 3 8 0.125 20 4 16 0.0625 26 5 32 0.03125 32 6 64 0.01563
Signal To Quantization Noise Ratio
38 7 128 0.00781 44 8 256 0.00391 50 9 512 0.00195 56 10 1024 0.00098 62 11 2048 0.00048 68 12 4096 0.00024 74 13 8192 0.00012 80 14 16384 0.00006 86 15 32768 0.00003 92 https://en.wikipedia.org/wiki/Quantization_(signal_processing) 16 65536 0.00001 98 These values are for a signal matched to the full-scale range of the converter. If a signal with a range of 5V is measured by an 8 bit ADC with a range of 10V then only 7 bits are effectively in use, and a signal to noise ratio of 44 rather than 50 will apply. Proof: Suppose that the instantaneous value of the input voltage is measured by http://www.skillbank.co.uk/SignalConversion/snr.htm an ADC with a Full Scale Range of Vfs volts, and a resolution of n bits. The real value can change through a range of q = Vfs / 2n volts without a change in measured value occurring. The value of the measured signal is Vm = Vs - e, where Vm is the measured value, Vs is the actual value, and e is the error. The maximum value of error in the measured signal is emax = (1/2)(Vfs / 2n) or emax = q/2 since q = Vfs / 2n The RMS value of quantization error voltage is whence The Signal to Noise Ratio (SNR) is defined as It is normally quoted on a logarithmic scale, in deciBels ( dB ). or The RMS signal voltage is then The error, or quantization noise signal is Thus the signal - to - noise ratio in dB. is since Vfs = 2n q, then which simplifies to N.B. This equation is true only if the input signal is exactly matched to the Full Scale Range of the converter. For signals whose amplitude is less than the FSR the Signal - to - Noise Ratio will be reduced. Download a .pdf file of the analysis of quantization error and signal to noise ratio
Help Rules Groups Blogs What's New? Teardown Videos Datasheets Advanced Search Forum EDA Theory Elementary Electronic Questions How do I solve quantization errors in ADC system? + Post http://www.edaboard.com/thread40731.html New Thread Results 1 to 8 of 8 How do I solve quantization errors in ADC system? LinkBack LinkBack URL About LinkBacks Thread Tools Show Printable Version Download This Thread Subscribe to this Thread… Search Thread Advanced Search 22nd June 2005,16:25 #1 KrisUK Newbie level 4 Join Date May 2005 Posts 7 Helped 0 / 0 Points 1,398 Level 8 How do I solve quantization error quantization errors in ADC system? How do I work out quantization error in a ADC system? I looked around on different sites from a recommendation from another user and came to the conclusion it is the max voltage divided by the number of bits. Is this correct? Thank you. 22nd June 2005,16:25 22nd June 2005,16:52 #2 Kral Advanced Member level 4 Join quantization error in Date Mar 2005 Location USA Posts 1,326 Helped 278 / 278 Points 11,626 Level 25 Re: Quantization Error The weighting of the LSB is equal to the (Reference Voltage)/2^n, where n is the number of bits. The Quantization error = 1/2 LSB. If the ADC is bipolar (can represent both positive and negative values, then the LSB weighting is 2X the above value. The quantization error is still 1/2 LSB. The total error includes the quantization error plus scale factor (gain) error, non-linearity errors. Regards, Jon 22nd June 2005,17:22 #3 banh Advanced Member level 1 Join Date Dec 2004 Posts 458 Helped 17 / 17 Points 3,856 Level 14 Quantization Error quantization error/noise is the difference between the actual sampled value and the quantized value. 2 cases: if the the actual sampled value is between 2 quantized levels -> it will either be rounded off or truncated. rounding -> take the nearest quantized level. truncated -> take the level below it. hence: the error is - rounding off: - truncated where Q is the resolution. Last edited by BlackMamba; 27th August 2010 at 12:44. 22nd June 2005,17:22 22nd June 2