So I've been posting loads on here recently and it's been really helpful. Apologies for the short number of posts in a few days. Anyway, I've been simulating the Bit Error Rate for different coding schemes recently and I am now simulating a convolutional code with a code rate of 1/3 and it is decoded using a Viterbi decoder which I think I've finally got working.
I need to assume the encoded signal is modulated by BPSK and is subjected to AWGN, simulated by adding Gaussian noise with a variance of:
Ο^(2) = N0/(2Eb)
where N0 is noise power and Eb is energy per bit
Now, previously I've done this by doing:
SNRdb = 1:1:12;
SNR = 10.^(SNRdb/10);
corrupted_signal = (sqrt(SNR(j)) * codeword) + randn(1, length(codeword));
So I define the SNR values I want to use, in decibel form. Convert this to a linear form and then for each SNR value, the received signal with noise is equal to the square root of the current SNR value multiplied by the incoming signal. This is then added to a randn vector which has the same length as the incoming signal and each value is drawn from the normal distribution.
In this case, I assume that sqrt(SNR) is the standard deviation, so in the case of:
Ο^(2) = N0/(2Eb)
We'd instead have:
corrupted_signal = (sqrt(0.5*(1/SNR(j))) * codeword) + randn(1, length(codeword));
But that can't be right surely as it's having the opposite effect as intended? The output of the entire sqrt bit is decreasing as SNR increases meaning that there's a higher chance that bits could be flipped when decoded. How do I go about incorporating this variance into my algorithm when adding noise?
I am trying to use LQR to resolve a continuous-time / finite horizon problem, but with a non Gaussian noise (dWt in image) with jumps in the state process dxt. The system is fully observable and the cost function J(u) has a cross state/control term 2.x't.N.ut. If there was no noise in the state process, my understanding is that LQR would definitely be the optimal solution.
Also, if there wasn't 2.x't.N.ut in the cost function, and if the noise was Gaussian I think I could use LQG (with a zero observation noise) to show that LQR is the optimal solution.
https://preview.redd.it/tfzu5oe2vwz61.png?width=494&format=png&auto=webp&s=01e302970f26e1f1430e2da795d52c2cf94dc1eb
To overcome the non-Gaussianity I found this wiki page quite useful (https://en.wikipedia.org/wiki/Separation_principle_in_stochastic_control), as it mentions a generalization of LQG to non-Gaussian noises with jumps. However in that page there is no cross state/control term 2.x't.N.ut. And in none of the courses about LQG that I could find as well...
Does anyone have an idea how to show that LQR is the optimal control when the state process noise is not Gaussian and when there is a term 2.x't.N.ut in the cost function?
I am wondering what order is better when adding effects to LR images for training a model (BasicSR). Which order would likely train images to get overall better results? Thanks.
I am having task about adding Complex gaussian noise in to signal in time domain. I already created complex Gaussian. But i dont know how to add it into Signal. It is in time domain. How to create Gaussian signal in time domain from sequence of complex number?
im not sure how to design a filter that can filter out the noise from a pulse signal generator being sent to the rectangular 16 QAM Modulator that than passes through the AWGN, rectangular 16 QAM Demodulator and through a time scope. Im using the filter designer and ive tried out the butterworth filter but the recovered signal is not the same as the original signal.
ISBN: 9780387989938, 0387989935
URL: https://www.springer.com/gp/book/9780387989938
Thanks for inboxing in advance.
Hi! I am looking into performing Gaussian Process regression on a dataset that was collected over several years. As you might imagine, old and new training data points with similar features do not necessarily follow the same trend and do not have the same value/label.
I would like to give more importance to newer data when making a prediction in a region where new and old data overlaps. However, some regions of the domain of the dataset is only covered by old data. In this case, the prediction should only be based on this old data, but have a higher variance/uncertainty.
Is there any way to associate an importance weight (or different noise) to every data used to train/fit the Gaussian Process regressor? And is there a Python library that already supports that? Any pointers / recommended tutorials/readings would be appreciated. Thanks!
I haven't delved into statistical signals processing at all so please be patient with me if this is a rudimentary question. I've heard the phrase "adding noise to a signal/noisy signal" thrown around a lot but never really understood what it means in terms of signal value. There are two operations in particular that I typically come across: adding noise to a signal and removing noise from a signal. I don't know how either operations are done in practice, though that is what I'm trying to figure out.
I'd like to take a shot at the former operation and describe what I think a noisy signal is. From statistics, I learned that a probability distribution is a function that assign 'weights' to values (in the discrete sample space) or range of values (in the continuous sample space). The weights tell you how likely a value (or a value from an interval) will 'appear'/be 'selected'/'occur'/'observed' (in the sense that the side of a coin 'appears' or a red marble is 'selected' or the number of people are 'observed' in a time interval or a voltage value 'occurs' in a signal).
Say you had a signal x(n) where 'n' is some number in the range n=0,1,...,N. Assume the noise has some probability distribution D(t), which can be Normal (Gaussian), Uniform, etc. but note that 't' is continuous. A noisy version of x can be obtained by taking the value that is 'observed', D(t) and adding it to x(n) for all possible values of 'n'.
Hi,
I was wondering how a timeserie could be gaussian without being white?
I`ll explain why. Let says W is a not-exactly-white gaussian noise. It's not exactly white because it is band limited in high frequencies. If I could sample this noise very fast, outside of it's band, wouldn't I see that a sample at time t is now correlated with its previous sample at time t-1? Then sample at t would be deterministic, since there is no information between t and t-1 at this sample rate.
Suppose I have time series data that is accurately modeled as gaussian white noise with mean mu and variance sigma^2. I would like to write down a probability density characterizing the probability of observing a periodic signal in the gaussian noise. The 6th slide here: https://astrostatistics.psu.edu/su12/lectures/TSA_EDF_SumSch.pdf
provides a density, but I'm struggling to understand where it comes from
Hey all, first time posting here. My job is requiring me to look into DSP, something which I have essentially no background in aside from an introductory Signals & Systems course I took nearly 4 years ago.
I want to corrupt a simulated "ideal" signal with Gaussian white noise. I have the SNR, so is it as simple as adding the gaussian random noise to my signal, or is it more complex? This is what I'm doing right now in MATLAB:
noise = randn(N,1);
noise = noise/(abs(max(noise));
noisy_signal = signal + mean(signal)/SNR * noise;
Is this valid? It seems too simple to just be this, but all the resources I've found so far focus more on how to generate the random distribution itself, rather than how to corrupt the signal with it.
Any help is appreciated.
I am doing some stochastic ODE simulations (using RODEProblem) where the added noise zero mean Gaussian white noise with a given covariance matrix. Initially misread the description of CorrelatedWienerProcess and only noticed that it gives Brownian instead of Gaussian noise when plotting the noise realization of a simulation. However the listed noise processes do not list Gaussian white noise. It is only stated that the default is Gaussian white noise, however when doing a simple simulation using f(u,p,t,w) = w and plotting the corresponding noise yields this:
https://preview.redd.it/z0clru3wwue31.png?width=600&format=png&auto=webp&s=80030434f77f07fafdf4ac2b4eb4b2bf463e6624
which is not zero mean or Gaussian (with a constant variance). Does someone know how to actually have Gaussian white noise (with a given covariance matrix) in stochastic ODE simulations?
If I have a signal that I measure with an antenna (e.g. FM radio station or something in radar), the standard practice is to do quadrature demodulation and look at the signals in their quadrature and in-phase forms. Then, the usual model for receiver noise is a circularly-symmetric Gaussian noise. Does this come from a physical receiver noise model for the real signal measurements after it gets transformed to its complex representation? Is it possible for a real signal after demodulation to contain non-circularly symmetric Gaussian noise? I'm trying to understand if something like a widely linear estimator makes sense when the original data came from a real signal.
What is the proper way of adding gaussian noise to an image?
If my image has 100 pixels, do I create 100 noise pixels that follow the specified gaussian distribution and just add this noise to original image?
Or does it involve some sort of convolution?
Thank you so much.
From discrete-time Gaussian white noise, how to obtain a white-ish signal whose magnitude stays under 1 (so I can play it back as audio)?
I know of some ways to magnitude-limit audio-signals in general, but I don't know what they would do to the spectrum of white noise?
I'm trying to add a Gaussian noise in a image with noise level of Ο = 40 , i got this function in c++ :
void fpAddNoiseGaussian(float *u, float *v, float std, long int randinit, int size)
{
srand48( (long int) time (NULL) + (long int) getpid() + (long int) randinit);
//srand48( (long int) time (NULL) + (long int) randinit);
for (int i=0; i< size; i++) {
float a = drand48();
float b = drand48();
float z = (float)(std)*sqrt(-2.0*log(a))*cos(2.0*M_PI*b);
v[i] = u[i] + (float) z;
}
}
However when i try to compute the RMSE after denoising i get different results between the matlab version and c++ version
this is the equivalent (in my opinion) function i tried to recreate in matlab
for k = 1:height
for j = 1:width
noiseR = sigma*sqrt(-2*log(rand()))*cos(2.0*M_PI*(rand()));
noiseG = sigma*sqrt(-2*log(rand()))*cos(2.0*M_PI*(rand()));
noiseB = sigma*sqrt(-2*log(rand()))*cos(2.0*M_PI*(rand()));
Im_wnoise(k,j,1) = double(im(k,j,1)) + noiseR;
Im_wnoise(k,j,2)= double(im(k,j,2)) + noiseG;
Im_wnoise(k,j,3) = double(im(k,j,3)) + noiseB;
end
end
and Thanks in advance !
I'm working on making a network more robust in its classification given limited data, and am exploring network augmentation techniques to do so. Do you think multiplying network activations with noise from a tight gaussian distribution would help push away that decision boundary, or would it cause more trouble? For stability, I am using BatchNorm.
Is there a function to get gaussian noise in Processing rather than Perlin noise? By this I mean that I want the noise pattern to be random, 0's next to 1's possible rather than gradual shifting, but still based on a seed like Perlin noise. randomGaussian is the only think I have found, but it doesn't say that it is seed based. Thanks.
Adding Gaussian noise to the hidden representation would have a regularising effect and make the decoder interpret the hidden codes as filling a smooth space, without a KL divergence penalty on the loss. I know the KL bound loss makes it a neater solution in theory, and that the variance of the added noise depends on the inputs rather than being fixed, but in practice these things are tricky. If the aim is to regularize, is adding Gaussian noise not an attractive and simpler solution?
I have multiple copies of the same noisy signal. From this I can see that the noise is not gaussian. Where should I look for denoising methods that take into account the empirical noise distributions?
If it matters, the true signal should be sparse in the frequency domain (eg ~10 nonzero entries in a ~1000 point sample).
In most of the signal models, why do we assume the noise to be Gaussian / complex circular Gaussian?
