Quantization Error Data Acquisition Process
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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). quantization step size formula The difference between the original signal and the reconstructed signal is the quantization analog to digital conversion error and, in this simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and
Pulse Code Modulation
digital signal processing, is the process of mapping a large set of input values to a (countable) smaller set. Rounding and truncation are typical examples of quantization processes. Quantization is involved to
Adc
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 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. sampling 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 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
stored in a computer for further processing. Analogue signals are "real world" signals - for example physiological signals such as electroencephalogram, electrocardiogram
Nyquist Theorem
or electrooculogram. In order for them to be stored and manipulated by a computer, these signals must be converted into a discrete digital form the computer can understand. An example of an A/D board which performs the analogue to digital conversion. This board is placed inside the computer where it communicates with the rest of the computer hardware https://en.wikipedia.org/wiki/Quantization_(signal_processing) and software. An alternate way to acquire a signal is to use an integrated device which comprises the electronics necessary to acquire as well as amplify the signals (shown to the right). Powerlab* recording system has an A/D board as well as amplifiers and communicates with the computer through its USB port. (ADInstruments)* Using A/D conversion and a http://www.medicine.mcgill.ca/physio/vlab/biomed_signals/atodvlab.htm computer to analyze data has many advantages over older non-computerized methods. Computer data is easily transported and manipulated. Computer analysis of signals is far more efficient than analysis by hand and paper. Most importantly, real-time analysis can be performed - this means that signals can be analyzed as they are acquired during the course of an experiment Sampling Consider the signal shown in the figure which is part of an electroencephalogram. It is an analogue signal, since it is continuously changing in time. Any arbitrarily given value that is within the range of the signal can be obtained simply by measuring electrical activity at the right point in time. The object of A/D conversion is to convert this signal into a digital representation, and this is done by sampling the signal. A digital signal is a sampled signal, obtained by sampling the analogue signal at discrete points in time. These points are usually evenly spaced in time, with the time between being referred to as the sampling interval. In the figure, the sampling interval is 2.5 millisecon
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