# 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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### Difference of two independent lognormal random variables by Fourier transform methods?

Is it possible to calculate the difference $X_1-X_2$ of two independent lognormal variables $X_1$ and $X_2$ where $\log(X_1)\sim N(\mu_1,\sigma_1)$ and $\log(X_2)\sim N(\mu_2,\sigma_2)$? Could I ...
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### Characteristic function and Fourier transform for a discrete random variable!

Let $\phi_{x}(t)= E [ e^{itx}]$ be the characteristic function If X is a continuous random variable, then: $\phi_{x}(t)= E [ e^{itx}] = \int e^{itx} f(x)dx$ (being $f(x)$ the probability density ...
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### Method to calculate optimal nbasis (K) for fourier basis

Is there any method to calculate the optimal K for fourier basis transformation? For example if I were to use RMSE, it seems that as K increases RMSE keeps going lower. I'm thinking of the elbow-...
25 views

### Estimating Fourier spectrum from multiple time series of a system

I have a set of N time series, each of length T, that describe separate realisations of a single physical system. For each series, I can compute an FFT to find the Fourier spectrum up to a period 2/T, ...
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### Long term time-series prediction for non-stationary but regular water flow data

I am looking at a very interesting time series dataset for the volume of water flow through some groundwater sensors. Our goal is longer term prediction of water levels, such as 1 - 5 years in the ...
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### Spectral analysis in R, how to interpret periodogram

I'm relatively new to spectral analysis and have been working through some online tutorials. I have some time series data that I would like to examine for periodicity / repeating patterns. When I ...
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### Can you perform a Fourier transform of a Frequency / Time plot? (Number of phone taps (t))

I'm working on a thesis problem. I need to analyze tapping behaviour (number of phone taps). The raw data is the time stamp of every app, and the app in use. It was recommended to me that I create a ...
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### Representing a time-series smoothed curve as a sinsoidal?

So attaches is an example of the kind of time series data I am working with. So far I have used Gaussian filters with sigma=3 and 6 to smooth the data, which has worked very well (especially sigma=3). ...
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### Fourier transforms for noise reduction

Given a signal, which is regularly sampled over time and is noisy. The standard method is with a Fourier transform to reduce the noise and minimise the change to the signal. ...
44 views

### Why SARIMA has better accuracy on weekly dataset than on daily one?

I am studying time series right now. So, I have this dataset. My aim is temperature prediction. I've found out that ARIMA can't work with long period seasonality. So, I've resampled daily dataset ...
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### Fourier analysis to retrieve components of individual spectra

I have a basic, simple question, I am a physics student, and searching internet gives me a lot of signal processing theory but couldn't find this basic answer, which I plan to implement in my speech ...
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### Log-likelihood function for a filtered Fourier spectrum

I have time series data from which I am trying to infer parameters using MCMC. I normally infer parameters about the data in the time domain, using a Normal log-likelihood. However, I now have to ...
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### Exactly how are cyclical components computed?

So suppose we have some sort of a time series model. y_t = trend_t + cyclical_t + x_t + epsilon_t So, I'm interested in obtaining the seasonal component. Here "x_t" refers to other potential ...
33 views

### FFT for a binary time-series

I have a multivariate time-series of a binary values where 0 means that some state was not observed in the given second and 1 meaning that it was observed. I know that for a time-series consisting of ...
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### Measuring weather impact on sales as a crossed random effect

I'm trying to model sales of a clothing brand having longitudinal data (unbalanced panel: 20 stores with 50 - 157 weeks of datapoints). There are many regressors in my analysis, but I believe that ...
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### Discrete Fourier transform (DFT) of 2 signals using a single DFT

Given two different(x,y) and independent signals, can one find dft of both of them using a single dft chip and using that that chip only once. I tried finding dft of x+jy but was not able to find ...
27 views