The Fourier transform decomposes a signal (a function of time) into frequencies, giving the energy at each frequency.
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10 views
How to generate synthetic data with specific spatiotemporal correlation
My dataset represents a field evolving over time, so has dimensions [X,Y,T].
I would like to generate synthetic data with the same autocorrelation structure and spatial correlations as the real data (...
0
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0answers
21 views
Need help understanding output of a periodogram
In my effort to understand the output of a periodogram I created a series (s) where 1,1,1,1,1,1,1,1,1,10 is repeated 100 times and then created a periodogram of this series using the following R code:
...
0
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1answer
75 views
Discrete Fourier transform of an exponential decay
I have a vector with an exponential decay signal, using Numpy:
t=np.arange(128)
a=0.1
decay=np.exp(-a*t)
I would like to compute the discrete Fourier transform (...
0
votes
1answer
102 views
Forecasting with ARIMA ( Training and Test Data split)
I have an hourly time series of the average parking occupancy with data available from September 2017 up until June 2018. I would like to use the ARIMA model with external regressors to produce a ...
4
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0answers
94 views
Fourier transform of a Gaussian process
I would like to discuss and ask a question regarding the Fourier transform of a Gaussian process, if it makes sense.
For that purpose, let me describe the following situation.
Let $z(s)$ be a ...
1
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0answers
25 views
Sampling from characteristic/moment generating function
Suppose I am given a probability distribution only via its characteristic or moment generating function and I want to sample from that distribution to generate paths in a Monte Carlo simulation. Is ...
0
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0answers
17 views
Finding common trends in time-series
I have a 10 relatively noisy time-series. I want to check if there are any similar trends in the 10 sets.
My simple way of initially looking would just be to cross-correlate each time-series with ...
0
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0answers
49 views
Applications of FFT algorithm in statistics? [duplicate]
Are there any applications of the FFT algorithm in basic statistics i.e.: estimating a density distribution?
I would like to learn more about it - and it would be nice to work on an actual example ...
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0answers
15 views
Fourier Transform based imputation
Fourier Transform based imputation
Can any body please assist me in understanding the Fourier Transform based imputation algorithm shown in Figure.
I am struggling to understand ts and te.
Link of ...
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0answers
11 views
How does the variance of a simulated Gaussian random field scale with the number of terms in the Fourier decomposition?
I numerically simulated a Gaussian random field and am trying to verify that the program is working correctly. One way is to check the variance of the result vs. the theoretical prediction. However I'...
2
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0answers
16 views
Linear regression on circulant matrices
I am reading the paper on High-Speed Tracking with Kernelized Correlation Filters
and I am a bit stuck on the equivalence of Ridge regression in the frequency domain. Minimizing the typical equation ...
0
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0answers
74 views
How to interpret the Output of the following ARIMA model
How to interpret the output of the below ARIMA(with Fourier Terms) code
y <- msts(ts(dataAR$Total[57:331]), seasonal.periods=c(30.4375,91.3125))
Model
...
2
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0answers
28 views
Time series/ ARMA Simulation
Given: I have a question, given a continuous real spectral density f(w), -infinity
my idea:
I would folding, discretize and truncate the spectral density to get a real (one-sided) discrete spectral ...
0
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0answers
21 views
Standardization of cyclical features for Clustering
I am about to start a project in data mining sales data using the well-known algorithm, t-SNE.
Specifically, I have 4 millions of observations and 75 attributes for every sale.
A graphical example ...
0
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0answers
90 views
FFT machine learning model for different rotation speeds
I am working on a machine learning model, that can classify different failure patterns of a rotating machine / motor based on a supervised approach. My features for the model are based on the ...
0
votes
1answer
106 views
Calculating right values of Periodogram using Fourier Analysis
In the book, Economic Cycles: There Law and Cause By Henry Ludwell Moore, he plots Periodogram of rainfall of Ohio valley. He uses 72 years data (1839-1910) and tries to find the most dominant cycle ...
1
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1answer
241 views
tbats() model not capturing seasonality (weekly data)
I have below 4 years of weekly data which has complex seasonality of varying seasonal length.
1) My first question is what should be the correct assigned frequency for this series (frequency() comes ...
0
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0answers
22 views
Full frequency space description of a continuous-time random process (e.g. signal) in
I don't know if signal processing or math would be a better forum, but I'll start here.
Consider an ensemble of stationary random processes $x(t)$ that has the following properties:
The PDF is $P[x]$...
3
votes
1answer
257 views
Proof of Herglotz Theorem in Time Series Analysis
I am studying time series, following Time Series Theory and Methods by Brockwell and Davis. I am reading the proof of the Herglotz Theorem, I have the following questions.
First, the proof given in ...
3
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0answers
105 views
Kernel density estimation with FFT for a univariate non-parametric regression
The non-parametric regression model to be estimated looks like the following
x_t = b(x_t-1) + epsilon_t
Forfinding the optimal bandwith h in the kernel ...
1
vote
1answer
60 views
Spectral density and Riemann Stieltjes Integral
I am confused with a part about spectral densities. I found it in Time Series Theory and Methods by Brockwell and Davis.
I don´t understand how is applied the Riemann Stieltjes Integral in this ...
0
votes
2answers
90 views
Is this a well-studied problem? Problem: Optimally unlagging multiple time-series
Is the problem of optimally lagging/unlagging multiple time-series with integer lags to maximize a sum of pairs of cross correlations or coherence an already well-studied problem? If so, references? ...
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0answers
30 views
Model Specification with dlmModTrig
I'm trying to figure out how to fit a dlm model to highly seasonal data (traffic counts per hour). The final goal is to determine the effect of a policy intervention that happened at time point x.
My ...
1
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2answers
105 views
Power spectral density of the output of a linear time invariant system with a weakly-stationary process
Please note that I have no background whatsoever in Fourier analysis and very little in time series.
This is exercise 2.10 in Theodoridis' Machine Learning:
Show that the autocorrelation of the ...
1
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3answers
937 views
Spectral Analysis in R - the periodogram
I am doing a spectral analysis in R using the spec.pgram() function. Suppose I have observations for $y_1$ to $y_n$ which are a time series with annual observations....
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0answers
24 views
How to interpret uncertainties in interpolated and smoothed timeseries?
I have a years worth of surface reflectance data, collected daily via satellite. However, some days are totally cloudy, so there were no observations.
That being said, I use linear interpolation to ...
9
votes
1answer
175 views
Why are random Fourier features non-negative?
Random Fourier features provide approximations to kernel functions. They're used for various kernel methods, like SVMs and Gaussian processes.
Today, I tried using the TensorFlow implementation and ...
0
votes
1answer
37 views
Generating time series for electricity demand
I'm working on a project, trying to model electricity consumption and generation from a bunch of PV generators to see how much of the demand can be satisfied by the production in the "town".
Most ...
2
votes
0answers
172 views
How to define a loss function for discrete fourier series?
In each batch there are 8000 sample points, and I apply discrete Fourier transform on them. The original samples are real valued, so only the half of the result is needed. The end result is 4000 ...
0
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0answers
89 views
Modeling trend and seasonality with Fourier basis and a time and intercept component
I am trying to model a time series $Y$ (for prediction) with a linear model based on a Fourier basis and a trend based on time $t$. It is clear that $Y$ has both seasonal and linear trend ...
3
votes
0answers
30 views
Representation of Noise in Fourier transform
I perform an experiment where I sample $M(k)$ which is in theory related to $|f(x)|^2$ via $M(k)=\int e^{ikx}|f(x)|^2\,dx$. I perform the discrete FT on my data in order to obtain $|f(x)|^2$. Without ...
0
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0answers
427 views
Fitting ARIMAX model with auto.arima function, how to find the best K?
I have
1. electricity load data collected by hour for 17 month
2. temperature collect at same time frame
I would like to fit an ARIMAX model to predict electricity load for 1 week. Take ...
1
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2answers
677 views
Dealing with multi seasonality in time series
I am new in R and time series analysis and need some help. I am currently trying to create a tool to forecast the demand of power for a company. On my data set I have 17550 observations that ...
0
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0answers
29 views
Fourier frequencies
When reading "Multiple time series" (E. J. Hannan 1970 - p 215), I came across the following statement: Noting $w(\lambda)$, the Fourier transform at frequency $\lambda$ and $N$ the sample size.
I ...
2
votes
1answer
454 views
Finding out frequency of peaks using the Fourier transform
I have a signal that varies in time as shown below. I have just shown a 5 s interval of data (from 97 s to 102 s). The sampling frequency is 1000 Hz.
My goal is to find out the frequency of the ...
1
vote
0answers
32 views
Comparing power in FFT frequencies biased by number of bins?
I have some EEG data recorded from a mouse with tremor. When I do an FFT on the data, it generally looks like an exponential distribution. I'm interested in any frequency peaks that are ...
0
votes
0answers
65 views
How to implement Bartel's Test of Significance?
I read about Bartel's test of significance for cycles in a few places like books or commercial software manuals, but I could not find any scientific writings on the subject except for this one paper ...
1
vote
0answers
35 views
How to measure a mean frequence of fft transform
I have this time series (utilization of app by day of an user)
And this fourier transform of the above time series
How can I extract one number that express the mean frequency of this time series?
...
1
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0answers
55 views
Regression for Analysing Fourier Transform of a Complex Function
Regression for Analysing Fourier Transform of a Complex Function
I need to analyse a linear system which is y = FT{x},
where Input x and output y are both complex function (A*exp(jθ)).
If I only ...
0
votes
0answers
164 views
FFT as feature for neural network
i am trying to make a classifier that determines whether the audio sample provided is a girl or a boy. however i am only getting 50% accuracy on my classifer at the moment.
I want to know if its the ...
1
vote
1answer
140 views
Energy savings prediction model using stochastic processes and Monte Carlo Simulation
I want to build a model that quantifies the energy savings from a building retrofit project. For example a company is using a heating oil radiator system, that is meant to be replaced by a gas ...
1
vote
0answers
117 views
detecting change point in the time series on a 2 dimensional space
I have a 2 dimensional geographic space. There are crime events occuring at different regions in the space over time. I am looking particularly at property crimes like burglary. If I look at the time ...
1
vote
0answers
372 views
Get the amplitude of the components of a periodic signal from Fourier (FFT)/Wavelets analysis
I have a signal looking approximatively as the one in the first subplot below (*), and I would like to:
extract the periods of the main components of the signal;
associate an amplitude to these ...
6
votes
3answers
1k views
What information can I gain from the fourier transform?
I have acceleration data in 3D vectors (x,y,z).
For detecting certain patterns within the ...
3
votes
0answers
113 views
Deseasonalizing a time series using a Wiener-Kolmogorov filter
I am trying to eliminate seasonality from a time series using Wiener-Kolmogorov filter, I am following the methodology explained in here this paper about signal extraction which is the same followed ...
1
vote
1answer
921 views
Deseasonalizing data with fourier analysis using MATLAB [closed]
I am trying to eliminate seasonality from my data using Fourier analysis in MATLAB. Following this post https://stackoverflow.com/questions/19285684/fast-fourier-transform-for-deasonalizing-data-in-...
3
votes
1answer
181 views
How to compute bernoulli distribution PDF from CF
The characteristic function for a Bernoulli distribution is
$$\phi(t) = (q+pe^{it}) \text{ where } p+q=1$$
I also know that the relationship between $\phi(t)$ and the pdf $f(k)$ is the Fourier ...
10
votes
2answers
2k views
From a statistical perspective: Fourier transform vs regression with Fourier basis
I am trying to understand whether discrete Fourier transform gives the same representation of a curve as a regression using Fourier basis. For example,
...
1
vote
1answer
1k views
Covariance and power spectral density of a signal?
I am reading an article on signal processing and I'm not sure of a few things. It defines the covariance function of a signal $y = y(t)$ as
$$\text{cov}(y) = E[y(t)y^\ast(t-k)].$$
And then it says ...
1
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0answers
19 views
The small error probability P for a dataset
P = $p\{\frac{|\epsilon(k)-\bar{\epsilon}|}{S_1} < 0.6745\}$
Say we want to calculate the probability shown in the formula above.
I have the values for all $\epsilon$ parameters and $S_1$. ...
