Discrete sources are a subject of interest in their own right for text, computer. Chapter 20 spectrum of quantization noise and conditions of whiteness when the input to a quantizer is a sampled time series represented by x1, x2, x3. It also can refer to the number of quantization levels. The characteristics of a uniform quantizer are pictured in fig. Suppose that the input time series is stationary and that its statistics satisfy the conditions for multi. Aug 17, 2018 in this video, i have explained basics of quantization by following outlines. Color quantization cq is an important operation with many applications in computer graphics and image processing and analysis. Natural sampling s s f d f null at 3 pam and pcm pam pulse amplitude modulation.
From digital signals to analog signals dac signal reconstruction from sampled data iii. Spatial and greylevel resolutions will be introduced and examples will be provided. Quantization is the process of mapping continuous amplitude analog signal into discrete amplitude digital signal. Image sampling and quantisation sampling of a continuous 1d function 2 all the frequency domain information of a bandlimited function is contained in the interval if the whittakershannon sampling theorem or nyquist sampling theorem 4. Ee3414 multimedia communication systems i experiment one sampling and quantization yao wang and xiaofeng xu 1. Lloydmax quantizer lloyd,1957 max,1960 m1 decision thresholds exactly halfway between representative levels. Solution depends on input pdf and can be done numerically for commonly used pdfs e. We will assume here, that the independent variable is time, denoted by t and the dependent variable could be. Typically, a frame grabber or digitizer is used to sample and quantize the analogue video signal.
Quantization levels are the centroidof their region 2. Buy this book on university of central arkansas, i agree that the library of this. Sampling digital signals sampling and quantization faithfully when the sampleinstants happen to coincide with the maxima of the sinusoid, but when the sampleinstants happen to coincide with the zerocrossings, you will capture nothing for intermediate cases, you will capture the sinusoid with a wrong amplitude. Sampling allows the use of modern digital electronics to process. The quantization noise power is the area obtained from integrating the power spectral density function in the range from. Quantization we measure discrete amplitudes in bits. The sampling theorem suppose a signals highest frequency is a lowpass or a bandpass signal. Each of these levels represents a fixed input amplitude. Assign points to a quantization level and reconstruct image. Difference between sampling and quantization compare the. In this lecture we will talk about two key stages in digital image processing. Interpolation is the process of guessing signal values at arbitrary instants of time, which fall in general in between.
Also, it is desirable to treat very rare inputs di. Lloyd 129 abstractit has long been realized that in pulsecode modulation pcm, with a given ensemble of signals to handle, the quantum values should be spaced more closely in the voltage regions where the signal amplitude is more likely to fall. Sampling digital signals sampling and quantization somehow guess, what value the signal could probably take on in between our samples. Quantization the number of bits available to describe sampling values determines the resolution or accuracy of quantization. That is, the time or spatial coordinate t is allowed to take on arbitrary real values perhaps over some interval and the value xt of the signal itself is allowed to take on arbitrary real values again perhaps within some interval.
Sampling and quantization digital image processing. Chapter 5 sampling and quantization often the domain and the range of an original signal xt are modeled as contin uous. A common example is the conversion of a sound wave a continuous signal to a sequence of samples a discretetime signal. Clustering algorithms have been extensively applied to. That is, the time or spatial coordinate t is allowed to take on arbitrary. It is the conversion of x axis infinite values to digital values. Ee3414 multimedia communication systems i experiment. Sampling and quantization in digital image processing. Compute the new quantization levels as the mean of the value of all points assigned to each quantization level.
In signal processing, sampling is the reduction of a continuoustime signal to a discretetime signal. It is often convenient to talk about the sampling frequency fs. An introduction on implementing the shown examples in matlab will be also given in this lecture. Lloyd 129 abstractit has long been realized that in pulsecode modulation pcm, with a given ensemble of signals to handle, the quantum values should be. Ee368b image and video compression quantization no. Both sampling and quantization result in the loss of information. Sampling converts a timevarying voltage signal into a discretetime signal, a sequence of real numbers. Need of sampling and quantization in digital image processing. Pdf effects of sampling and quantization on singletone frequency.
Sampling and quantization will be defined properly. Analog signals consist of continuous values for both axes. Mostly the output of image sensors is in the form of analog signal. Pdf relationship between sampling rate and quantization noise. The analog signal, denotedxt, is continuous in both time. Now the problem is that we cannot apply digital image processing and its techniques on analog signals. Pdf few works have been done about the dependency of the quantization noise with the sampling rate for uniform quantizers. Statistical theory of quantization instrumentation and. Pdf the effects of sampling and quantization on frequency estimation for a single sinusoid are investigated. The method of sampling chooses a few points on the analog signal and then these points are joined to round off the value to a near stabilized value. Spectrum of quantization noise and conditions of whiteness. In this video, i have explained basics of quantization by following outlines. The more samples you take, the more pixels, you get. An analogtodigital converter adc can be modeled as two processes.
For a signal x with given pdf find a quantizer with m representative levels such that fx x solution. Increasing the transmitted signal power employing modulation and demodulation technique employing suitable coding and decoding methods reducing noise interference with help of improved filtering. Consider an analog signal with frequencies between 0 and 3khz. Quantization and sampling test digital image processing. Uniform quantization an overview sciencedirect topics. The concept of sampling is directly related to zooming. Pdf quantization and sampling of not necessarily band. The sampling rate is the number of samples taken in the duration of one second. The pulse may take any real voltage value that is proportional to the value of the original waveform. In digital signal processing and related fields, sampling and quantization are two methods, rather steps, used in the discretization of an analog signal in converting it to a digital signal. In effect, scalar quantization digitizes an analog signal. Solution depends on input pdf and can be done numerically for. In other words, quantization converts the dependent variable voltage in this example from continuous to discrete.
Sep 03, 2012 1 comparators, gmc filters, sc filters in cmos technology ppt 2 i lab session ppt ppt ii lab session manual pdf day 3 prof nagendra krishnapura basics of sampling and quantization vedio. The quality of a quantizer output depends upon the number of quantization levels used. The sampling theorem signal quantization and dithering ii. But for the same length of video and audio, the file size will be much larger than the low quality signal. That is, no continuous amplitude signal can be reconstructed from its quantized samples with zero distortion regardless of the sampling rate, even. Make appropriate connections for scope selector and pico scope interface according to the steps given below. The analog signal, denotedxt, is continuous in both time and amplitude. Consider an electrical signal whose horizontal axis represents time in seconds. Quantization nonuniform quantization problems with uniform quantization only optimal for uniformly distributed signal real audio signals speech and music are more concentrated near zeros human ear is more sensitive to quantization errors at small values solution using nonuniform quantization. Whereas, when uniform quantization is used, the zoom strategy is a useful control policy, which is divided into two stages. In matlab, you can generate samples from a sine wave of frequency f at a sampling rate r for s seconds in the following way. The logarithmic quantization is mainly used with linear systems and with infinite quantization levels. Basics of quantization in digital communication by.
This rate is called sampling rate or sampling frequency. With the advent of electronics and computers, almost all the technological functions are digitized so they can be handled by computers or other digital systems. Introduction the purpose of this lab is for you to understand the principles of sampling a continuous time signal, increasing or decreasing the sampling rate of a discrete time signal, and for quantization. Craig 11 an analog signal that varies quickly must be sampled more frequently than an analog signal that varies slowly. Now let us examine the oversampling adc, where the sampling rate is much bigger than that of the regular adc. The continuously varying amplitude of an analog signal is also continuous in time. Least squares quantization in pcm nyu computer science. Then a proper sampling requires a sampling frequency at least satisfying the number is called the nyquist frequency the number is called the nyquist rate example.
The first thing we have to do, is to obtain signal. Lloydmax quantizer lloyd,1957 max,1960 m1 decision thresholds exactly halfway between representative. With the advent of electronics and computers, almost all the technological functions are digitized so they. Quantization step an overview sciencedirect topics. Notice that we carefully avoid comparing a and c, as this would lump the sampling and quantization together. Scalar quantization is a process that maps all inputs within a specified range to a common value. Sampling of audio signal with n64,16, 4 and 2 levels. Online access to spie ebooks is limited to subscribing institutions. The digitization of analog signals involves the rounding off of the values which are approximately equal to the analog values.
This process maps inputs in a different range of values to a different common value. In this quiz we will ask about two key stages in digital image processing. Rayburn digital audio combines sampling quantization quantization turning a level into a number imagine you have two water glasses. The sampling period t s is the spacing between two adjacent samples, i. A common example is the conversion of a sound wave a continuous signal to a sequence of samples a discretetime signal a sample is a value or set of values at a point in time andor space. Illustration of digitization process we will look into two stages of the. Starting from the basic definition of a discretetime signal, we will work our way through fourier analysis, filter design, sampling, interpolation and quantization to build a dsp toolset complete enough to analyze a practical communication system in detail. Ee398a image and video compression quantization no. Higher average signal to quantization noise power ratio than the uniform quantizer when the signal pdf is non uniform which is the case in many practical situation. Sampling and quantization often the domain and the range of an original signal x t are modeled as continuous. Quantisation noise power is the noise power due to quantisation noise. Then quantisation noise power is given as, e 2 2 f d.
No information is lost, but the energy is redistributed in the frequency domain. The sampling rate or frequency f s is the number of samples per second hz. Image representation, sampling and quantization antonio r. Color quantization using coreset sampling request pdf. The discrete amplitudes of the quantized output are called as representation levels or reconstruction levels. Clustering algorithms have been extensively applied to this problem. The sampling rate determines the spatial resolution of the digitized image, while the quantization level determines the. Quantization replaces each real number with an approximation from a finite set of discrete values. Sampling sampling period t quantization interval q binary encoding binary codebook yao wang, 2006 ee3414.
781 1512 606 1445 1076 692 1054 1075 1447 362 23 461 365 702 1391 905 1422 1267 131 690 826 1092 175 1202 1003 793 403 981 393 539 330 1462 547