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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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,
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Fourier terms to model seasonality in ARIMA models
I would like to use Fourier terms to model seasonality in an ARIMA model. The reason for using Fourier terms instead of a seasonal ARIMA model is that the frequency of the time series is very high (...
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Similarity of two discrete fourier tranforms?
In climate modelling, you're looking for a models that can adequately portray the Earth's climate. This includes showing patterns that are semi-cyclical: things like the El Nino Southern Oscillation. ...
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Fourier bases for a stationary signal & relation to PCA for natural images
Why does PCA of a translation-invariant signal give a Fourier basis?
I've found proofs for this, but I'd love some intuitions.
Any help is greatly appreciated!
EDIT:
Sorry that this question ...
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Dimensionality reduction of multiple signals using Fourier transform
I have $N$ recorded signals, $x$, each of which have been sampled 672 times across a time period of a week (= 15 min intervals). I will denote $x_{ij}$ as the $j$th sample for the $i$th recorded ...
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Fourier transform of distributions
Which distributions are their own Fourier transform besides the normal distribution and the generalized arcsine distribution?
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Is it possible to have seasonality at 24, 12, 8 periods in hourly based wind power data?
I have taken hourly-based wind power data, by taking its periodogram after making it stationary in R. It gives me four seasonal patterns at periods of 24, 12, 08, and 06, as shown in the figure below.
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Fitting the parameters of a stable distribution
I have a data set and I have to fit this data set with a stable distribution. The problem is that the stable distributions are known analytically only in the form of the characteristic function (...
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Rebuilding a signal using the fast fourier transform [closed]
I've created a signal by adding a sine wave and a cosine wave using R:
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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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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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How to identify a non-periodic time-series?
I am working on a problem where I have to first classify whether a time-series is periodic or not and then, if it is periodic identify its period(s) (the time-series could have multiple periodicities, ...
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Decompose a time series into superposition of step functions?
Background
I have time series data comprising hourly observations of a sensor's readings over a period of almost a year. The sensor records an environment whose baseline measurements should have ...
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How to calculate harmonic equations from a complex wave
I’m working through an online example that explains spectral analysis in R. Let’s say you have a complex wave:
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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-...
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How do i interpret the output of fourier {forecast}
I have come across a sales forecasting problem. It involves using Fourier transformation. But I have trouble understanding the output.
what are the variables and values in the output (fplot1)? how do ...
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