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65

The color burst is also an indicator that there is a color signal. This is for compatibility with black and white signals. No color burst means B&W signal, so only decode the luminance signal (no croma). No signal, no color burst, so the decoder falls back to B&W mode. Same idea goes to FM stereo/mono. If there is no 19 kHz subcarrier present, ...


26

In the absence of a valid color burst signal, the "color killer" circuit disables the color difference signals, otherwise you would indeed see colored noise. This is mainly intended for displaying weak signals in B/W without the colored noise. One step further is to mute the entire signal, substitute stable sync signals, and display a blue or black field ...


25

White Gaussian noise in the continuous-time case is not what is called a second-order process (meaning $E[X^2(t)]$ is finite) and so, yes, the variance is infinite. Fortunately, we can never observe a white noise process (whether Gaussian or not) in nature; it is only observable through some kind of device, e.g. a (BIBO-stable) linear filter with transfer ...


21

Isn't white noise supposed to have a flat magnitude response? (equal amounts for all frequencies) The expected magnitude response of white noise is flat (this is what JasonR calls the power spectral density). Any particular instance of a white noise sequence will not have precisely flat response (this is what JasonR's comment refers to as the power ...


19

You would generate bandlimited Gaussian noise by first generating white noise, then filtering it to the bandwidth that you desire. As an example: % design FIR filter to filter noise to half of Nyquist rate b = fir1(64, 0.5); % generate Gaussian (normally-distributed) white noise n = randn(1e4, 1); % apply to filter to yield bandlimited noise nb = filter(b,1,...


17

Roughly speaking, they are the amount of noise in your system. Process noise is the noise in the process - if the system is a moving car on the interstate on cruise control, there will be slight variations in the speed due to bumps, hills, winds, and so on. Q tells how much variance and covariance there is. The diagonal of Q contains the variance of each ...


16

You can use a standard inpainting algorithm. These algorithms replace marked pixels in an image with the pixel values that surround these marked pixels. The challenge here is to detect the grid (my tests seem to show that it is not a completely regular grid). So, I came up with this solution: from PIL import Image import requests from io import BytesIO ...


15

Math tools We can do the calculation using some basic elements of probability theory and Fourier analysis. There are three elements (we denote the probability density of a random variable $X$ at value $x$ as $P_X(x)$): Given a random variable $X$ with distribution $P_X(x)$, the distribution of the scaled variable $Y = aX$ is $P_Y(y) = (1/a)P_X(y/a)$. The ...


14

L1 norm minimization (compressed sensing) can do a relative better job than conventional Fourier denoising in terms of preserving edges. The procedure is to minimize an objective function $$ |x-y|^2 + b|f(y)| $$ where $x$ is the noisy signal, $y$ is the denoised signal, $b$ is the regularziation parameter, and $|f(y)|$ is some L1 norm penalty. ...


14

Noise is random, but like most random phenomena, it follows a certain pattern. Different patterns are given different names. Consider rolling a die. This is clearly random. Roll the die 1000 times, keeping track of each result. Then, calculate the histogram of the result; you'll find that you got each of 1, 2, 3, 4, 5 and 6 approximately the same number of ...


13

Your question is a bit harsh, because it's kind of vague. I will give you a few points, maybe it will help. What's the same? The intuitions behind both bilateral filtering and anisotropic diffusion are the same: averaging is good to remove random noise; averaging should only concern pixels that belong to the same region (in the sense that they are pixels ...


13

Intuition: The intuition is this: Your noise is some event or events that are rare, and that when compared to other events, look like outliers that shouldn't really be there. For example, if you are measuring the speeds of every car on the highway as they pass by you and plot them, you will see that they are usually in the range of say, $50$ mph to $70$ ...


12

You could form a statistical test, based on the autocorrelation of the potentially-white sequence. The Digital Signal Processing Handbook suggests the following. This may be implemented in scilab as below. Running this function over two noise sequences: a white noise one, and a lightly filtered white noise one, then the following plot results. Script for ...


12

Basic dithering without noise shaping Basic dithered quantization without noise shaping works like this: Figure 1. Basic dithered quantization system diagram. Noise is zero-mean triangular dither with a maximum absolute value of 1. Rounding is to nearest integer. Residual error is the difference between output and input, and is calculated for analysis only....


11

Starting at an even more basic level than the other (much smarter) answers, I'd like to pick up on this part of the question: This seems contradictory to me as on one side it is random then on the other side their distribution is considered normally distributed. Perhaps the issue here is what ‘random’ means? To be clear: ‘random’ and ‘normally-...


10

You're probably looking for the Hough transform or one of it's extensions. The simplest version of this transform is linear and appropriate for detecting straight lines. In the transformed space (Hough space), angles and distances are found as points where curves intersect. Libraries for calculating the Hough transform exist in C++ - OpenCV (Has ...


10

Wiener deconvolution is an approach to solve the deconvolution problem that relies on the filter proposed by Wiener. The equation is the same in denoising and deblurring, except that the filter $G$ (to stick with Wikipedia's notations) that you should use is different. To make things clear: denoising consists in the case where the degradation kernel $H$ is ...


10

Phase Noise and Frequency Noise are not two different noise sources, they are artifacts of the same noise, it is just a matter of what units you want to use. Frequency and Phase are directly related as frequency is phase changing with time, so if you have one you will always have the other; frequency and phase are related by derivatives and integrals: the ...


9

"Noise" in this context refers to anything unwanted added to the signal, it doesn't necessarily mean it is gaussian noise, white noise, or any random well-described process. In the context of quantization, it is a purely algebraic argument. One can view quantization as the addition of an unwanted signal ("noise") equal to... the difference between the ...


9

Just as a small addition to Jason's answer: usually you need to generate bandlimited noise with a given variance $\sigma^2$. You can add this code to the code given in Jason's answer: var = 3.0; % just an example scale = sqrt(var)/std(nb); nb = scale*nb; % nb has variance 'var' Note that you have to do the scaling after filtering, because in general ...


9

Because each step in the processing chain is linear we consider a case with only noise and no coherent signal. Denote the noise $\xi(t)$. The $I$ and $Q$ signals are \begin{align}\ I(t) &= \xi(t) \cos(\Omega t) \\ Q(t) &= - \xi(t) \sin(\Omega t) \, . \end{align} We express the effect of the filter as a convolution with the time response function $h$, ...


9

Is it possible to reconstruct the original pure signal? No, that is information-theoretical impossible. Also, that signal doesn't exist, probably, to begin with ;) However, you can definitely increase the the SNR simply by averaging; that becomes pretty obvious when you consider the signal of interest to be correlated within your recording, whereas your ...


8

The easiest approach: First apply Median filter for salt and pepper noise, and then use Gaussian blur to eliminate Gaussian noise.


8

A speech communication channel as used in telephony typically has a frequency response of 300 Hz to 3 kHz. Although this rejects a lot of the energy in normal speech, intelligibility is still quite good - the main problem seems to be that certain plosive consonants, e.g. "p" and "t", can be a little hard to discriminate without the higher frequency ...


8

You could try low-pass filtering the input signal to get smoother zero-crossings (or even band-pass filtering if you have a good idea of the frequency location of the sine wave). The risk is that if sample-accurate phase information is essential to your application, the additional lag from the filter might be a problem. Another approach: instead of trying ...


8

For a start, any non-linear system will not have an easily-identifiable frequency response. So, it's really a nonsensical question. I intend no offense; nonsensical questions are often the most enlightening! However one way to try to answer your question is to assume that the LTI filter involved is the mean (rather than the median) of the windowed data. ...


8

When you say that the "information content may remain the same," do you mean the information in the total signal, or the information of the desired signal? Hopefully this will answer both cases. I know Shannon entropy much better than Kolmogorov so I'll use that, but hopefully the logic will translate. Let's say $X = S + N$ is your total signal ($X$), ...


8

SNR stands for Signal to Noise Ratio. It is a ratio and as such does not have any units, it describes the proportion of signal to undesired noise. There is no single correct measure of SNR, it differs depending on the application. In the equation you have given, the SNR is broken down in the following way: 1) Calculate the power ratio $$\frac{\sigma_s^2}{\...


8

Intuitively this is true, because averaging a zero mean noise processes approximates its expectation value - which is zero. More rigorously: If the signal $x$ that you want to observe (estimate, actually) is constant for all observations $y$ we can write the $n\text{th}$ observation as $$ y_n = x + r_n $$ where $r_n$ is the noise which is different for ...


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