5

There are many way to tackle this: Time - Frequency Analysis Classic choice would be a spectrogram but probably a Fourier Synchrosqueezed Transform would do a better job (Have a look at even more advanced approaches ssqueezepy - Synchrosqueezing, wavelet transforms, and time frequency analysis in Python by @OverLordGoldDragon). Parameter Estimation Methods ...


4

Wouldn't this be equivalent to discarding all those frequencies in the input layer? No, it won't for 2 facts: Just like a CNN isn't a linear regression due to having non linear function in between. So the Activation Layers on the frequency domain mean things are not propagated linearly in the forward pass. The filters are adaptive (Learned). Namely each ...


4

This is an open discussion. In my opinion, any field we couldn't figure near optimal solution (And in most cases we only have Linear Optimal solution) using Deep Learning will replace classic methods given enough data to work with. The power of data driven features vs. intuitive (Though mostly right yet never cover everything) will prevail. I don't see it as ...


4

Firstly, I am confused if I am supposed to filter my signals to get rid of any frequencies above the Nyquist frequency. My sampling frequency is 32Hz and my time series is somewhat noisy and has some artifacts. I am also unsure of which filter to select for this. That ship has sailed. Let $S=\left\{\left.\alpha e ^{i(\omega t+\varphi)}\right|\alpha > 0, ...


4

I've kind of grouped your subjects into larger overall subjects. Note that there's a lot of overlap here, with the possible exception of actually making it work in a microprocessor (except -- in my opinion the best person to implement something is someone who understands it. So -- overlap). Specifically, you could claim that it's all applied math. Or all ...


3

The operator $ \mathbb{E} \left[ \cdot \right] $ is the Expectation Operator. In the context above it means you run over all the pairs of x, y and average the values.


3

Yes. The FIR filter model you're used to is a series of Neurons with weighted inputs, and a linear activation function. In other words, a standard FIR filter is a neural network. I mean, it's called "CNN". The C is exactly the operation a filter does.


3

The Fourier transform of a sampled (discrete time) signal can only have information between -Fs/2 and +Fs/2, and that information repeats such that X(f +Fs) = X(f), such that Fs is the sampling frequency. This means that when sampling an analog signal, you probably want to low pass that signal to make sure it has no frequencies above Fs/2, the Nyquist ...


3

You should use the one you need for your problem, when you know which components of your signal are of interest to you. Let's say you have in your electronic editing an ADC digitizing 40M samples per second to study a heart rate of 70 beats per minute, you are very likely to work with useless information, that's why it will be better to down-sample your ...


2

i am also quite skeptical of the presented image restoration. in audio, there are papers like this and this. i am sure there are more. i just stumbled upon them by googling "AES interpolating gaps in audio data".


2

These Images are FAKE !!! There is absolutely no way, no algorithm, no nothing that exist that can tell you whether the eyes of a girl are blue or black by just looking at her lips !!! You can guess, something, good or bad, based on your prior training and the probabilities based on that, but that's just a guess. The fact that the synthesized images look so ...


2

Following undergraduate lectures serve as the basis: 1-) Signals and Systems (Oppenheim's book) 2-) Probability and Random Processes (Kay's book) 3-) Linear feedback systems (Ogata's book) However, they can fall quite theoretical (without practical focus) and also include much more material than necessary for specialised applications. For example, just to ...


2

Some use the Frequency-Time representation as an additional source and try to do what you ask. Some papers on that: Single Channel Source Separation with ICA Based Time-Frequency Decomposition (PDF Source). Musical Source Separation: An Introduction. By the way, at the end, probably Deep Learning will yield the best results for this kind of task. Pay ...


2

This is an interesting question. For answering it I will assume a time sampled signal. The way I see it, it something like Image Segmentation where indeed we have many methods which require little or no explicit assumptions. So, the first things comes to mind it to cluster data by its value. Yet there won't be any significance to the time axis which is ...


1

If you are interested about the state of the art I would suggest you to read about chimes. This was submitted to the Deep Noise Suppression challenge at interspeech 2020. You can also search for the other submissions if you want, you can see the results of the challenged are here. Links accessed at Aug 11th 2021


1

Question 1: Yes you are correct, the power spectral density is the power distribution per unit frequency so is a continuous function of frequency. Question 2: The single number as given can be an estimate of total power. What they gave is completely incorrect starting with the formula as given: $$P = lim_{T \rightarrow \infty}\frac{1}{T}\int_0^T|x(k)|^2dt$$ ...


1

Your signal (with initial par x0 =0.1) is already noise like and high frequency. It will be hard to distinguish it from the added white noise... One thing you can do is to interpolate (resample) the time series by a large enough factor and then later add the white noise. This will artifically help to separate the noise spectrum and your signal spectrum but ...


1

Well, when you're training something against a dataset, you're training it to work on that kind of data. Since we have no idea of what the neural network "uses" from the input images to fulfills its purpose, these might be things where our computer graphics aren't quite like real-world images. We're "trained" with real-world imaging, ...


1

In the case above the mathematics are pretty simple: Use cascaded Haar filters to extract features from the image. You may have a look at Haar Cascade Classifiers in OpenCV Explained Visually. Use Ada Boost to generate an Ensemble of classifiers to detect a face. For overview of this approach (First done by the Viola Jones Detector) you may have a look at ...


Only top voted, non community-wiki answers of a minimum length are eligible