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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.
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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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

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

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

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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.
Pulse modulation can be categorized broadly into two types-
#Analog and
#Digital
The analog modulation can again be of two types-
#Pulse Amplitude Modulation (PAM)
#Pulse Time Modulation (PTM)
The Pulse Time Modulation (PTM) can further be classified into two types of modulation-
#Pulse Width Modulation (PWM)/Pulse Duration Modulation (PDM)
#Pulse Position Modulation (PPM)
Pulse Code Modulation (PCM) is a digital pulse modulation technique.
You can see the classification of pulse modulation,
Pulse Code Modulation (PCM)
Now we will discuss the digital form of pulse modulation technique. This form of pulse modulation technique is known as Pulse Code Modulation (PCM).
Pulse code modulation is a technique to convert analog signals into digital signals.
After converting the signal into digital form, it becomes possible to transmit the digital signal through digital communication network and at the receiving end, it is converted back into it's original analog form.
Pulse code modulation process involves the following three stages -#Sampling
#Quantization and
#Coding
Sampling and Quantization of analog signal, sampling og signal, Quantization of signal
Sampling and Quantization of analog signal
this image shows the following-
#Signal in its original analog form
#The sampled signal obtained after sampling of this analog signal and
#Quantized signal obtained after performing the quantization process.
Now we are going to discuss, the process of sampling and quantization. During the discussion, please see the image carefully -
The first waveform given in the image is of the analog signal, that we want to transmit over the digital communication network. But since it is in analog form, therefore first it needs to be converted into digital form. So to do this job, we take the help of Pulse Code Modulation (PCM).
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 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.
Pulse Code Modulation Waveform
The image given below shows pulse code modulated waveform.
Pulse Code Modulation Waveform, Pulse Code Modulation, PCM waveform
Pulse Code Modulation Waveform
You can see in the image that PCM wave contains only two levels amplitude.
These levels are represented by 0's and 1's. So it is clear that, here we have converted an analog signal having infinite number of levels of amplitude into just two levels of amplitude represented by 0's and 1's. Hence an analog signal has been converted into a digital signal.
Pulse Modulation Techniques
https://www.youtube.com/playlist?list=PLDp9Jik5WjRvjqQ6ruRFC6hZcxnOsp3BE
#Modulation #modulationTechniques

Views: 18010
Engineering Made Easy

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
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Production Bytes

Sampling is a core aspect of analog-digital conversion. One huge consideration behind sampling is the sampling rate - How often do we sample a signal so we can accurately recreate it?
This may seem trivial at first, but serious problems can arise if we use a bad sample rate, as this can lead to aliasing - The failure to reconstruct the original signal, causing it to appear as a completely different wave of a lower frequency.
To combat this problem, we have to make use of the Nyquist-Shannon Sampling Theorem, which tells us what sample rate to use to prevent aliasing from happening. Today, we take a look at all these points and see just how they link together, to allow us to have the common sample rates (eg. 44100 Hz) we see today!
Want to see it for yourself? Try your hands on this interactive web application, and see how sampling rate and the quality of the reconstructed signal go hand in hand! https://resources.nerdfirst.net/sampling
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0612 TV w/ NERDfirst

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.
-------------------------
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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Gyaanism

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
Sales Manager
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FOSCO CONNECT

Demostrates the effects of quantisation using an audio example

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David Dorran

Hi guys in this lecture Quantization Noise and Signal to Noise Ratio (SNR) of PCM system are explained along with its Significance.
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Knowledge in Depth

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: 3807
David Dorran

A video by Jim Pytel for Renewable Energy Technology students at Columbia Gorge Community College

Views: 111585
Columbia Gorge Community College

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: 20649
rashi agrawal

PCM - method of analog to digital conversion
Introduction
Today my topic is Pulse Code Modulation or PCM- a method used to convert analog signals to digital signals.
PCM consists of three steps: sampling, quantizing, and encoding. PCM may sound very complicated because it involves many big words, such as pulse, amplitude, modulation, sampling, sample rate, quantization or quantizing process, bit depth, and so so, but it is actually a very simple process if you take it apart and look closely one step a time.
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Sunny Classroom

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

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: 8052
nptelhrd

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
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More courses at http://ocw.mit.edu

Views: 19928
MIT OpenCourseWare

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: 24749
Madhan Mohan

Here we derive the quantisation error.

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Digital Signal Processing

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!

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Adam Panagos

Audio out of sync with the beat? Audio quantizing to the rescue!
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Mitchel Pigsley

Alexander Knaub
Institut of Telecommunications, University of Stuttgart
http://webdemo.inue.uni-stuttgart.de/webdemos/02_lectures/uebertragungstechnik_1/sampling_theorem/

Views: 512
Universität Stuttgart

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: 5955
Microchip Technology

This video explains in detail sampling, sampling theorem and reconstruction, nyquist theorem and quantization of analog signal with the help of waveform of sampled signal. The sampling and quantization techniques used in pcm to convert analog signals into binary signals.
For more details you can visit my BLOG-
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SAMPLING THEOREM AND RECONSTRUCTION (SAMPLING AND QUANTIZATION)
What is Sampling and why it is required?
A continuous time signal at the transmitting end is converted into discrete time signal, it is done as it is easier to process digital signals in comparison to analogue signals.
If we want to convert analogue signals into digital signals then first of all continuous time signal is converted into discrete time signal with the help of sampling process and after this process, this sampled signal is converted into digital signal by the process of quantization.
Sampling Theorem:
A continuous time signal can be completely represented in its samples and then can be recovered back, if the sampling frequency is greater than or equal to the twice of the maximum frequency present in the signal.
i.e. 'fs' is greater than or equal to '2fm'
Here fs is sampling frequency
fm is maximum frequency present in the signal.
It is essential to take sufficient number of samples to completely represent a signal by its samples and also to reconstruct the signal back to its original form from its samples. This video is created by Lalit Vashishtha, Founder and owner of 'Engineering Made Easy, YouTube Channel. .
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Continuous Wave Modulation (AM, FM and PM)
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Laplace Transform (Basic to Advanced Level)
https://www.youtube.com/playlist?list=PLDp9Jik5WjRv1K8TkyD1NtI3CwjjdQOVn
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Vectors Basics
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Optical Fibers (Basic to Advanced Level)
https://www.youtube.com/playlist?list=PLDp9Jik5WjRuxzZArqomE59SFmhVv5qPO
Electronics Fundamentals
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Signals and Systems
https://www.youtube.com/playlist?list=PLDp9Jik5WjRswczwmEVUtsfMMJSBwdiqy
Communication Systems (Analog and Digital )
https://www.youtube.com/playlist?list=PLDp9Jik5WjRuUyDT6961r8pkelgJMG8fG
Pulse Modulation Techniques
https://www.youtube.com/playlist?list=PLDp9Jik5WjRvjqQ6ruRFC6hZcxnOsp3BE
Digital Modulation Lectures [HD]
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Solved Numerical Problems in Engineering [HD]
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Energy Bands in Solids [HD]
https://www.youtube.com/playlist?list=PLDp9Jik5WjRuIS4hbKhxr7e1sueAboaQA

Views: 7921
Engineering Made Easy

Definition of the signal to noise ratio (SNR) and simple computations with it. More instructional engineering videos can be found at http://www.engineeringvideos.org.
This video is licensed under the Creative Commons BY-SA license http://creativecommons.org/licenses/by-sa/3.0/us/.

Views: 186644
Darryl Morrell

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

Views: 3156
Aaron Parsons

Lecture 40: In this lecture Prof Aditya K. Jagannatham of IIT Kanpur explains the following concepts in Principles of Communication Systems-I
1. Concept of Quantization.
2. Uniform Quantizer.
3. Mid-tread Quantizer.

Views: 9622
Principles of Communication Systems-I

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.

Views: 6423
ChipDipvideo

Sampling and quantization and its applications to digital video signals.

Views: 928
Greg Durgin

Reason for choosing this topic is to clear the basic concepts used in all applications.

Views: 87
Communication Engineering

Codes:
%Sampling Theorem
clear all;
close all;
clc;
f=input('Enter frequency');
%T=1/f;
fs1=input('Enter the sampling frequency');
t=0:0.1:100;
t1=0:10:500;
x=sin(2*3.14*f*t); %2*pi*f*t
subplot(2,1,1);
plot(t,x);
y=sin(2*3.14*f*t1/fs1);
subplot(2,1,2);
stem(t1,y);
-------------------------------------------------------------
How to Sample an Analog signal in Matlab
ADC
DSP
Digital Signal Processing
Matlab Tutorial
Matlab Basic
Matlab for Beginner

Views: 26988
Sk Rezwan

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: 4044
nptelhrd

A video by Jim Pytel for Renewable Energy Technology students at Columbia Gorge Community College

Views: 113522
Columbia Gorge Community College

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Academy of Technology
Academy of Technology is an online resource in Urdu and Hindi languages.
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Pulse code modulation?
What is PCM?
What is sampling?
What is quantization?
What is encoding?

Views: 39580
Academy-khi

Lecture 47: In this lecture Prof Aditya K. Jagannatham of IIT Kanpur explains the following concepts in Principles of Communication Systems-I
1. Introduction to Differential Pulse Coded Modulation.
.
2. Quantization and Signal Reconstruction in DPCM.
3. DPCM schematic diagrams.

Views: 8682
Principles of Communication Systems-I

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

Views: 740
Aaron Parsons

An A Level Physics revision video covering Digital Sampling, Signal Spectra and Bandwidth

Views: 47700
DrPhysicsA

Views: 5192
itechnica

This video runs over the basics of signal sampling and analog to digital conversion.
Watch the next part of this at: https://www.youtube.com/watch?v=zZAk0sKI0VY
The video was created as part of the Khan Academy Talent Search.
#khanacademytalentsearch

Views: 4570
Adrian Henry

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: 5100
nptelhrd

An overview of the Quantize functions in Pro Tools and how they can be used to modify the timing of both audio and MIDI data.

Views: 58394
Eric Kuehnl

sampling and quantization in digital image processing

Views: 12645
Last Night Study