# 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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### 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 ...
2answers
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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 ...
1answer
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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? ...
3answers
121 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 ...
0answers
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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 ...
1answer
272 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?
1answer
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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 $x(t)$. ...
1answer
128 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 ...
0answers
15 views

### Selective JPEG compression

note: my question is not answered here: Selective image compression? - I couldn't find it, I looked for "selective" and "adaptive" compression, maybe, I put the search query ...
1answer
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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 ...
1answer
56 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 ...
1answer
44 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{...
2answers
147 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 ...
3answers
157 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 ...
2answers
85 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."...
2answers
101 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 ...
1answer
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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 ...
0answers
27 views

### Help in LBG Vector Quantization - Splitting Factor

I'm currently making a program for speech recognition. In the step of codebook generation using the LBG (Linde-Buzo-Gray) algorithm, I've read that the splitting factor $\varepsilon = 0.01$ (generally)...
0answers
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### Quantization types

Suppose i have input sequence {-1.3,1.2,-0.2,-0.5,0.4,0.89,1.3} Which are uniformly quantized through a quantizer having range (-1.5,1.5) with 4 levels My calculted answers for- First method:mid rise ...
0answers
31 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 ...
2answers
604 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: ...
1answer
237 views

### 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 ...
2answers
60 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?
0answers
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### Is there a common adaptive image color quantization (posterization) method?

I know there are a lot of methods to quantize colors in an image given a number of colors. For example the k-mean algorithm enables to reduce the number to k colors. I'm looking for an adaptive method ...
2answers
68 views

### 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,...
2answers
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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 ...
1answer
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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 ...
2answers
217 views

### 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 ...
1answer
604 views

### 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 ...
1answer
2k views

### 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 ...
1answer
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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 $\ X$ ...
3answers
211 views

### 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 ...
3answers
365 views

### 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. ...
1answer
120 views

### 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 ...
1answer
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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 ...
1answer
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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. ...
0answers
39 views

### 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 ...
0answers
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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?
1answer
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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
1answer
422 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 ...
1answer
47 views

### 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 ...
1answer
302 views

### 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 $\hat{x}(-1)=0$ ...
1answer
298 views

### 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). ...
3answers
788 views

### 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 ...
2answers
222 views

### 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 ...
1answer
1k views

### How to determine a quantization table for image compression with DCT?

The quantization table is given on the JPEG Wiki page. How was this table derived? I'm currently doing a project where I have to come up with custom quantization table for an image, but I don't know ...
1answer
539 views

### 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 ...
2answers
101 views

### Why is distorted / quantized white noise still white noise?

White noise can be created by setting every sample in the time domain to a random number with a gaussian distribution. Every sample is random, so the frequency response is obviously random. Easy ...
2answers
1k views

### Quantization level versus bandwidth [closed]

Why is it that increasing the number of quantization levels $L$ results in an increase in the signal's bandwidth?
1answer
60 views

### THD requirement for generated sine

I need to generate a sine signal using a DAC with a certain THD specification, say 0.1% @ 1KHz. As a first approach I’m considering it to be an ideal DAC along with an ideal LPF for aliasing removal ...