Quantization Error Sound
Contents |
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 quantization error definition original signal and the reconstructed signal is the quantization error and, in this quantization error formula simple quantization scheme, is a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process how to reduce quantization error 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 some degree in nearly all digital signal quantization error in pcm 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. An analog-to-digital converter is an example of a quantizer. Contents 1
Quantization Error Example
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 involved in quantization can be defined in a rather general way. For example, vector quantization is the application of quantization to multi-di
6 : Quantization Noise Demo Madhan Mohan SubscribeSubscribedUnsubscribe958958 Loading... Loading... Working... Add to Want to watch this again later? Sign in to add this video to a playlist. Sign in Share More Report Need to report the video? Sign in to report inappropriate content. Sign
Quantization Of Signals
in Transcript Statistics 4,477 views 18 Like this video? Sign in to make your quantization error in analog to digital conversion opinion count. Sign in 19 0 Don't like this video? Sign in to make your opinion count. Sign in 1 Loading... Loading... quantisation noise Transcript The interactive transcript could not be loaded. Loading... Loading... Rating is available when the video has been rented. This feature is not available right now. Please try again later. Published on Oct 14, 2012In this Demo https://en.wikipedia.org/wiki/Quantization_(signal_processing) a piece of music has been taken and it is played with various bit depth from 24 to 2 and the quality of the signal is seen.by Madhan Mohanhttp://www.youtube.com/user/ThePowerDSP Category Education License Standard YouTube License Show more Show less Loading... Autoplay When autoplay is enabled, a suggested video will automatically play next. Up next Quantization Part 7 : Quantization Examples - Duration: 4:33. Madhan Mohan 4,468 views 4:33 Quantization Part 5: Bit Depth Vs https://www.youtube.com/watch?v=_cRFBBnUFug Quantization Noise - Duration: 3:50. Madhan Mohan 2,493 views 3:50 Quantization Part 8: Dynamic Range - Duration: 5:13. Madhan Mohan 1,879 views 5:13 Quantization Part 9: Signal to Noise Ratio (SNR) - Duration: 4:41. Madhan Mohan 12,060 views 4:41 DSP Lecture 23: Introduction to quantization - Duration: 1:03:51. Rich Radke 8,100 views 1:03:51 Mod-01 Lec-16 Quantization Noise - I - Duration: 51:25. nptelhrd 2,156 views 51:25 Quantization and Coding in A/D Conversion - Duration: 8:31. Barry Van Veen 10,595 views 8:31 Quantization Part 1: What is quantization - Duration: 4:03. Madhan Mohan 27,677 views 4:03 signal to quantization noise ratio derivation - Duration: 18:44. Signals Systems 557 views 18:44 Sampling Part 4 - Aliasing - Duration: 4:02. Madhan Mohan 4,664 views 4:02 Quantization Part 3 : Quantization understanding with equations - Duration: 4:49. Madhan Mohan 7,096 views 4:49 Sampling Part 1-Why sampling theorem is needed? - Duration: 6:35. Madhan Mohan 7,124 views 6:35 Analysis of Quantization Error - Duration: 15:04. Barry Van Veen 9,107 views 15:04 Quantization Part 4 : Bit Depth - Duration: 4:01. Madhan Mohan 4,273 views 4:01 22. Sampling and Quantization - Duration: 53:01. MIT OpenCourseWare 11,617 views 53:01 Lecture 20 - Quantization Noise Spectrum (contd), Flash A/D Converter Basics - Duration: 32:45. Satish Kashyap 3,347 views 32:45 Tech Talk: Signal to Noise Ratio SNR Explai
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 http://www.skillbank.co.uk/SignalConversion/snr.htm coded as n bits bits, n levels, 2n Weighting of LSB, 2-n SNR, 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 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 86 15 32768 0.00003 92 quantization error 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 quantization error in 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