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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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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Computing Speech Signal Energy for the TMS5220

I am writing a C++ program that performs LPC analysis on speech data and then compresses it in a format acceptable to the TMS5220 Voice Synthesis Processor. During LPC analysis, I compute the energy ...
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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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L-2 distortion and entropy

How can I compute derive L-2 distortion and entropy obtained by quantizing a distribution. Assuming that we have PDF of distribution and successive approximation quantization. Is there any relation ...
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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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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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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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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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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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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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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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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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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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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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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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