14
votes
Accepted
Compute SQNR (Signal to Quantization Noise Ratio)
The signal voltage is a sinusoid signal variant from $-V$ to $+V$, thus the RMS value
$$V_{rms} = \frac{V}{\sqrt{2}} = \frac{2^N \Delta V / 2}{\sqrt{2}}$$
because $2V = 2^N\Delta V$ where $\Delta V$ ...
- 6,725
11
votes
Accepted
Quantization SNR of sine wave doesn't match 1.761 + 6.02 * Q
Some issues here:
Your SNR formula only applies to full scale sine waves, your sine wave has -6dB amplitude so your SNR will be 6 dB lower
The formula also implies rounding, not truncation, that's ...
- 48.2k
8
votes
Precise 5th and 7th harmonics of a sampled sine wave
This answer discusses the harmonic spectra of the quantized sequence in five cases:
limit $f/f_s \to 0$,
synchronous sampling of a cosine with rational $f/f_s$,
synchronous sampling of a sinusoid of ...
- 13.7k
7
votes
Quantization SNR of sine wave doesn't match 1.761 + 6.02 * Q
I was doing quite a bit wrong, but the key thing that I was missing was the fact that the SNR needs to be calculated over the whole Nyquist spectrum instead of only looking at the peaks.
This article ...
- 522
6
votes
Accepted
confusion sampling vs quantization?
Sampling is the process of making the x-axis (time) discrete and quantization is the process of making the y-axis (magnitude) discrete. You can sample without quantization (such as done with an ...
- 55k
6
votes
Accepted
Signal to Quantization Noise ratio concept
Give me an A! Give me a D! Give me a converter! What have we got? An A/D converter! Go Team!
Let $X$ denote a standard Gaussian random variable with pdf $\phi(x)$ and complementary CDF $Q(x)$. Let $Y$ ...
- 20.9k
5
votes
Accepted
Is there any literature discussing PDF after quantization?
any discrete random variable has a p.d.f. that is a summation of dirac delta functions.
$$ p_\mathrm{y}(\alpha) = \sum\limits_i P_i \ \delta(\alpha - y_i) $$
where $\sum\limits_i P_i = 1 $.
if $y[n]...
- 21.4k
5
votes
Accepted
Why use a 1-bit ADC in a Sigma Delta Modulator?
First of all, because it's easy to build a 1-bit ADC. It's a comparator. It's literally the easiest ADC you can build. The $\Delta\Sigma$ ADC was invented (or, rather, published) in 1962¹ !
The 2-bit ...
- 32.5k
5
votes
Accepted
Why are we always interested in mean-squared distortion?
Consider a band-limited function $u(t)$ sampled at an appropriate sampling rate $f_s=1/T$ such that it is perfectly represented by its samples $u(kT)$. If those samples are quantized resulting in ...
- 92.5k
5
votes
Signal to Quantization Noise ratio concept
Thus, for a partial statistical characterization of the quantizer in terms of output signal-to-(quantization) noise ratio, we need only find the mean-square value of the quantization error Q.
All ...
- 13.3k
5
votes
Accepted
Quantization error standard deviation
In the case of uniform quantization, and under some light hypothesis for the signal, the error can be modeled as an additive IID signal, independent of the signal, and with uniform distribution ...
- 5,024
5
votes
Difference between ADC dynamic range and voltage resolution?
ADC resolution is the level of one quantization step in the units of magnitude desired (such as volts to refer to the input, or counts to refer to the digital output levels). The resolution is the ...
- 55k
5
votes
Accepted
How does a quantized signal represent all magnitudes?
You can’t recover, that’s what quantization error is.
Because the quantized values $q_1$ and $q_2$ are identical, recovering the exact original amplitude difference between $s_1$ and $s_2$ is ...
- 6,814
4
votes
Does delta-sigma ADC also reduce Gaussian noise on input signal to ADC or just quantization noise?
No! The ADC (delta sigma or not) can not reduce the uncertainty in the input. It sounds to me that your friend has not made up a real signal flow diagram and then formed equations. The answer to ...
- 425
4
votes
Is it theoretically possible to perfectly quantize a continuous signal?
I'd like to point out Heisenberg Uncertainty principle, based on which theoretical achievable precision is limited. It states that one can not measure two complementary qualities (e.t. here time and ...
- 1,976
4
votes
Accepted
Optimal amplitude of an $m$-bit sinusoid
The phase of the sinusoid does not matter: A phase shift of a sinusoid is equivalent to shifting it in time, which results in a time shift of both the quantized sinusoid and the quantization error. ...
- 13.7k
4
votes
Accepted
How we can quantize a sampled signal in MATLAB?
First you will need to determine the number of quantization levels. I am going to assume a power of two for digital convenience's sake.
...
4
votes
Accepted
Fixed Point Design Resources
Make your block diagram
At each point where significant quantization can happen, add noise
Analyze your system's behavior with that added noise
If you know that the quantization effects will be ...
- 13.3k
4
votes
Accepted
Unclear point about quantization
Quantization is a process of representing real values of a signal using integer numbers. That process results in loss of accuracy, which is determined by the selection of the smallest value of ...
- 406
4
votes
Oversampling in quantization
Let $x(t)$ be your continuous-time bandlimited signal, modeled as a WSS random process with a PSD of $S_{xx}(\Omega)$ in the band $\Omega \in[-W,W]$, $\Omega$ in radians per second.
Sampling $x(t)$ at ...
- 28.4k
4
votes
Quantization error standard deviation
The author is modeling quantization noise as being white (i.e., each sample is independent of previous or following samples) with each sample being a zero-mean, uniformly distributed random number ...
- 13.3k
4
votes
Accepted
Confusion implementing Quantization in MATLAB?
Why i am getting same quantized signal in xq2 and xq3,
Very poor choice of test signal.
A 10 Hz cosine wave sampled at 100 Hz has only 3 different values that keep repeating (in flipped in sign and ...
- 48.2k
4
votes
How does a quantized signal represent all magnitudes?
An Analog to Digital Converter (ADC) quantizes the input relative to its "full scale voltage". Typically you will need to scale the input signal so it fits reasonably well into range of the ...
- 48.2k
3
votes
Accepted
Why harmonic components appear only after a certain level when a signal is clipped?
Is this a well-known phenomenon?
Yes, of course. You will see harmonics as soon as your clip point is lower than the maximum amplitude in the time domain. The latter is a function of the relative ...
- 48.2k
3
votes
Accepted
How to Reverse Color Quantization?
Are there any algorithms that, for example, take neighboring pixels into consideration in order to determine a better estimation for each pixel?
That would essentially be a low-pass filter.
So, yes, ...
- 32.5k
3
votes
Accepted
A query on the non-uniform quantization
To make it more clear, I suppose your question is
Why it is said that the compressor gain at low input amplitudes is higher, while the step size of a nonuniform quantizer is small in that region. ...
- 4,315
3
votes
Is it theoretically possible to perfectly quantize a continuous signal?
No, and the reason is not so much a question of how fast one can sample a continuous-time signal (as the accepted answer and another one says) but rather the impossibility of representing a real ...
- 20.9k
3
votes
Is it theoretically possible to perfectly quantize a continuous signal?
Is it theoretically possible to perfectly quantize a continuous signal?
No. A quantization has an information content obviously countable as bits.
Now, if you have a continuously distributed 1D ...
- 32.5k
3
votes
Accepted
Lloyd Max Quantization and Clustering : Part 1
Different.
Lloyd-Max is a special type of scalar quantizer design which is optimized (in terms of MSE) to source pdf. Hence the quantizer is generally non-uniform.
Lloyd's algorithm (and the more ...
- 4,315
3
votes
Accepted
Quantization level versus bandwidth
Say you quantize a signal with $L=2^n$ levels. Then, every quantized sample is represented by $n$ bits. So, as you increase $L$, you need more and more bits to represent the samples. This means that ...
- 15.4k
Only top scored, non community-wiki answers of a minimum length are eligible