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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AWGN model of Quantization Noise
[Edit answer moved from OP edit to "Answers" as per comment suggestion]
I'm trying to create a simple model of a signal chain (image sensor) that includes an ADC but I'm failing to observe ...
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Detect digitally time stretched audio made back to tape
Can anyone tell me how I might detect and measure a digitally time stretched audio signal (Pro Tools) when subsequently made back onto tape?
Could quantization of the signal be detectable on tape and ...
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Signal averaging of a digitized noisy signal
If I have a signal that is lower than the noise power, I may want to use signal averaging over time to increase SNR.
However, when the signal has been obtained after digitization, there is ...
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What order to apply noise shaping and anti-aliasing to an idealized synth
I am trying to write a small synth code that goes something like this,
I have an abstract symbolic sound representation, sine/square/saw waves. To generate final sound and make it sound good I thought ...
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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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how to calculate step size for uniform quantizer?
so I am a little bit confused about the formula of the step size in a uniform quantizer.
from what I have studied:
StepSize = $\displaystyle\frac{maxValue-minValue}{2^n}$, where ...
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Which command should be used for quantization of a signal in MATLAB?
I want to convert analog signal to digital form using Matlab. I know that this will need two steps (sampling and quantization) but I am confused which command should be used for quantization? ...
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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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What are the purposes of color extraction using k-means clustering?
Using K-means clustering it is possible to reduce the amount of colors in an image. What are the purposes of using this method for extracting colors from an image?
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Performance Effects of Dropping ADC Least Significant Bits before DSP processing (Besides the Obvious)
What would be the effect of dropping LSBs of an ADC on the performance of a DSP system apart from the obvious reduction in dynamic range. For example if there is a 14 bit ADC and only 10 bits are used,...
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Question on discrete signals and quantization
Suppose we have 2 different levels of a quantized signal.
Let's say that the range is $[-1,1]$. The number of bits necessary to encode these levels is$\log_2(2) = 1$. However if the value of the ...
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How do you find the null to null bandwidth for the signal below?
My tutor does not explain it very well. Can someone please explain to me the reasoning and what null to null bandwidth actually is?
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What is the best coding strategy?
There is a dataset of $N$ elements, each represented by $K$ bits. Now due to hardware limitations to reduce memory for storage, they have to be reprocessed into $K'$ bits each, and $K'<K$. What is ...
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Do you append 00 or 10 when oversampling
Say I have an 8-bit ADC and I oversample at such a rate as to obtain 2 additional bits. So, before I apply the low-pass filter, I need to append two extra bits to the 8-bit signal of the ADC. Do I ...
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How to add quantization noise (SQNR) to thermal noise (SNR) in a total value?
How can I add the BAQ (Block Adaptive Quantizer) compression noise to the input SNR? In the end is a quantization noise to be added to a thermal noise. I got the following formulation, but I dont ...
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How to decode a MIMO stream using V-BLAST?
I am attempting to implement the V-BLAST algorithm for MIMO streams as described by Wolniansky et al. in the following paper: https://ieeexplore.ieee.org/document/738086 (I am not commenting on its ...
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Estimating quantification and sampling error
I have a signal sampled from $\mathbb{R}^2$ at a frequency of $2\text{Hz}$. It is quantized from $\mathbb{R}^2$ to $\mathbb{N}^2$, seemingly using the round operator.
How can I estimate the error ...
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Confusion implementing Quantization in MATLAB?
I am quantizing a continuous time signal in three different cases(using different number of bits)
But Why i am getting same quantized signal in xq2 and xq3,despite using different values of D(...
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Simulating quantization of ADC using device SNR
Suppose I have ADC microphone with a given SNR in the sense that is related to its quantization. From this tutorial we have the following connection how bit-depth determines SNR, Eq. (9):
$$
\mathrm{...
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Scalar vs Vector signal Quantization
I am studying about scalar vs vector quantization, and I have an assignment to implement (in MATLAB) a scalar quantizer , using the Lloyd-Max algorithm, and a vector quantizer via k-means clustering.
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Quantization error standard deviation
Here I found that "pure" quantization error standard deviation of the signal is $1/\sqrt{12}$ of LSB. Where does it come from?
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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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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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A question about quantization and dequantization calculations
Suppose we have a 2x2 image as follows:
What does each dequantised image look like after it has first been quantised to 7, 4 and 2 bits respectively?
I solve this question by initially quantising as ...
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Digital Signal Quantized Processor Complexity
In “traditional” digital signal processing, the complexity is computed as a number of multiplication the operation requires, e.g. the computation of the N-point DFT via the decimation-in-frequency FFT ...
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Question on PCM Sampling and Quantization order
I had a doubt in my mind regarding the orders of sampling and quantization in PCM. What is the impact if the order is reversed, that is, the continuous time signal is first quantized and then sampled? ...
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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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How to find the minimum no of bits required to express the filter coefficients in fixed point format from Histogram plot?
I have designed a filter in MATLAB and now I have to convert the filter coefficient in fixed point format from floating point format. For that my professor asked me to find histogram first and then ...
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What is formula for quantization step size?
I have read from different web links,different formulas of quantization step size as shown highlighted in attached snapshot,but what is actual/correct formula?
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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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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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How to measure correlation between 1 bit samples and theoretical original waveform?
I'm investigating quantization error.
I have an analogue waveform that looks like this and is of theoretically infinite resolution:-
I've sampled it as (8 bit oscilloscope readings & 0b1) to ...
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Spectral Property of Bandlimited Quantized Signal
recently I meet a problem.
I generate a random Gaussian signal $x$ with mean $0$ in MATLAB. And use a $4$th lowpass Butterworth filter to acquire $x'$. Then I use the binary rounding quantization ...
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Is there an optimal way to quantize log-likelihood ratios of an AWGN channel?
My understanding is that given an AWGN channel and BPSK modulation, an LDPC decoder that uses message passing takes as input log-likelihood ratios $L$ of the following form by Bayes' rule:
$$
L=\frac{...
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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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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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Unclear point about quantization
Quantization of Continuous-Amplitude Signals
This point is not clear to me:
"The smallest quantization levels ($\pm\Delta$) correspond to the least significant bit of the binary code word."...
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Non-Uniform Quantization
I was reading a research paper on companding schemes for non uniform quantisation. In paper one of the motivations for non-uniform quantisation is that distortion at larger amplitude values is less ...
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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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SNR of μ-law companding
I know the snr after μ-law compression is
$\text{SNR}\approx\frac{3L^2}{[\ln(1+ \mu)]^2}$
when $\mu \gg \frac{\max_t m(t)}{\text{rms}(m(t))}$,
where $m(t)$ is the message signal, and
$L$ the number ...
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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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How to quantize filter coefficients to 10 bits
I am trying to learn digital filter design. One of the concept is quantization of filter coefficients. I used Designfilt to design an lowpass IIR filter and obtained coefficients. Now I want to ...
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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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Binary image? Only black and white? [closed]
By name, a binary image is one that has two levels. But is it essential that those two colors are black and white? Or any other combination also allowed as shown in attached snap. Snap is output image,...
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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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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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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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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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