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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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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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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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43 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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17 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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36 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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24 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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43 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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192 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
102 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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233 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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43 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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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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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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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
221 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 (...
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1k 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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229 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 ...
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1answer
121 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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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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101 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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44 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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31 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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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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112 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 ...
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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
186 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
405 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 ...
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1answer
384 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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146 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
75 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
133 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
164 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
322 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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50 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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255 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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40 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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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 ...
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1answer
711 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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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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44 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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84 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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231 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 ...
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1answer
205 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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159 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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542 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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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 ...
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136 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 ...
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1answer
1k 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-...