Basics of quantization in digital communication by. No information is lost, but the energy is redistributed in the frequency domain. Assign points to a quantization level and reconstruct image. In signal processing, sampling is the reduction of a continuoustime signal to a discretetime signal. Quantization we measure discrete amplitudes in bits. The characteristics of a uniform quantizer are pictured in fig. Lloydmax quantizer lloyd,1957 max,1960 m1 decision thresholds exactly halfway between representative. Discrete sources are a subject of interest in their own right for text, computer. Make appropriate connections for scope selector and pico scope interface according to the steps given below. Ee398a image and video compression quantization no.
The more samples you take, the more pixels, you get. The sampling theorem suppose a signals highest frequency is a lowpass or a bandpass signal. Sampling and quantization in digital image processing. From digital signals to analog signals dac signal reconstruction from sampled data iii. Pdf the effects of sampling and quantization on frequency estimation for a single sinusoid are investigated. 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. Sampling of audio signal with n64,16, 4 and 2 levels. Also, it is desirable to treat very rare inputs di. Mostly the output of image sensors is in the form of analog signal. The continuously varying amplitude of an analog signal is also continuous in time. Clustering algorithms have been extensively applied to. Color quantization using coreset sampling request pdf. Quantization the number of bits available to describe sampling values determines the resolution or accuracy of quantization. The logarithmic quantization is mainly used with linear systems and with infinite quantization levels.
In other words, quantization converts the dependent variable voltage in this example from continuous to discrete. With the advent of electronics and computers, almost all the technological functions are digitized so they. Analog signals consist of continuous values for both axes. Sampling and quantization digital image processing.
The analog signal, denotedxt, is continuous in both time. Ee3414 multimedia communication systems i experiment. Compute the new quantization levels as the mean of the value of all points assigned to each quantization level. Sampling and quantization will be defined properly. It is the conversion of x axis infinite values to digital values.
That is, the time or spatial coordinate t is allowed to take on arbitrary. Rayburn digital audio combines sampling quantization quantization turning a level into a number imagine you have two water glasses. Statistical theory of quantization instrumentation and. Quantization replaces each real number with an approximation from a finite set of discrete values. The pulse may take any real voltage value that is proportional to the value of the original waveform. Sampling allows the use of modern digital electronics to process. 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. 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. Consider an analog signal with frequencies between 0 and 3khz. Scalar quantization is a process that maps all inputs within a specified range to a common value.
The quantization noise power is the area obtained from integrating the power spectral density function in the range from. Sampling converts a timevarying voltage signal into a discretetime signal, a sequence of real numbers. Pdf effects of sampling and quantization on singletone frequency. For a signal x with given pdf find a quantizer with m representative levels such that fx x solution. It also can refer to the number of quantization levels. The sampling theorem signal quantization and dithering ii. In this quiz we will ask about two key stages in digital image processing.
Suppose that the input time series is stationary and that its statistics satisfy the conditions for multi. 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. Aug 17, 2018 in this video, i have explained basics of quantization by following outlines. The discrete amplitudes of the quantized output are called as representation levels or reconstruction levels. Both sampling and quantization result in the loss of information. In this lecture we will talk about two key stages in digital image processing. The sampling rate or frequency f s is the number of samples per second hz. 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. The digitization of analog signals involves the rounding off of the values which are approximately equal to the analog values. Clustering algorithms have been extensively applied to this problem.
Ee3414 multimedia communication systems i experiment one sampling and quantization yao wang and xiaofeng xu 1. Difference between sampling and quantization compare the. Need of sampling and quantization in digital image processing. Quantization levels are the centroidof their region 2. Quantization is the process of mapping continuous amplitude analog signal into discrete amplitude digital signal. Quantisation noise power is the noise power due to quantisation noise. Least squares quantization in pcm nyu computer science. An analogtodigital converter adc can be modeled as two processes. 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.
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. Then quantisation noise power is given as, e 2 2 f d. 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. 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. Consider an electrical signal whose horizontal axis represents time in seconds. Sampling sampling period t quantization interval q binary encoding binary codebook yao wang, 2006 ee3414. Whereas, when uniform quantization is used, the zoom strategy is a useful control policy, which is divided into two stages. Spatial and greylevel resolutions will be introduced and examples will be provided. Illustration of digitization process we will look into two stages of the. 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. The first thing we have to do, is to obtain signal. The sampling period t s is the spacing between two adjacent samples, i. Spectrum of quantization noise and conditions of whiteness.
Interpolation is the process of guessing signal values at arbitrary instants of time, which fall in general in between. Pdf few works have been done about the dependency of the quantization noise with the sampling rate for uniform quantizers. Lloydmax quantizer lloyd,1957 max,1960 m1 decision thresholds exactly halfway between representative levels. Natural sampling s s f d f null at 3 pam and pcm pam pulse amplitude modulation. Now the problem is that we cannot apply digital image processing and its techniques on analog signals. This rate is called sampling rate or sampling frequency. The sampling rate determines the spatial resolution of the digitized image, while the quantization level determines the. Buy this book on university of central arkansas, i agree that the library of this. An introduction on implementing the shown examples in matlab will be also given in this lecture. The concept of sampling is directly related to zooming. This process maps inputs in a different range of values to a different common value. Quantization step an overview sciencedirect topics.
Ee368b image and video compression quantization no. Image representation, sampling and quantization antonio r. Increasing the transmitted signal power employing modulation and demodulation technique employing suitable coding and decoding methods reducing noise interference with help of improved filtering. We will assume here, that the independent variable is time, denoted by t and the dependent variable could be.
Craig 11 an analog signal that varies quickly must be sampled more frequently than an analog signal that varies slowly. Pdf quantization and sampling of not necessarily band. The sampling rate is the number of samples taken in the duration of one second. Each of these levels represents a fixed input amplitude. Notice that we carefully avoid comparing a and c, as this would lump the sampling and quantization together. Quantization and sampling test digital image processing. 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. 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. Pdf relationship between sampling rate and quantization noise. In effect, scalar quantization digitizes an analog signal.
In this video, i have explained basics of quantization by following outlines. Sampling and quantization often the domain and the range of an original signal x t are modeled as continuous. Online access to spie ebooks is limited to subscribing institutions. Typically, a frame grabber or digitizer is used to sample and quantize the analogue video signal. 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. But for the same length of video and audio, the file size will be much larger than the low quality signal. A sampler is a subsystem or operation that extracts samples from a continuous signal. That is, no continuous amplitude signal can be reconstructed from its quantized samples with zero distortion regardless of the sampling rate, even. Now let us examine the oversampling adc, where the sampling rate is much bigger than that of the regular adc. 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. Color quantization cq is an important operation with many applications in computer graphics and image processing and analysis. Solution depends on input pdf and can be done numerically for. Solution depends on input pdf and can be done numerically for commonly used pdfs e. Chapter 5 sampling and quantization often the domain and the range of an original signal xt are modeled as contin uous.
Uniform quantization an overview sciencedirect topics. The analog signal, denotedxt, is continuous in both time and amplitude. 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. It is often convenient to talk about the sampling frequency fs. A common example is the conversion of a sound wave a continuous signal to a sequence of samples a discretetime signal. 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. 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.
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