Questions tagged [fourier-transform]
The Fourier transform decomposes a signal (a function of time) into frequencies, giving the energy at each frequency.
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43 views
K in Fourier series - How to find value of K to use it in ARIMA?
I am using the forecast library for doing some time series forecasting. I need to forecast number of sold items. I am planning to add holidays as xreg in auto.arima. The holiday will be a 0/1 list, ...
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6 views
Comparison of two groups of time-series
I have time series data collected from two sensors. Suppose that they are microphone recordings from a man and a woman. Each signal, e.g. the one below, is 5000 samples. They don't share some ...
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21 views
spatial correlation function, power spectral density function and homogeneity condition
Suppose that the spatial correlation function $R_{VV}(\mathbf{x})$ of a zero-mean random field $V(\mathbf{x})$ ($\mathbf{x} \in \mathbb{R}^3$) and its power spectral density function $\widehat{R_{VV}}(...
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1answer
143 views
Continuous time Fourier representation
I have learned that the Fourier transform of a continuous-time unit-periodic stochastic process is:
$$x(t) = \sum\limits_{k=-\infty}^{\infty} a_k e^{i2\pi kt} \quad \quad \text{ where } \quad \quad ...
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2answers
45 views
Inverse Fast Fourier Transform in R
plot(fft(fft(1:100),inverse = "true")/100)
plot(1:100)
In the above example, I was expecting the plots to be identical.
The first, however, returns:
while the ...
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0answers
37 views
Frequency analysis of categorical/binary data
I want to do frequency analysis with a data set of consecutive binary values, such as "Rainy - Sunny - Rainy - Rainy - Rainy - Sunny - ...". Using this data, I want to extract the frequency (= the ...
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1answer
72 views
Maximum number of Fourier terms in forecast package
I am using the forecast package in R to get some Fourier components - namely, function fourier(ts, K, ..). For a time series <...
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18 views
About the power spectrum and confidence upper limit
For now, I have a coupled system with 5 variables and use the Runge-Kutta method to integrate.
...
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19 views
Significance testing of signal-to-noise ratio
I have three 18-second, 32-channel resting state EEG time series sampled at 500 Hz using dry EEG electrodes (condition 1) and three more 18-second, 32-channel resting state EEGs also sampled at 500 Hz ...
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40 views
Adaptive knot selection for B-spline fitting
When fitting a B-spline for regression purposes I've seen a lot of cases where knots are fixed uniformly ,but in some situations this could lead to poor estimations because the behaviour of the curve ...
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0answers
26 views
Non-linear regression. Obtain B.spline coefficients using Fourier Transform?
I came up with a idea to estimate the coefficients of a B-spline fit by using the Fourier Transform but I don't know if it makes any sense to estimate them in this way.
Given that
$$s(x)=\sum_kc(k)\...
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58 views
How to fit a model to both daily and weekly periodic data using linear regression and fourier transform
I have a variable, y, in 30 minute intervals, and is highly dependent both on the time of day and the day of the week - mainly Sundays. It is also dependent on bank holidays, which could by any day of ...
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231 views
Forecasting seasonality with Fourier terms in R
I am using the auto.arima from the forecast package in R to determine the optimal K-terms for fourier series.
After I do that, ...
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1answer
139 views
R forecast multiple seasonality optimal model search using fourier and msts objects
Hi I have hourly data (one obs one hour) with multiple seasonality. I would like to fit an ARIMA model using forecast R package taking into account the multiple seasonality, maybe taking also in ...
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328 views
Time Series Analysis: Fourier Transform [closed]
I've recently studied Fourier transform and I've applied it on a time series data, since I am still confused between time and frequency domain I doubt the authenticity of my code to calculate Fourier ...
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62 views
Fourier Output Meaning
I just ran a fourier series on weekly sales data for 3 years worth of data.
I optimally chose the number of k-terms based on the AIC.
First 6 lines of my data:
...
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0answers
54 views
RKHS norm and Fourier transform link
In the notes here, it is stated that norms of some reproducing kernel Hilbert spaces can be written in terms of Fourier transforms, and this is often used to argue that a higher RKHS norm implies a ...
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18 views
Is there a concept of weakly periodic in stats? If so, what is it called?
Ok, say we have a signal that reoccurs within every T+x time where T is a constant and x is a random number small in size compared to T. We know that a function is actually periodic if F(x) = F(x+T), ...
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51 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:
...
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1answer
255 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 (...
3
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1answer
2k 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 ...
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301 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 ...
3
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1answer
147 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 ...
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0answers
21 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 ...
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0answers
112 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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1answer
50 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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37 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'...
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28 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 ...
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0answers
55 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 ...
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1answer
212 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 ...
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1answer
449 views
tbats() model not capturing seasonality (weekly data)
I have below 4 years of weekly data which has complex seasonality of varying seasonal length.
I have assigned the first 160 data points as training and the rest as test with frequency=52. It seems ...
3
votes
1answer
440 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 ...
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0answers
162 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 ...
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1answer
86 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 ...
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2answers
145 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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2answers
181 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 ...
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3answers
2k 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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1answer
392 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 ...
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1answer
58 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 ...
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0answers
273 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 ...
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0answers
48 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 ...
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2answers
2k 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 ...
2
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1answer
792 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 ...
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0answers
41 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 ...
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0answers
46 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?
...
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0answers
93 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 ...
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1answer
222 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 ...
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0answers
172 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 ...
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599 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 ...
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3answers
2k 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 ...
