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Auto-correlation function, an inverse problem

Let's look at the case $x[n] \in \mathbb{R}$, where $x[n]$ is real. Autocorrelation is basically convolution of the signal with it's time inverse. This can be easily expressed in the frequency domain....
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6 votes
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Recommended Resources / Literature Search Terms for a Solutions to a Specific Kind of Multi Harmonic Signal Structure

If I understand this problem correctly you have access to 2 signals: Noise Signal - $ w \left[ n \right] $. It is composed of a linear combination of harmonic signals. Something like $ w \left[ n \...
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5 votes

Algorithm for detecting the time where the signal is above a threshold

There is a book by Basseville and Nikiforov called "Detection of Abrupt Changes : Theory and Application" that they released to the public as a PDF several years ago (it's out of print, now, I believe)...
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5 votes

Is R suitable for digital signal processing

Since the bulk of R’s DSP capability comes from the signal package which was ported over from the open source project Octave (itself influenced by MATLAB), there's no intrinsic limitation of R. What ...
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  • 1,690
5 votes

Spikes in time series

I would try a median filter. Let your original signal be $f[n]$. Median filter $f[n]$ using $N$ pixels, where $N > 2 \times S + 1$, where $S$ is the maximum number of samples in the spike. The ...
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  • 3,591
5 votes
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Show That the Power Spectrum Density Matrix Is Positive Semi Definite (PSD) Matrix

Pay attention that for a Scalar Random Process the Power Spectrum Density is non negative. Namely, let $ y \left[ n \right] \in \mathbb{R} $ be a WSS Random process with its Auto Correlation function ...
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5 votes

Auto-correlation function, an inverse problem

There is in general, as @Hilmar's answer points out, no unique solution to the question of a sequence that has the given perodic autocorrelation function. In the simplest case, that a shifted ...
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5 votes

Comparing multiple signals for similarity

...best results come from a weighted ensemble of techniques... Maybe they do, depending on the application. But each one of the similarities mentioned, is equivalent to the other at least when we are ...
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  • 10k
5 votes
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How would you use machine learning for peak detection?

To be honest, I don't think CNNs, RNNs and LSTM are useful for this kind of problem – a bandpass filter followed by a threshold would be. Now, that would have three parameters: Lower cutoff ...
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5 votes
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Synchronizing 2 time series signals at slightly different sampling frequencies

If you are confident that the relationship is a ratio of integers, then resampling would be a fine approach. One would be matched to the other by upsampling by 1008 and then downsampling by 996 which ...
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  • 36.2k
5 votes
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Impulse response of Time Varying Channel

In the context of wireless communications, the channel impulse response (CIR) is often estimated indirectly via the time-varying transfer function (TVTF) $H(t, f)$, defined by: $$ H(t, f) = \mathcal ...
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  • 2,102
4 votes

Issue with the time vector returned by $\tt signal.spectrogram$ function

The default parameters of signal.spectrogram are: nperseg = 256 noverlap = nperseg/8 = 32 This means that: The length of ...
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  • 10.4k
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What is the type of these signals?

Types of signals: According to their range set (values): Real Valued, Complex valued ; According to their dimensions: Scalar, Vector ; According to their values: Continuous Amplitude, Quantized ; ...
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4 votes
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Index of stationarity of a time domain signal

This a very complicated question, and I would say a still open topic. The concept of stationarity is manifold, from pure statistics to applied DSP (strict, strong, wide-sense, quasi-stationarity, ...
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4 votes
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How to Mesure the smoothness of a signal

A number of features will return some estimate of the smoothness of a signal. In general, these are all measures of dispersion with slightly different takes on "dispersion". The choice of the "right" ...
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  • 10k
4 votes

Window period(overlap) and FFT

In addition to what others have already said, I'll try to answer it from a purely practical point of view (this is also a variant of the overlap-add technique). If your FFT length is 2048, then an ...
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4 votes
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Linear Predictive coding vs AR modeling

LPC reduces to AR modelling only if the stochastic time process is stationary (does not change distribution parameters over time) and ergodic (average over time is equivalent to mean of ensemble ...
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4 votes
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Why Cramér spectral representation and not DTFT for stochastic process

I will introduce some terminology and intuition that will be helpful when reading other references. It will be neither complete nor completely rigorous. The measures that we first encounter in real ...
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  • 561
4 votes

Help with denoising signal and periodogram analysis resources

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 ...
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3 votes
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Terminologies - lags, order in time series model

Q1: should the model generate a time series of length 'N=16` i.e, would the output of the above model $\mathbf{y} = [y_1,y_2,\ldots,y_N]$ contain 16 elements where $n = 1,2,\ldots,16$? If one thinks ...
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3 votes

Difference between Gaussian and moving average filters for peak detection and doppler shift detection?

A centered moving average filter is a finite impulse response (FIR) filter that affects the same weight to all the samples in the window. If you only care about time domain properties, and do not care ...
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3 votes

How does one calculate a pole-zero plot?

Suppose you are given a system with transfer function $$H(z)=\frac{(1-3z^{-1})(1-7z^{-1})}{(1-4z^{-1})(1-6z^{-1})} $$ Poles Poles are the values of $z$ for which the entire function will be ...
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  • 367
3 votes
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How do I convert a timeseries to a different frequency band?

Mathematically, shifting the frequency of a signal is pretty easy: Following @OlliNiemitalo's answer, the 0.003 frequency shift can either be done in time domain, or frequency domain. I recommend ...
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3 votes
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What is the filter with the less phase shift?

Technically, the most reactive filter is the all-pass filter with a gain of 1, this filter has no phase shift at all. But it is not a really useful filter. Here's what you need to take in account : ...
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  • 3,544
3 votes
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How to make a Power Spectral Density Plot in R

From further research I've discovered that the frequency is given by the index of the FFT multiplied by the sampling rate and divided by the size of the array. And the amplitude is the magnitude of ...
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3 votes
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How do I obtain the fourier series coefficients for a signal obtained by multiplication of two signals of different frequency?

The product $x(t)y(t)$ of two periodic signals with fundamental periods $T_x$ and $T_y$ is not a periodic signal unless $T_x$ and $T_y$ are rational multiples of one another; that is, $T_x = aT_y$ ...
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3 votes
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Is this statement correct from DSP aspect?

It's almost a matter of philosophy, i.e., difficult to argue hard facts. On the one hand all the features you mention can be extracted from the raw signals. So in theory the network should be able to ...
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  • 2,268
3 votes

Help with denoising signal and periodogram analysis resources

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 ...
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  • 1,018
3 votes
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Good test for periodicity between signals

Something you could do is calculate the FFT of both signals and define some criterion for periodicity. For example, you pick the highest component of each FFT and compare the two (one from each signal)...
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  • 162
2 votes

Algorithm for detecting the time where the signal is above a threshold

For discarding events where the signal is not very different from the threshold (special case: oscillation), have you considered using a hysteresis? If the signal rises above the threshold ($t_{on}$-...
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