Maximum 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 (yellow) and the difference between the original signal and the reconstructed signal (red). The difference between the original signal and quantization error formula the reconstructed signal is the quantization error and, in this simple quantization scheme, is quantization noise in pcm a deterministic function of the input signal. Quantization, in mathematics and digital signal processing, is the process of mapping a large quantization of signals 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
What Is Quantization
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 Basic types of quantization quantization error definition 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 resolution with four levels of quantization compared to analog.[2]
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Quantization Error Example
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Quantization Example
5 Upcoming SlideShare Loading in …5 × 1 1 of 12 Like this document? Why not share! Share Email Chap 4 byTanuj Patel 4575views Chapter 6m bywafaa_A7 4342views Chapter 3 - https://en.wikipedia.org/wiki/Quantization_(signal_processing) Data and Signals byWayne Jones Jnr 94408views Chap 3 byTanuj Patel 11165views Pulse code modulation byAbhijay Sisodia 36619views Chap 6 byTanuj Patel 3142views Share SlideShare Facebook Twitter LinkedIn Google+ Email Email sent successfully! Embed Size (px) Start on Show related SlideShares at end WordPress Shortcode Link Chap 5 44,340 views Share Like Download Tanuj Patel Follow 0 0 1 Published on Jul http://www.slideshare.net/tanuj125/chap-5-13717464 22, 2012 Published in: Education, Technology, Business 3 Comments 19 Likes Statistics Notes Full Name Comment goes here. 12 hours ago Delete Reply Spam Block Are you sure you want to Yes No Your message goes here Post Kommisetty Murthyraju , ASSOCIATE PROFESSOR,BHIMAVARAM at Shri Vishnu Engineering College for Women (SVECW) thanks 3 months ago Reply Are you sure you want to Yes No Your message goes here SimoSam Kun at Facebook Thank you for your great efforts. May you tell you reference? 10 months ago Reply Are you sure you want to Yes No Your message goes here Tsegay E , electric drive and other related with power system at duc good 3 years ago Reply Are you sure you want to Yes No Your message goes here Divya Batra , Student at Amity School of Engineering & Technology 1 week ago Laxmi Pavana Gayathri , Summer Intern at student 1 month ago Achint Duggal 4 months ago Eng Bella Nora 5 months ago زمن الطائي 5 months ago Show More No Downloads Views Total views 44,340 On SlideShare 0 From Embeds 0 Number of Embeds 80 Actions Shares 0 Do
Community Forums > Science Education > Homework and Coursework Questions > Engineering and Computer Science Homework > Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors Dismiss Notice Dismiss Notice Join Physics Forums Today! https://www.physicsforums.com/threads/quantization-error-voltage.423079/ The friendliest, high quality science and math community on the planet! Everyone who loves science is here! Quantization Error Voltage Aug 19, 2010 #1 kukumaluboy 1. The problem statement, all variables and given/known data Q1 A linear PCM system has an input signal 2cos6000PIt volt. Determine, (a) the minimum sampling rate required, (b) the number of bits per PCM codeword required for a signal to quantization noise ratio of at least 40 dB, (c) the maximum quantization error quantization error voltage, (d) the dynamic range in dB. (a) 6000 Hz (b) n = 7 (c) 15.63 mV (d) 42 dB 3. The attempt at a solution a) By Nyquist theorom , for a analog signal to be accurate reproduced, it should be sampled at a rate of not less than 2 times the highest frequency. 2cos6000PIt = 2cosPIft therefore highest f= 6000/2 = 3000Hz Sample f= 2 x 3000Hz = 6kHz b)SNq = 6n maximum quantization error (in dB) Therefore 40dB <=6n (bigger or equals to) n= 7 bits c) How to Do d)Dynamic Range = 6n = 6*7 = 42 dB kukumaluboy, Aug 19, 2010 Phys.org - latest science and technology news stories on Phys.org •Game over? Computer beats human champ in ancient Chinese game •Simplifying solar cells with a new mix of materials •Imaged 'jets' reveal cerium's post-shock inner strength Aug 19, 2010 #2 Zryn Gold Member a) By Nyquist theorom , for a analog signal to be accurate reproduced, it should be sampled at a rate of not less than 2 times the highest frequency. This quote says that given the highest frequency component of B Hz, 2B Hz is sufficient a sampling rate to prevent aliasing. Nyquist requires a sampling frequency greater than twice the highest frequency component. Thus given the highest frequency component of B Hz, you must have 2B + 1 Hz sampling rate to prevent aliasing. c) How to Do Lets say you have an analogue sin wave with an amplitude of x, and you split that wave into 2^n different voltage levels for your digital approximation. How many volts are there per digital voltage level? Now lets say that the analogue signal is right smack bang in the middle of one of these digital levels, what happens if you go up to the next level