Search results “Quantisation of signals”

This video discusses sampling and quantization of analog signal with the help of waveform of sampled signal and quantized signal. The sampling and quantization technique s used in pcm to convert analog signals into binary signals.
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Sampling of signal
The second part of this image, shows the sampled signal. In the process of sampling of the signal, we convert the continuous time signal into discrete time signal. You can see this conversion in the sampled signal shown in the image. The analog signal was continuous in time, since it had some value at every instant of time. But in the sampled signal, which is discrete in time, the value of the signal is present only at certain instants of time. Accuracy of the sampling increases with increase in frequency of the sampling. But some sampling error is introduced because of this sampling process, since it is not possible to have infinite sampling frequency practically.
Sampling of the analog signal is performed with the help of sampling theorem. So let me define here, what is sampling theorem.
Sampling Theorem:-
A continuous-time signal can be completely represented in its samples and recovered back into its original form if the sampling frequency is greater than or equal to twice the highest frequency present in the modulating signal (message signal).
It can be represented mathematically as-
fs is greater than or equal to 2fm
Here 'fs' is the sampling frequency and 'fm' is the highest frequency present in the modulating signal.
Quantization of Signal
To understand the process of quantization look at the image given above. In the process of quantization, amplitude of the signal is cut horizontally into a number of fixed levels. Now the value of the signal is rounded-off (approximated) to the nearest level of amplitude. These certain levels of amplitude are shown in the image on the vertical axis.
Here we have divided the amplitude range (peak to peak amplitude) into 'l' number of levels. The magnitude of each level is equal to the peak to peak amplitude range divided by the number of levels. It is important to note here that, quantized signal is just an approximation of the original signal. As the number of levels increases, the accuracy of quantization increases.
Pulse Code Modulation (PCM) technique uses the process of quantization to convert analog signals into digital signals. This video is created by Lalit Vashishtha, Founder and owner of 'Engineering Made Easy, YouTube Channel. .
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Pulse Modulation Techniques
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Energy Bands in Solids [HD]
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Engineering Made Easy

What is quantization and why it is needed in Digital signal processing is discussed in this part.
By P. Madhan Mohan
http://www.youtube.com/user/ThePowerDSP

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Madhan Mohan

Hi guys in this Lecture Concepts of "Quantization" along with Quantization noise and it's calculations are discussed.
After this Lecture you will be able to understand basic concept behind quantization in Digital Systems.
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Knowledge in Depth

Quantization is explained with an example. A 2 bit quantizer is taken for explanation.
By P.Madhan Mohan
http://www.youtube.com/user/ThePowerDSP

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Madhan Mohan

QUANTIZATION||DIGITAL COMMUNICATION||5TH SEM||LEC. 6

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KS ACADEMY

http://AllSignalProcessing.com for more great signal-processing content: ad-free videos, concept/screenshot files, quizzes, MATLAB and data files.
Real sampling systems use a limited number of bits to represent the samples of the signal, resulting in quantization of the signal amplitude to a limited set of values. The quantized values are then coded in a binary format for representation and storage in a digital system, such as a computer.

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Barry Van Veen

ECSE-4530 Digital Signal Processing
Rich Radke, Rensselaer Polytechnic Institute
Lecture 23: Introduction to quantization (11/24/14)
0:00:06 Intro to quantization
0:01:47 A few comments on Nyquist rates of audio signals
0:05:11 Block diagram of quantization and transmission
0:08:26 Graph of a quantizer
0:10:52 Quantization terminology: transition and reconstruction levels, codewords
0:12:37 Uniform quantizers
0:15:11 Modeling quantization error
0:18:27 Signal-to-noise ratio (SNR)
0:19:01 SNR for a uniform quantizer
0:20:23 6 dB per bit
0:22:02 Why uniform quantizers aren't great in practice
0:24:32 Non-uniform quantizers
0:25:50 Log-spaced quantization levels
0:28:53 Log-spaced quantizers have constant relative error
0:30:27 mu-law quantizer
0:36:48 Optimal quantizers
0:40:36 Deriving the error variance
0:42:27 Minimizing the variance
0:43:58 Reconstruction levels should be at interval centroids
0:46:21 Transition levels should be halfway between reconstruction levels
0:47:25 The Lloyd-Max quantizer: iterate between fixing transition and reconstruction levels
0:49:58 Potential problems
0:51:08 Adaptive quantizers
0:53:09 Feed-forward adaptation
0:55:14 Adapting the step size based on the signal variance
0:57:41 Feedback adaptation
1:01:50 Differential quantization
Follows Sections 6.3.2-6.3.3 of the textbook (Proakis and Manolakis, 4th ed.).

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Rich Radke

Views: 42689
GATE ACHIEVERS

LECT-29: Quantization Process & Quantization noise

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EPOV CHANNEL

This presentation introduces the concept of quantisation error which arises during the capture of a discrete signal from a continuous signal

Views: 3613
David Dorran

Quantization (Signal Processing)In computer science, quantization is the process of splitting the set of continuous or discrete values into the finite number of intervals. Quantization is used in signal processing including audio/video compression processes. In the elementary quantization an integer value is divided into a natural number. Such number is called a quantization factor.In uniform (linear) quantization the set of values is split into equal intervals. In other words, an input value is divided by a constant value (quantization interval) and an integer part is taken from the quotient. Please, do not confuse quantization and discretization (and quantization interval with discretization interval respectively). In discretization a time-variable value (signal) is compared with a preset interval (discretization interval). Thus, in discretization the signal is split against the time component (horizontal component, as shown in the plot). Quantization brings signal to pre-set values by splitting it across the level (vertical component, as shown in the plot). Signal processed through quantization or discretization is called a digital signal.In signal digitization quantization level is also called a disretization depth or bit count. Discretization depth is measured in bits and stands for the number of bits specifying the signal amplitude. The higher discretiztion depth is, the more precisely a digital signal corresponds to an analogue one. In uniform quantization discretization depth is also called a dynamic range and measured in decibels (1 bit roughly corresponds to 6 dB).In level quantization sample values are represented by digital signals. In binary quantization the range of signal voltage from Umin to Umax is divided into 2n intervals. The value of yielded interval (quantization interval) is expressed by the formula.N-bit binary code, which is the number of interval expressed by a binary number is assigned to each interval. The code of the interval where the voltage of a sample lies is assigned to that signal sample. Thus, an analogue signal is represented through a sequence of binary numbers which correspond to the signal value in certain moments, i.e. by a digital signal. Note that each binary number is represented through a sequence of low and high-level pulses.

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ChipDipvideo

Lecture Series on Digital Communication by Prof.Bikash. Kumar. Dey , Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in

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nptelhrd

In this tutorial we understand the concept behind resolution of images. We explore the Sampling and Quantization problem and code the sampling using bi-linear interpolation using Matlab.

Views: 17658
rashi agrawal

This video explains Pulse Code Modulation (PCM). Pulse Code Modulation (PCM) is a type of pulse modulation technique. This video also includes quantization in pcm and sampling of the signal. This video is created by Lalit Vashishtha, Founder and owner of 'Engineering Made Easy, YouTube Channel. .
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Pulse Modulation Techniques
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Digital Modulation Lectures [HD]
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Engineering Made Easy

A lecture on the effects of sampling signals with fixed numbers of bits, and of rounding in binary arithmetic.

Views: 2937
Aaron Parsons

This video provides the brief overview of quantization process along its needs in order to digitize the analog signal.
For downloading the slides kindly visit https://ashutoshrastogi.in/students/third-year-students/poc/

Views: 2001
Ashutosh Rastogi

Producing & Recording Electric Guitar ➥ http://recordproduceguitar.com
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A video on quantizing drums and how shifting the timing of only the bass drum can affect the entire feel of a drum groove.

Views: 7697
Pro Audio Files

This video explain the problem which is die to quantization process with example.

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itechnica

A solved problem involving uniform quantization and quantization error.

Views: 1284
SigProcessing

http://www.fiberoptics4sale.com/wordpress/what-is-pulse-code-modulation-pcm/
http://www.fiberoptics4sale.com/wordpress/
In a brief sentence, pulse code modulation is a method used to convert an analog signal into a digital signal. So that it can be transmitted through a digital communication network, and then converted back into the original analog signal.
The PCM process includes three steps: Sampling, Quantization, and Coding.
In the sampling process, the magnitude of the analog signal is sampled regularly at uniform intervals. The obtained values are called samples.
For a 4 kHz voice channel, the sampling rate is 8000 Hz, which means the signal is sampled 8000 times per second.
The samples will then be converted to digital numbers as we will see in the quantization process.
Quantization is the process of converting the obtained samples into discrete digital values. The most basic type of quantization is called uniform quantization.
In an uniform quantization, the vertical axis, which represents the amplitude, is divided into equal sized steps. As shown in this figure, the range between 1 volt and -1 volt is divided into 16 steps, each step represents 0.125 volt.
All the samples whose amplitude falls within an step, take the same step value.
However, the quantization process introduces an error. This is because that the real amplitude of a sample is replaced by an approximate value. This error is called quantization noise or quantization distortion.
In uniform quantization, the quantization distortion presents a problem. For example, let's assume a quantization error of 0.05 volt, if this happens at a high level signal, such as 5 volt, the noise ratio is 0.05 volt divided by 5 volt, which is 1%, not too bad. But if the same quantization error happens at a low level signal, such as 0.5 volt, the noise ratio is 0.05 volt divided by 0.5 volt, which is 10%.
Simply put, for uniform quantization, the signal to noise ratio is good at high level signals, but bad at low level signals. That is why non-uniform quantization was introduced.
In non-uniform quantization process, the steps are not of equal size. Small steps are used for small signal values and large steps for large values. The purpose of doing so is to achieve that the signal-to-noise ratio is nearly independent of the signal level.
This is done by favoring low-level voice over higher-level voice. In other words, more code groups are assigned to speech at low levels than at the higher levels, progressively more as the level reduces. This is shown in this figure.
There are two types of non-uniform quantization methods in popular use today. They are the A-law and the u-law. Let's first look at the A-law.
A law follows the logarithmic formula listed here, with A equals to 87.6.
We can see that the curve consists of linear piecewise segments, seven above and seven below the origin. The segment just above and the segment just below the origin consists of two linear segments. Counting the collinear elements by the origin, there are 16 segments. Each segment has 16 8-bit PCM codes assigned. These are the codewords that identify the voltage level of a sample at some moment in time.
Each codeword, often called a PCM "word", consists of 8 bits. The first bit tells the receiver if the sample is a positive or negative voltage. We can see that all PCM words above the origin start with a binary 1, and those below the origin start with a binary 0.
The next 3 bits in sequence identify the segment. There are eight segments above the origin and eight below the origin.
The last 4 bits, shown as XXXX, indicate exactly where in a particular segment that voltage line is located.
The second is called u-law. It follows the logarithmic formula listed here with u equals to 100.
The North American T1 system uses the u-law quantization and coding process. The process is similar to that of A-law.
Colin Yao
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FOSCO CONNECT

What is SNR and the importance of SNR is explained. The SNR equation is also derived.
By Madhan Mohan
http://www.youtube.com/user/ThePowerDSP

Views: 23663
Madhan Mohan

the video presents only the process flow involved in conversion of analog to physical quantity (signals) to its digital equivalence . it doesn't explain the mathematics involved in the conversion.

Views: 14257
G S Shirnewar

In this two-part video tutorial I will explain dithering from the ground up. For your convenience, here are the links to the two parts:
Part 1: http://www.youtube.com/watch?v=U2mwXiJqAgA
Part 2: http://www.youtube.com/watch?v=tb6X3WZ3-Uc
You do not need any special background in signal processing, audio or dithering to follow the current videos. However, you should know what bit depth means. If you don't, fear not! Just watch my short video tutorial about bit-depth and sampling rates right here:
http://www.youtube.com/watch?v=zC5KFnSUPNo
What's in Part 1: Dithering is all about getting rid of quantization noise. What is quantization noise? Glad you've asked, because that's exactly what we're going to cover in the first part! Shortly put, quantization noise is the noise introduced whenever we reduce the bit depth of our signal. For example, most audio is recorded using 24 bits of resolution, but modern audio CDs only have 16 bits of resolution, implying that a reduction in bit depth must be applied. This reduction will introduce some artifacts known as quantization error, or quantization noise. This "noise" will have some jarring, unpleasant frequency components which we'd like to get rid of.
What's in Part 2: In the second part we will cover dithering. To "dither" a signal means to add some form of random noise to it because lowering its bit depth. This dither noise has a beneficial effect: while it doesn't eliminate quantization noise, it gives it a more random, "white" nature which is less disturbing to the listener. When the amount of white noise equals approximately 1 bit in magnitude, the quantization error becomes a lot like white noise. This is because quantization involves rounding the input signal either up or down. When the noise becomes on the order of 1 bit, the rounding becomes random, and therefore the quantization error becomes random as well.
DITHERING TYPES
Dithering requires that we add random noise to our signal before downsampling. This noise should have a flat spectrum - in other words, be white. However, there is more than one way to generate white random noise. Probably the easiest and most efficient way is to use what's known as a triangular probability distribution function, or TPDF. You might have seen these initials in your dithering plugin. This is an excellent way to efficiently dither. Although we won't discuss the heavy mathematical theory of dithering in this video, I'll just mention that TPDF white noise decouples the first and second moments of the quantization noise.
Another option consists of using noise with a non-flat spectrum. For example, you'd might add noise that has more high-frequency components, such as Blue Noise. This is referred to as shaped noise, shaped noise dithering, or colored dithering. What this tries to do is force the dithered quantization noise to occupy higher frequencies that are outside the human audio range. Once again, personal experimentation is key to deciding whether you want to use colored dithering or not, but this is truly a very fine point. You will be fine if you just stick to TPDF. However, a word of caution: only apply colored dithering at the FINAL stage of your processing. If you need to dither audio at some point DURING mixing, use TPDF. This is because subsequent processing of the audio can cause the colored noise to creep into the audible listening range and create nasty artifacts. So: Use TPDF at all stages before mixing, and use TPDF or colored dithering during the final mixdown.
LINKS OF INTEREST
Here is a wonderful guide to dithering written in 2002 by Nika Aldrich, targeted at the audio engineer:
http://www.users.qwest.net/~volt42/cadenzarecording/DitherExplained.pdf
This is truly geared towards the audio enthusiast and does not go into any math. It is heavily illustrated and references industry standard plugins such as Apogee's UV22.
Wikipedia's entry on dithering: http://en.wikipedia.org/wiki/Dither
My Other Videos
My Youtube channel has many other video tutorials covering various topics in both audio and music, mostly geared towards piano playing. Here are a few examples:
Bit depth and sample rate explained: http://www.youtube.com/watch?v=zC5KFnSUPNo
Song writing Tips and Tricks - Rhythmic Doubling: http://www.youtube.com/watch?v=U_HNwZTrMIk
Reading Sheet Music for Beginners: http://www.youtube.com/watch?v=-dgrr28NXdU
The 2-5-1 Harmonic Progression Tutorial: http://www.youtube.com/watch?v=XDHKeUSERuI
Playing Left hand Piano Arpeggios: http://www.youtube.com/watch?v=DiZBq0U2BgU
An Exercise for Developing Piano Right-Hand Technique: http://www.youtube.com/watch?v=cqIRSJ-GZsE

Views: 22579
MangoldProject

This is part two of my video series on Digital Audio.
This Episode covering some more in depth aspects of the area.
Watch Part 1 here:
https://www.youtube.com/watch?v=W2-FP7twy8s
Production Bytes Facebook Page:
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Veranova's Music:
http://www.facebook.com/OfficialVeranova
Thanks for watching!
Veranova

Views: 103160
Production Bytes

Sampling and quantization and its applications to digital video signals.

Views: 863
Greg Durgin

http://adampanagos.org
In the previous video we examined the impact of downsampling an audio signal. In this video, we examine the impact of changing the number of quantization levels used to store the signal amplitudes.
An original WAV music file is loaded in Matlab that uses 8-bit quantization. The signal is then re-quantized to both 6-bit and 4-bit quantization levels and plotted to visualize the impact of fewer quantization levels on the signal. While signals with fewer quantization levels require less storage space, it comes at the cost of introducing additional quantization error.
If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!

Views: 2203
Adam Panagos

MIT MIT 6.003 Signals and Systems, Fall 2011
View the complete course: http://ocw.mit.edu/6-003F11
Instructor: Dennis Freeman
License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

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MIT OpenCourseWare

VLSI Data Conversion Circuits by Dr. Shanthi Pavan, Department of Electrical Engineering, IIT Madras. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 4744
nptelhrd

In this exercise we will show a code that make the convertion of an analog signal to a digital signal.

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Physics.

Quantisation divides the signal into equal quantisation steps.

Views: 8786
Digital Signal Processing

Continuation of a lecture on the effects of sampling signals with fixed numbers of bits, and of rounding in binary arithmetic.

Views: 703
Aaron Parsons

This lecture deliverd our honarable teacher Zadiduk karim sir. I captured this video in our class. i think this video helpful for every body.
you like our video, then please like, comment & share with your friends .Give us feed back in the comment & Subscribe our New vision channel for notification about every new video.
Thank you...

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Abu Jafar Md Khaled

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itechnica

This video discusses quantization and related concepts, such as quantization error and LSB, with respect to the analog-to-digital converter.
http://www.microchip.com/dataconverters

Views: 4943
Microchip Technology

This video covers the part-1 of UNIT-5 out of two parts. The problem on coefficient quantization error in both direct form and cascade form are described and solved here. Subscribe the channel for more updates on this series of videos and share this with your friends.

Views: 447
gheetha indoctrinates

Lecture Series on Digital Signal Processing by Prof.T.K.Basu, Department of Electrical Engineering, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 7681
nptelhrd

http://adampanagos.org
The Sampling Theorem tells use the rate at which we must sample a continuous-time signal if we want to preserve all signal information (i.e. avoid aliasing). The Nyquist rate is the lowest sampling rate that avoids aliasing and is equal to 2 times the largest signal frequency, i.e. fs = 2*fm.
If you enjoyed my videos please "Like", "Subscribe", and visit http://adampanagos.org to setup your member account to get access to downloadable slides, Matlab code, an exam archive with solutions, and exclusive members-only videos. Thanks for watching!

Views: 9960
Adam Panagos

Hi guys in this lecture concepts of NonUniform Quantization and Compandor are explained.
If you like it do subscribe my channel also like it & share it with your colleagues.
Thanking you.
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Digital Signal Processing : https://www.youtube.com/playlist?list=PLHDdxli24zbhaoZ17oHf8X0dPF98ZPIK_
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Views: 9118
Knowledge in Depth

sampling and quantization in digital image processing

Views: 4287
Last Night Study

Lecture 41: In this lecture Prof Aditya K. Jagannatham of IIT Kanpur explains the following concepts in Principles of Communication Systems-I
1. Quantization and Mid-rise quantizers.
2. Concepts of quantization error.
3. Probability density function (PDF) and power of the quantization noise.
4. Quantization noise power versus Quantizer resolution.

Views: 6000
Principles of Communication Systems-I

This explains why we describe quantization rates in the digitization of speech signals in terms of powers of 2. For UMass Linguist 414.

Views: 278
Kristine Yu

We see both Analog and Digital devices around us. But have you ever observed the difference between them or what in particular makes them different. Well we do that in this video and discuss a lot of Science related to Signals, Waves and Music. We discuss about the future, Nyquist Rate and much more.
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Further Reading :
https://en.wikipedia.org/wiki/Analog_signal
https://en.wikipedia.org/wiki/Digital_signal
http://www.linear.com/products/analog-to-digital_converters_(adc)
https://en.wikipedia.org/wiki/Bit_rate
https://en.wikipedia.org/wiki/MP3
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Music Used : Italian Morning by Twin Musicom is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Artist: http://www.twinmusicom.org/

Views: 75032
Gyaanism

It gives numerical on Signal to Quantization Noise Power Ratio
#ekteacher
#Quantizationerror
#PCM
#Pulsecodemodulation
#Bitduration
#bandwidthofPCM
#Bitrate
#Parametersofpcm
#quantizationnoise
#signaltonoiseratio
#SQNR

Views: 58
ek teacher

Lecture Series on Digital Communication by Prof.Bikash. Kumar. Dey , Department of Electrical Engineering,IIT Bombay. For more details on NPTEL visit http://nptel.iitm.ac.in

Views: 284593
nptelhrd

Demostrates the effects of quantisation using an audio example

Views: 1214
David Dorran

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