Questions tagged [quantization]

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6
votes
1answer
208 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). ...
5
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1answer
3k views

Compute SQNR (Signal to Quantization Noise Ratio)

I'm studying the quantization of an audio signal and in particular the SQNR (Signal to Quantization Noise Ratio). The book on which the study says that: where: N is the number of bits in the ...
5
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1answer
345 views

What is “hard quantization” strategy?

I am working on classification and several times I encountered with this term. What is hard quantization strategy? What does it differ from soft approach?
4
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3answers
285 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 ...
4
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2answers
65 views

What distribution is the easiest to compress?

I'm currently playing around with some compression algorithms and I'm asking myself if there is a type of data distribution / noise distribution that is easier to target with quantization (meaning ...
3
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4answers
1k views

Why does D/A Quantization Error Result in a Noise Floor from a Physics Perspective

For the last week or so I have been trying to understand how quantization error results in the noise floor outside of a mathematical perspective and I haven't really had any luck finding a source that ...
3
votes
1answer
30k views

What is “Maximum Quantization Error”?

I have an formula for this "Maximum Quantization Error" but i dont know what it is based in. Its just thrown in my study material without further explanation. It is defined as: $$Q = \dfrac {\Delta ...
3
votes
1answer
113 views

Does delta-sigma ADC also reduce Gaussian noise on input signal to ADC or just quantization noise?

The motive for posing this questions arises from a difference of analysis between a colleague an myself. Our general environment is in the construction of an analog front-end which takes in signals ...
3
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2answers
85 views

Why are vector quantizers not used in video codecs?

Using a vector quantizer (VQ), groups of image samples (or motion compensated and/or transformed data) can be quantized as vectors. I'm curious about why VQs are not preferred in the modern, highly ...
3
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2answers
2k views

Audio signal dither and noise shaping

I'm trying to get a handle on the importance of the error feedback term in noise shaping operation in typical audio dither algorithms. I'm thinking in terms of four signals. The original signal, the ...
2
votes
3answers
273 views

Is it theoretically possible to perfectly quantize a continuous signal?

So, I'm completely new to digital signal processing, but while reading a piece this morning about quantization it got me daydreaming: could a machine ever be fast enough to sample the position and ...
2
votes
1answer
111 views

Why harmonic components appear only after a certain level when a signal is clipped?

I recently observed this phenomenon that when a signal is clipped the harmonics start to appear only after a certain level. The Python code to reproduce the effect is given below. The signal has 3 ...
2
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2answers
2k views

A query on the non-uniform quantization

I have read that non-uniform quantization boosts the smaller amplitude signals by a large amount. However the larger amplitude signals receive a small gain. As shown in the below diagram (Compressor ...
2
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2answers
259 views

DCT: Alternatives to quantization

When using the discrete cosine transform are there commonly used alternatives to quantization to decide which dct components to keep/are important? If not, how do people come up with quantization ...
2
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1answer
86 views

Quantizing a filtered signal

In the process of trying to learn dialup, I've managed to learn/figure out everything except how to convert a demodulated/filtered signal back into the original data. Here I have a random two-bit ...
2
votes
1answer
823 views

Signal to Quantization Noise Ratio (SQNR)

I have this problem in my homework (following picture). How do find the signal to quantization noise ratio at the output? I don't want the solution. I just want to know a better approach to tackle ...
2
votes
1answer
951 views

Lloyd Max quantization and clustering : Part 1

The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case of a vector quantizer (VQ) designed with the Linde Buzo Gray (LBG) algorithm. In k-means clustering, we are given a ...
2
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1answer
118 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 $\hat{x}(-1)=0$ ...
2
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1answer
224 views

What is the no overload region of a quantizer?

I was watching a video on quantization noise and the instructor kept referring to the "no overload" region of a quantizer? Could anyone please explain what that term means?
2
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0answers
54 views

Modelling of quantization noise with logarithmic steps

I have to modell the quantization noise of ADC. I only know that the maximum relative error is 1 dB. Since this is logarithmic, I find it hard to formulate an appropriate model for the quantization ...
1
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1answer
234 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 ...
1
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1answer
22 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 ...
1
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2answers
146 views

Are time series data always contain noise?

I wonder if every time series data should contain noise or not. For example I am taking the price of a ticker, say Yahoo, every hour and noting the values. Does this data contains noise or not?
1
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3answers
929 views

ensure stability against coefficient quantization

for a filter: $$ H(z)=\frac{1+0.1z^{-1}}{1+0.1z^{-1}+0.9998z^{-2}} $$ Which precautions could be taken to ensure that the filter does not become unstable because of coefficient quantization? I've ...
1
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1answer
7k views

Quantization Image using MATLAB

I'm trying to quantize an image 8 bits to 4 or 2-bits uniformly. I searched internet, interestingly I could not find what I want exactly. Then I wrote an simple code for it myself. I'm curious about ...
1
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1answer
1k views

Sampling rate effect on quantizer SNR

I am currently reading the 'Coding' chapter on Rabiner & Schafer's Book on speech processing. In one of its exercises, the reader is given a simple A/D converter using 16-bit uniform ...
1
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2answers
254 views

In image compression using transforms, how to deal with the transformed coefficients as they are not integers?

I am new to the field of image compression. While going through various texts, I read about how transforming the image to another domain using, for example, the wavelet transform, or the DCT, makes it ...
1
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2answers
59 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 ...
1
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1answer
33 views

Is it necessary to scale a signal for quantization noise analysis?

I am doing a series of tests to analyse the round-off (quantization) noise performance of single and two stage biquad cascades (direct form 1), at different sampling rates. The system I am simulating ...
1
vote
1answer
986 views

Difference between clustering and quantization : Part 2

The Lloyd-Max quantizer is a scalar quantizer which can be seen as a special case of a vector quantizer (VQ) designed with the Linde Buzo Gray (LBG) algorithm. In k-means clustering, we are given a ...
1
vote
1answer
157 views

Proper rounding when converting between digitized values and floating point

I have some very large files that are unsigned 8 bit (0 to 255), real valued. I need to do some simple tuning and decimation. In the past, when I've dealt with low bit rate samples, I've run into ...
1
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1answer
66 views

For image quantization, is it necessary to sample image?

When we want to quantize an image, is it necessary to do sampling? When we know that image is a discrete signal, is it necessary to find the best samples with Nyquist rate?
1
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0answers
42 views

What is wrong with my 3D DCT quantization?

I'm implementing 3D DCT quantization as in Quantization of 3D-DCT Coefficients and Scan Order for Video Compression (sorry about the paywall). They propose the following equation for generating the ...
1
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0answers
102 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 ...
1
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3answers
147 views

Is the incoming sample in a standard DPCM already quantized?

I began learning about DPCM and i've got one issue I am not sure about: Is the incoming sample m[k] (see image for reference) already quantizied or not? I think it is but with an (assumed) very fine ...
1
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0answers
120 views

Which type of quantization is better?

If a signal's amplitude has a uniform PDF, which is better in the sense of producing a smaller quantization error: optimal scalar quantization or quantization with compressor (non-uniform quantization)...
1
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0answers
107 views

Filter output quantization - does this limit effective coefficient quantization?

I am implementing a filter in hardware, and the intended maximum data input is 16-bit. The question is, if the output is to be re-quantized to 16-bit, does this mean certain coefficients are ...
1
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0answers
69 views

Dealing with quantization level limiting dsp

There is a analog signal in the form as below: $$ f(t)=A \sin(\omega(t) t+\phi)+B \sin(\omega(t-t_1) t+\phi_1) $$ Where $$B<<A$$ We are going to calculate $\phi, \phi_1, t_1 $,using dsp. But ...
0
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1answer
80 views

Is there any literature discussing PDF after quantization?

Consider a random variable with a known distribution. I want to know if we quantized the variable the how the probability density function(PDF) would change? Specifically if the original PDF is ...
0
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2answers
281 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?
0
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3answers
617 views

why does quantisation noise sound like white noise?

To record sound and transform it to digital form, audio signals are recorded and its pressure levels are sampled and quantised. Why does quantisation noise sound like white noise?
0
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2answers
66 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 ...
0
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1answer
58 views

Correct way to quantize accelerometer data with microsecond precision?

I am analyzing large volumes of raw accelerometer data (~12 hours @ 200Hz) using Python. Some calculations (e.g. deriving Jerk) necessitate a time index with a regular interval. I have microsecond-...
0
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1answer
567 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{...
0
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1answer
33 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 ...
0
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1answer
469 views

Quantization error in sampling

Consider the analog signal, $$x(t) = 2\cos(3000\pi t)+3\sin(4000\pi t)+7\cos(6000\pi t)$$ If the sampling rate is 8000 samples per second and quantized at 8 bits, find: Discrete values at any two ...
0
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1answer
8k views

Analog to digital conversion using Python

I'm a beginner. I try emulate analog signal conversion to digital (including sampling by time and quantizing by level) using Python. Here is my code: ...
0
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1answer
169 views

Quantization SNR of bipolar signal

I want to estimate the SNR of a bipolar signal. I know that each bit increases the SNR at 6 dB. Do i have to subtract one bit for sign, so that for bipolar signals the SNR is (n-1) x 6 dB ?
0
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2answers
223 views

How does delta modulation work practically?

How does delta modulation work in practice? And where is it used? I find it confusing that, in 1-bit quantization we use only 2 level; if we apply this quantization, there will be loss in information. ...
0
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0answers
48 views

Encoder: Quantization in Frequency Domain

The article, "Let’s build an MP3-decoder!" describes quantization noise in the time domain: [masking] This property is very useful: not only can the nearby masked signals be removed; the audible ...