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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Quantization SNR of sine wave doesn't match 1.761 + 6.02 * Q
I am trying to show with numpy that the quantization noise of a sine wave matches the SNR formula of SNR = 1.761 + 6.02 * Q.
The numpy code is simple:
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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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Compute SQNR (Signal to Quantization Noise Ratio)
I'm studying the quantization of an audio signal and in particular the SQNR (Signal to Quantization Noise Ratio).
The book on which the study says that:
where:
N is the number of bits in the ...
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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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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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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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What is "hard quantization" strategy?
I am working on classification and several times I encountered with this term.
What is hard quantization strategy?
What does it differ from soft approach?
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Expected value of a quantized noisy signal
I am given a noisy signal $y(t) = x(t) + w(t)$, where $x(t)$ is my desired signal and $w(t)$ is the noise. In my scenario, the noise is very strong, much stronger than the desired signal $x(t)$. ...
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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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Difference between ADC dynamic range and voltage resolution?
Say I have a 10-bit SAR ADC with a $5 \ \text{V}$ reference. I calculate its resolution to be
$$\Delta V_\text{lsb} = \frac{5 \ \text{V}}{2^{10}} = 4.88 \ \text{mV} \approx 5 \ \text{mV}. $$
So for a $...
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What is "Maximum Quantization Error"?
I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation.
It is defined as:
$$Q = \dfrac {\Delta ...
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Practical IIR filter implementation
I'm trying to implement a digital IIR filter on an FPGA and would be happy for some inputs regarding the actual digital implementation. I don't have a lot of experience with FPGAs and digital filters ...
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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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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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Oversampling in quantization
Q: It is said that "to maintain the same quality in the two cases, we require that the power spectral densities remain the same". Why is this a measure of the same quality? Why is not
the ...
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A query on the non-uniform quantization
I have read that non-uniform quantization boosts the smaller amplitude signals by a large amount. However the larger amplitude signals receive a small gain. As shown in the below diagram (Compressor ...
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Audio signal dither and noise shaping
I'm trying to get a handle on the importance of the error feedback term in noise shaping operation in typical audio dither algorithms.
I'm thinking in terms of four signals. The original signal, the ...
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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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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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Why are vector quantizers not used in video codecs?
Using a vector quantizer (VQ), groups of image samples (or motion compensated and/or transformed data) can be quantized as vectors. I'm curious about why VQs are not preferred in the modern, highly ...
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In image compression using transforms, how to deal with the transformed coefficients as they are not integers?
I am new to the field of image compression. While going through various texts, I read about how transforming the image to another domain using, for example, the wavelet transform, or the DCT, makes it ...
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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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Design a quantization scheme around a desired quantization noise distribution
I have a - perhaps naive - question regarding the quantization noise/error. Assuming the goal is not the performance of the quantizer but rather being able to model the quantization noise exactly - ...
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Signal to Quantization Noise ratio concept
I was reading Simon S. Haykin's Digital Communications in order to understand the concept of quantization. However, on SQNR, I got stuck over the point where the author mentioned:
With the input $M$ ...
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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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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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ensure stability against coefficient quantization
for a filter:
$$ H(z)=\frac{1+0.1z^{-1}}{1+0.1z^{-1}+0.9998z^{-2}} $$
Which precautions could be taken to ensure that the filter does not become unstable because of coefficient quantization? I've ...
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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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Mean square error for a quantizer - problem in integral
There are similar questions about related problems that I honestly didn't understand. I believe this might be a lack of statistics knowledge of my part.
Quantization error standard deviation
Error ...
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Quantization error of SAR-ADCs
My question is related to the quantization error and the functionality of SAR-ADCs. In general, the quantization error of an ADC is defined as +-0.5LSB. If this concept is correct a voltage that ...
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Quantization and Sampling - putting it all together
So after I learned this two topic: quantization and sampling, I'm learning the way to look at both of them and try to optimize the split of a given amount of bit B to N and k, where N is the amount of ...
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Having converted a grayscale image to binary using `im2bw()`, is the converse operation possible?
I have converted a gray-scale image to binary using im2bw() now i wanna do the opposite. How can I do that in MATLAB?
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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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What is the difference between clustering and quantization?
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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DCT: Alternatives to quantization
When using the discrete cosine transform are there commonly used alternatives to quantization to decide which dct components to keep/are important? If not, how do people come up with quantization ...
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Quantizing a filtered signal
In the process of trying to learn dialup, I've managed to learn/figure out everything except how to convert a demodulated/filtered signal back into the original data.
Here I have a random two-bit ...
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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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Signal to Quantization Noise Ratio (SQNR)
I have this problem in my homework (following picture).
How do find the signal to quantization noise ratio at the output?
I don't want the solution. I just want to know a better approach to tackle ...
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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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Uniform quantizer for gaussian input signal
I have a gaussian signal $x$ with zero mean and unit variance. I am quantizing it by using a uniform quantizer of step size $q$ calculated by
$$q = \frac{x_\mathrm{max} - x_\mathrm{min}}{2^{M_\mathrm{...
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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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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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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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What is the no overload region of a quantizer?
I was watching a video on quantization noise and the instructor kept referring to the "no overload" region of a quantizer? Could anyone please explain what that term means?
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Modelling of quantization noise with logarithmic steps
I have to modell the quantization noise of ADC.
I only know that the maximum relative error is 1 dB.
Since this is logarithmic, I find it hard to formulate an appropriate model for the quantization ...
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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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Can we have an analogous sampling theorem for quantization?
Sampling theorem tells us how we can sample a continuous signal such that we can reconstruct it without any errors, or without losing information.
Quantization, on the other hand always results in ...
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Connection between SNR and the dynamic range of the human ear
For signal-to-noise ratio (SNR), SNR=6B dB is called the dynamic range of
the quantizer.
The dynamic range of the 16-bit quantizer is 6B = 6·16 = 96 dB. Note that the dynamic range of
the human ear ...
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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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