How To Reduce Quantization Error In Pcm
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the original analog signal (green), the quantized signal (black dots), the signal reconstructed from the quantized signal quantization error formula (yellow) and the difference between the original signal and the reconstructed uniform quantization signal (red). The difference between the original signal and the reconstructed signal is the quantization encoding in pcm error 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 quantization error definition 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 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
Quantization Noise
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 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 s
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
What Is Quantization
for signals coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, quantization noise in pcm dB 1 2 0.5 8 2 4 0.25 14 3 8 0.125 20 4 16 0.0625 26 5 32 0.03125 32 quantization step size formula 6 64 0.01563 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 https://en.wikipedia.org/wiki/Quantization_(signal_processing) 86 15 32768 0.00003 92 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 http://www.skillbank.co.uk/SignalConversion/snr.htm of the input voltage is measured by 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. Dow
ProtocolsTroubleshoot and AlertsConfiguration Example and TechNotes Waveform Coding Techniques Download Print Available Languages Download Options PDF (64.1 KB) View with Adobe Reader on a variety of devices Updated:Feb 02, 2006 Document http://www.cisco.com/c/en/us/support/docs/voice/h323/8123-waveform-coding.html ID:8123 Contents Introduction Prerequisites Requirements Components Used Conventions Pulse Code Modulation Filtering Sampling Digitize Voice Quantization and Coding Companding A-law and u-law Companding Differential Pulse Code Modulation Adaptive DPCM Specific 32 KB/s Steps Related Information Introduction Although humans are well equipped for analog communications, analog transmission is not particularly efficient. When analog signals become weak because of transmission loss, it is hard to separate the complex analog structure quantization error from the structure of random transmission noise. If you amplify analog signals, it also amplifies noise, and eventually analog connections become too noisy to use. Digital signals, having only "one-bit" and "zero-bit" states, are more easily separated from noise. They can be amplified without corruption. Digital coding is more immune to noise corruption on long-distance connections. Also, the world's communication systems have converted to a digital transmission format called how to reduce pulse code modulation (PCM). PCM is a type of coding that is called "waveform" coding because it creates a coded form of the original voice waveform. This document describes at a high level the conversion process of analog voice signals to digital signals. Prerequisites Requirements There are no specific requirements for this document. Components Used This document is not restricted to specific software and hardware versions. Conventions For more information on document conventions, refer to the Cisco Technical Tips Conventions. Pulse Code Modulation PCM is a waveform coding method defined in the ITU-T G.711 specification. Filtering The first step to convert the signal from analog to digital is to filter out the higher frequency component of the signal. This make things easier downstream to convert this signal. Most of the energy of spoken language is somewhere between 200 or 300 hertz and about 2700 or 2800 hertz. Roughly 3000-hertz bandwidth for standard speech and standard voice communication is established. Therefore, they do not have to have precise filters (it is very expensive). A bandwidth of 4000 hertz is made from an equipment point if view. This band-limiting filter is used to prevent aliasing (antialiasing). This happens when the input analog voice signal
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