Questions tagged [quantization]

Quantization, in mathematics and digital signal processing, is the process of mapping input values from a large set (often a continuous set) to output values in a (countable) smaller set, often with a finite number of elements. Rounding and truncation are typical examples of quantization processes.

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Fixed Point Design Resources

Can anyone point me to good methodologies for designing fixed point versions of possibly nonlinear signal processing algorithms? Are there any systematic methods other than simulation for optimizing ...
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984 views

How to implement a $1$-bit quantizer in Simulink?

I am trying to implement a delta-sigma modulator block diagram in Matlab Simulink but can't find a $1$-bit quantizer (which is required in the modulator) anywhere. Could anyone please tell me how to ...
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Does delta-sigma ADC also reduce Gaussian noise on input signal to ADC or just quantization noise?

The motive for posing this questions arises from a difference of analysis between a colleague an myself. Our general environment is in the construction of an analog front-end which takes in signals ...
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Is there any difference in Implementing sigma delta modulator using filters and state space model in FPGA?

Sigma delta modulation is extensively used in quantization to reduce quantization noise. In the literature one can see different architecture for example python-deltasigma to implement a modulator. ...
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437 views

Why use a 1-bit ADC in a Sigma Delta Modulator?

When looking at the discrete model of a Sigma-Delta Modulator as shown below, we can see that the quantizer is modelled as a white-noise source $e[n]$. From this model, we can derive the noise shaping ...
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A/D converter quantization noise

I read that in A/D converter we usually use rounding or two's complement truncation and not the sign magnitude or 1's complement truncation as in this case the quantization error is correlated to the ...
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From a physics perspective, why does D/A quantization error result in a noise floor?

For the last week or so I have been trying to understand how quantization error results in the noise floor outside of a mathematical perspective and I haven't really had any luck finding a source that ...
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Harmonics in Quantal Histogram

I'm studying what I believe to be a system that produces a (noisy) quantal response (i.e. there should be a minimum increment of response). To do this, I've plotted a histogram of some ~6000 amplitude ...
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What's the difference between quantization and coding?

From what I understand quantization takes an analog signal and assigns numerical values to it as convert it to a discrete signal. However coding converts a signal into binary. It seems like coding is ...
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Explanation for the quantization matlab function

I found this code on quantization on page 314 in the book Modern Digital and Analog Communication Systems by B.P.Lathi and Zhi Ding. I can understand only half of the code. Please, someone, help in ...
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Sampling Rate Effect on Quantizer SNR

I am currently reading the 'Coding' chapter on Rabiner & Schafer's Book on speech processing. In one of its exercises, the reader is given a simple A/D converter using 16-bit uniform ...
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QPSK matlab/simulink Quantisation effects

I am trying to simulate the effects of quantization of an ADC on different waveforms (e.g. QPSK,8PSK) in Simulink. For the case of QPSK the default BER curve would be generated with 2 bits per symbol ...
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495 views

How to determine a quantization table for image compression with DCT?

The quantization table is given on the JPEG Wiki page. How was this table derived? I'm currently doing a project where I have to come up with custom quantization table for an image, but I don't know ...
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Difference between formula of SNR and SQNR?

Is there any difference between formula/expressionsof SNR and SQNR? where SNR is Signal to noise ratio and SQNR is signal to quantization noise . The following DSP SE question shows both SNR and SQNR ...
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How we can quantize a sampled signal in MATLAB?

I have a continuous time signal $x(t)=\sin(2πft)$ where $0 \leq t \leq 3$. I want to sample the continuous time signal and then quantize that sampled signal and then plot both sampled and quantized ...
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Quantization step-size for a given signal based on its PDF

I am familiar with the principles of midtread and midrise quantizer. However, I have difficulties determining the step size where it hasn't been explicitly given. For example, the following ...
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Is it theoretically possible to perfectly quantize a continuous signal?

So, I'm completely new to digital signal processing, but while reading a piece this morning about quantization it got me daydreaming: could a machine ever be fast enough to sample the position and ...
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How to find the sampling vector of HD camera recording?

An HD camera records 1080p video (1080*1920, prograssive, 30 frames/sec) wiht croma subsampling 4:2:0 for a total of 90 minutes. The quantizer which is being used for the chroma representation has 256 ...
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How to calculate SNR of dead-band quantizer?

Suppose we have a dead-band quantizer with $\ N = 5 \ quantizing \ levels $ which uses $\ b = 3 \ bits $ for each produced symbol. The quantizer gets as input a uniformly distributed signal $\ X $ ...
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confusion sampling vs quantization?

while converting analog signal to digital equivalent,we have a process that is called analog to digital conversion and it has two main steps/stages sampling and quantization? I am confused whether y ...
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Realize Simulink block “Ideal ADC Quantizer” in Matlab

Yesterday I posted following topic: "FFT alternates '0' for a quantized SIN wave". During post editing I was perturbed by some affair, I didn't formulate correctly the problem. So, my post was blocked ...
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Why are we always interested in mean-squared distortion?

When dealing with quantizers, and in many other communications problems, the interest is usually on the mean-squared distortion or mean-squared error, rather than mean absolute error or anything else. ...
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1answer
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Variance of a signal

How to calculate the variance of noise samples modeled as follows: $n_a(t)$ is a Gaussian zero-mean white noise process with (two-sided) power spectral density $\frac{N_0}{2}$. $n_a(t)$ is passed ...
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Sample & Hold: Estimate jitter delay of an ADC

I've got a question regarding the effects of sample and hold. My input signal is $x$, and my output signal $x_{SH}$. The error between the signals is $e_{SH} = x_{SH}-x$. The sampling frequency is ...
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Signal to Quantization noise problem

a full scale signal of bandwidth 5 khz is sampled by an 10-bit ADC at a sampling rate of 2 Msa/sec calculate the Signal to Quantization noise of the resulting DT signal repeat for a 14-bit ADC at ...
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How to Reverse Color Quantization?

Are there any algorithms that attempt to perform the inverse of color quantization on an image? In other words, is there a smart way to increase the bit depth of image? The obvious answer would be to ...
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Novice question about mid-rise quantization

Accoarding to wikipage, the function for quantization has the ceiling of x/Ds. Is this the ceiling of something multiplied by Ds?
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Difference Between Clustering and Quantization : Part 2

The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case of a vector quantizer (VQ) designed with the Linde Buzo Gray (LBG) algorithm. In k-means clustering, we are given a ...
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Lloyd Max Quantization and Clustering : Part 1

The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case of a vector quantizer (VQ) designed with the Linde Buzo Gray (LBG) algorithm. In k-means clustering, we are given a ...
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How good is the Leech lattice for AWGN coding or MSE quantization of Gaussian sources?

Anyone know where to find graphs showing how well it works vs other schemes? thanks
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Separability vs. Resolution - Synonymous terms?

In terms of discrete representation of a variable, let's say time measurements in absolute values in [seconds], is there a difference between separability and resolution? When do speak of either ...
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Differential Pulse Code Modulation (DPCM)

In the following figure we see an encoder and a decoder of a Delta Modulation System, which is a simple DPCM System with a 1-bit quantizer: We assume that signal $x(n)$ is known, that $\hat{x}(-1)=0$ ...
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723 views

Quantization error in sampling

Consider the analog signal, $$x(t) = 2\cos(3000\pi t)+3\sin(4000\pi t)+7\cos(6000\pi t)$$ If the sampling rate is 8000 samples per second and quantized at 8 bits, find: Discrete values at any two ...
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Optimal amplitude of an $m$-bit sinusoid

A continuous-time sinusoid of zero-to-peak real amplitude $A \le 2^{m-1}-0.5$ (e.g., for $m=16$, $A \le 32767.5$) is quantized to $m$-bit resolution by rounding it to the nearest integer (Fig. 1). ...
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Precise 5th and 7th harmonics of a sampled sine wave

Does anyone know in decibels (to 1/100th of a dB) what the theoretical 3rd, 5th and 7th harmonic of a 0dB fs 24-bit (i.e. full-level; 0dB = -8,388,607 to 8,388,607) sampled sine wave without dither ...
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JPEG compression steps after quantization

I have a 3-channel (for colours) a png image that I opened and I splitted the image into 8x8 blocks I applied all of the blocks discrete cosine transform And then applied quantization I stored the ...
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Analog to digital conversion using Python

I'm a beginner. I try emulate analog signal conversion to digital (including sampling by time and quantizing by level) using Python. Here is my code: ...
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Why is distorted / quantized white noise still white noise?

White noise can be created by setting every sample in the time domain to a random number with a gaussian distribution. Every sample is random, so the frequency response is obviously random. Easy ...
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What is wrong with my 3D DCT quantization?

I'm implementing 3D DCT quantization as in Quantization of 3D-DCT Coefficients and Scan Order for Video Compression (sorry about the paywall). They propose the following equation for generating the ...
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680 views

Quantization level versus bandwidth [closed]

Why is it that increasing the number of quantization levels $L$ results in an increase in the signal's bandwidth?
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THD requirement for generated sine

I need to generate a sine signal using a DAC with a certain THD specification, say 0.1% @ 1KHz. As a first approach I’m considering it to be an ideal DAC along with an ideal LPF for aliasing removal ...
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What distribution is the easiest to compress?

I'm currently playing around with some compression algorithms and I'm asking myself if there is a type of data distribution / noise distribution that is easier to target with quantization (meaning ...
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69 views

What information does the abs(normalized_image - normalized_quantised_image) carry?

Given a grayscale image X2 And its (under)quantised version with 3 bits depth X3 What information does the abs(X2_normalized - X3_normalized) carry?As an example ...
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Quantization of Image which have taken from partially less dark

I have picture with high resolution with 20M memory space and this image has been taken from the standing away from the window in room which has significantly less light as compared to outside. Image ...
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How does delta modulation work practically?

How does delta modulation work in practice? And where is it used? I find it confusing that, in 1-bit quantization we use only 2 level; if we apply this quantization, there will be loss in information. ...
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Why harmonic components appear only after a certain level when a signal is clipped?

I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level. The Python code to reproduce the effect is given below. The signal has 3 ...
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How much will a low/high pass filter reintroduce quantization noise into a dithered signal?

For example, most audio signals are dithered prior to distribution. However, if a low or high pass filter is introduced after dithering or during playback, won't that negate some of the benefits of ...
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Is the incoming sample in a standard DPCM already quantized?

I began learning about DPCM and i've got one issue I am not sure about: Is the incoming sample m[k] (see image for reference) already quantizied or not? I think it is but with an (assumed) very fine ...
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Correct way to quantize accelerometer data with microsecond precision?

I am analyzing large volumes of raw accelerometer data (~12 hours @ 200Hz) using Python. Some calculations (e.g. deriving Jerk) necessitate a time index with a regular interval. I have microsecond-...
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Which type of quantization is better?

If a signal's amplitude has a uniform PDF, which is better in the sense of producing a smaller quantization error: optimal scalar quantization or quantization with compressor (non-uniform quantization)...