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.
122
questions
0
votes
0
answers
32
views
Cross-quantilogram method
What is this method in general?
What is the main difference between the quantile cross-spectrum (QS) approach developed by Baruník and Kley (2019) and the cross-correlation function (QS) developed by ...
- 5,247
0
votes
0
answers
21
views
Approximating variable-length coding by "aggregating" fixed-length coding
Consider the problem where I want to quantize a univariate standard Gaussian with two bits, and the objective is to minimize MSE reconstruction loss. According to these slides, the Lloyd algorithm and ...
- 113
0
votes
1
answer
76
views
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 ...
CommunityBot
- 1
4
votes
3
answers
228
views
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 $...
- 48.9k
1
vote
0
answers
77
views
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 ...
- 1
0
votes
1
answer
57
views
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 ...
- 48.9k
1
vote
1
answer
61
views
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?
- 19.3k
0
votes
0
answers
55
views
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 ...
- 101
2
votes
1
answer
116
views
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 ...
- 89k
1
vote
1
answer
220
views
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{...
- 29.6k
3
votes
1
answer
372
views
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 ...
- 19
1
vote
1
answer
686
views
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 ...
- 13.5k
-1
votes
2
answers
241
views
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? ...
- 42.7k
3
votes
1
answer
186
views
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 - ...
- 42.7k
8
votes
3
answers
1k
views
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:
...
- 101
0
votes
3
answers
2k
views
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?
- 5,247
0
votes
2
answers
251
views
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,...
- 573
0
votes
1
answer
69
views
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 ...
- 3,590
0
votes
1
answer
151
views
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 ...
- 42.7k
0
votes
1
answer
39
views
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 ...
- 11.9k
0
votes
1
answer
418
views
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{...
CommunityBot
- 1
0
votes
0
answers
58
views
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 ...
- 11
0
votes
1
answer
89
views
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 ...
- 14.9k
2
votes
1
answer
591
views
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 ...
CommunityBot
- 1
1
vote
1
answer
138
views
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? ...
CommunityBot
- 1
0
votes
1
answer
49
views
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 ...
CommunityBot
- 1
-1
votes
1
answer
150
views
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 ...
CommunityBot
- 1
0
votes
1
answer
114
views
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(...
- 3,735
0
votes
0
answers
137
views
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.
...
0
votes
2
answers
903
views
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?
- 11.9k
2
votes
3
answers
650
views
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 $M$ ...
- 20.2k
2
votes
1
answer
1k
views
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{...
1
vote
4
answers
329
views
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 ...
- 35.2k
1
vote
2
answers
269
views
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 ...
- 31.7k
2
votes
3
answers
505
views
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 ...
- 101
0
votes
2
answers
48
views
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 ...
- 3,310
4
votes
3
answers
1k
views
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 ...
- 3,735
0
votes
0
answers
50
views
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 ...
1
vote
1
answer
6k
views
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?
- 48.9k
5
votes
1
answer
153
views
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 $x(t)$. ...
- 42.7k
2
votes
1
answer
1k
views
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 ...
- 48.9k
0
votes
1
answer
86
views
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 ...
- 392
0
votes
1
answer
81
views
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 ...
- 42.7k
3
votes
2
answers
274
views
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 ...
- 28k
1
vote
3
answers
688
views
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 ...
- 42.7k
0
votes
2
answers
125
views
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."...
- 20.1k
1
vote
2
answers
666
views
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 ...
- 31.7k
2
votes
1
answer
54
views
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 ...
- 89k
0
votes
0
answers
420
views
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 ...
- 29.6k
2
votes
2
answers
196
views
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?
- 31.7k