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8 votes
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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....
Hilmar's user avatar
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7 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 ...
A_A's user avatar
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7 votes
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In time series analysis, is taking a multi-period difference equivalent to a band-pass filter?

What you are describing is two cases of a more general form of a Comb Filter (I encourage you to go through the link, but I'll adapt to your particular case here): $$y(n) = x(n) + \alpha x(n-K) $$ ...
Jdip's user avatar
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6 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 ...
dsp_user's user avatar
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6 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 ...
Marcus Müller's user avatar
6 votes

What is the proper way to compute a real-valued time series given a continuous $1/\sqrt{\omega}$ spectrum?

As an alternative to the frequency sampling method discussed in Dan's answer, I will suggest another approach based on the analytical expression of the inverse discrete-time Fourier transform (IDTFT) ...
Matt L.'s user avatar
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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 ...
geometrikal's user avatar
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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 ...
Dilip Sarwate's user avatar
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 ...
Dan Boschen's user avatar
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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 ...
Robert L.'s user avatar
  • 2,222
5 votes

How to estimate the local trend in a signal?

Start simple: just use a 1-D median filter of an appropriate length. If I do that with a length of 100 samples, I get the following for your first signal. The top plot shows the original signal (blue)...
Peter K.'s user avatar
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5 votes
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What is the proper way to compute a real-valued time series given a continuous $1/\sqrt{\omega}$ spectrum?

Bottom Line OP's approach is closest to the "Frequency Sampling Method" Use a linear frequency grid, not logarithmic. Populate the spectrum on both the positive an negative frequency axis, ...
Dan Boschen's user avatar
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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, ...
Laurent Duval's user avatar
4 votes

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 ; ...
Fat32's user avatar
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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 ...
jojeck's user avatar
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4 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 : ...
Ben's user avatar
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4 votes
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How to measure 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" ...
A_A's user avatar
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4 votes
Accepted

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 ...
Jonas Schwarz's user avatar
4 votes
Accepted

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 ...
Matthew Ciaramitaro's user avatar
4 votes
Accepted

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, $T_x = aT_y$ ...
Dilip Sarwate's user avatar
4 votes
Accepted

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 ...
Joe Mack's user avatar
  • 616
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 ...
Marcus Müller's user avatar
4 votes
Accepted

How to align timeseries by decimating while preventing aliasing?

scipy.signal.decimate applies an anti-alias filter before downsampling. See the documentation. Alternatively, you can use the resample_poly function if you need ...
Jdip's user avatar
  • 6,300
3 votes

How to measure the smoothness of a signal

Hurst exponent is a good option. For a better answer you must better explain your objective. For example if you are comparing signals and if they have the same length, amplitude, sampling frequency ...
Filipe Pinto's user avatar
3 votes
Accepted

Pattern recognition in time series 4x3000 vector

Assuming your time series are the same length, take your data and produce spectrograms, $S_k$, for each row of the $4 \times 3000$ data matrix $D$ that you have. Since these individual time series ...
spektr's user avatar
  • 263
3 votes
Accepted

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 ...
Peter K.'s user avatar
  • 25.9k
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 ...
Laurent Duval's user avatar
3 votes
Accepted

Why doesn't law of large numbers apply to this stationary time-series?

I believe that you are thinking that each value of $X_t$ is determined by a different realisation of $Y$, which in this example is not true. Suppose that $Y$ is the value that comes out from a dice ...
Tendero's user avatar
  • 5,020
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 ...
Florian's user avatar
  • 2,463
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 ...
Dan Szabo's user avatar
  • 1,038

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