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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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Calculation of Compression Ratio after DCT

I am seeking information about the compression ratios achieved at each stage of DCT-based compression processes. Specifically, I'm interested in understanding the compression ratio immediately after ...
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How does quantization do to tell the difference between one sampling point and one other?

The signal quantization consists in assigning to the different values of the sampled signal a value among the range of the $2^p$ values allowed by the $p$ bits used. As the different values of the ...
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Relation between harmonics and quantization [closed]

I'd like to make digital samples that construct sine waves. It's nothing but direct digital synthesis (DDS) before the digital-to-analog converter and filter. I want to make a sinewave sample that ...
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Output spectrum of the direct digital synthesis (DDS)

I have a question about the output spectrum of DDS, which consists of a phase accumulator and look-up table. Since the look-up table stores accurate information about sinusoidal waveform, I think ...
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What exactly is transmitted in the channel in lossy compression?

Consider the problem of lossily compressing a memoryless binary source $X \sim \operatorname{Bernoulli}\left(\frac{1}{2}\right)$ at target Hamming distortion $D < \frac{1}{2}$. According to the ...
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Filter away INT_MIN when doing DSP since -INT_MIN is undefined(?)

My problem is that I have a mic that delivers 24 bits 2's complement signed. There is nothing in that data sheet that hints at it not also delivering INT_MIN. The 8 ...
Øyvind Teig's user avatar
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Distortion-Rate function for standard Gaussian signals quantized with a uniform alphabet

Let's say $X \sim N(0, 1)$ is a standard Gaussian input signal and $Y \sim U\{y_1, y_2, \cdots, y_{16}\}$ follows a discrete uniform distribution (in fact, $\{y_1, y_2, \cdots, y_{16}\}$ is a ...
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delta modulation

I need to implement some sort of simple delta modulation for my homework. The test signal is $x(t)=10\sin(20\pi t)+\cos(100\pi t)$, sampled at $f_s=40f_{\tt{max}}$ Block scheme of delta modulator is ...
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ADC response inversion to Gaussian noise

Assuming the input to an ADC is a Gaussian white noise signal, and being a bit idealistic in all senses, is there a theoretical expression that links input power to output power which can be inverted, ...
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Correlated Quantization Noise

Normally, when we are dealing with quantization noise, we assume quantization noise as uncorrelated, which is white. In this case, we assume SNR = 6.02N + 1.76 where N = resolution However, if ...
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How to design an optimal LLR Quantization of LLR for LDPC Decoding under AWGN channel using BPSK(Known quantization boundaries)?

Recently I met an optimazition problem, i.e., finding an optimal quantizer which maps floating point LLRs to integers of range $-11,\ldots +11$, where the quantizer boundaries have been calculated out....
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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 ...
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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 ...
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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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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

Does anyone know how to detect and quantify a digitally time stretched audio signal when made back to tape?
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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 - ...
Bahar Az's user avatar
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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 ...
Miss Mulan's user avatar
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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 ...
Sander Zuckerman's user avatar
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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 $M$ ...
Pooja Agarwal's user avatar
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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 ...
Shashank V M's user avatar
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2 answers
324 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 ...
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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 ...
Dieguli's user avatar
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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 ...
Himadri Debnath's user avatar
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2 answers
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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?
DSP_CS's user avatar
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5 votes
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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 ...
Paul Uszak's user avatar
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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 ...
stander Qiu's user avatar
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1 answer
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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{...
austin's user avatar
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2 answers
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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 ...
DSPinfinity's user avatar
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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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