# 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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### Help with PSD graph interpretation and Time Series Analysis

I am pretty new to time series analysis and I am currently studying it. My latest work requires me to work with a time series that was generate by VASP AIMD. I tried power spectrum density analysis ...
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### Product of RVs of Which Distribution Approximates Normal Well?

Suppose that I have $N$ i.i.d. random variables with a distribution $Q$, which has mean around 1. That is $R_1, R_2,\ldots,R_N \sim Q$. I would like $\prod_{i=1}^N R_i$ to approximate a normal random ...
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### Fourier transform in information transfer in biological neural network

Principles of Neural Design by Peter Sterling and Simon Laughlin describes a usage of information theory in calculating the rate of information transfer in the brain. ...when successive signal states ...
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### What is the spectral density matrix, in the context of vector stochastic processes

I cannot seem to find any good/easy to read resources on the spectral theory, and in particular for multivariate stochastic processes. I want to know: Any resources explaining spectral theory ...
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### Forecasting Square Waves

I am involved in a social experiment with other college students. The experiment involves simulating current price of the market at which a given asset can be bought or sold for immediate delivery. We,...
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### Name of PDF? - projecting uniform probability distribution on the unit circle to the x-axis

Consider a uniform probability distribution on a circle of radius r, i.e. $\{(x,y) \in \mathbb{R}^2: x^2 + y^2 = r^2 \}$.If we wish to project onto the x-axis, we can consider each point on the circle ...
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### Approximation for a correlation matrix

I have a cross-correlation matrix of some parameter for each time period. E.g. expected economy growth for each months in the future, i.e. growth for Apr 2014, May 2014, ...., Dec 2018, and ...
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### The sampling frequency or sampling period for financial time series in doing DFT

The discrete Fourier transform (DFT) is widely utilized in computer engineering, and its formula is as follows: $$X(k)=\sum_{n=0}^{N-1}x[n]e^{-i\frac{2\pi}{N}nk},$$ where the result $X(k)$ refers to ...
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### How do I approximate a timeseries with a sum of sin and cos functions?

I have a time series and I am trying to approximate it using an equation of the type: y = A + B*sin(2*pi*x/n) + C*cos(2*pi*x/m) + D*sin(2*pi*x/q) + ... The ...
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### Fourier coeficients as feature to classification model

I have to solve a timeseries multiclass classification problem. Some of these classes (Class 0, Class 1 and Class 4) have timeseries that are really similar to each other, as follows: ...
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### How to test if a particular frequency is significant or not in a fourier frequency spectrum

I have got a timeseries data with which I plotted a frequency spectrum and I could eyeball all the significant peaks (significant frequencies) in the plot. But I want to do this for a spatial data (...
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### How to dectect sudden change in signal frequency? (analysis of EEG signals)

I am trying to analyze data from EEG electrodes to understand how brain activity changes in different coginitive states (for simplicity, assume that there are only 2 states: baseline (A) and chanelled ...
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### Interpretation of fast fourier transform in a simple time series

I am struggling with understanding the result of FFT in R. I have 729 observations, two years data. In the data I simulated there were more visitors every sunday. I divided 729/7 which is ...
1 vote
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### Are moduli of components of Fourier transformed Gaussian random vector still independent?

Suppose $X=[X_1,\ldots, X_n]^T$ is a random (column) vector such that: $X_i \stackrel{i.i.d}{\sim} \mathcal{N}(0,\sigma^2), \ 1 \le i \le n$ $\mathcal{F} \in \mathbb{C}^{n \times n}$ is the discrete ...
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### Rescaling matrix W in Random Fourier Features

I came across this beautiful idea of Random Fourier Features by Rahimi and Recht while working on optimising my GP model using Predictive Entropy Search. I understand the overall idea of approximating ...
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### How should I interpret parameters of the SARIMA model in time series analysis?

I am a bit confused as to why the SARIMA model requires four parameters beyond the ARIMA model just to remove the seasonal component from a time series. Obviously $m$ is required to specify the ...
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### Energy of a signal contained within a given band

Suppose I wish to compute the energy contained in a given frequency range using FFT. So, first, I compute FFT and take the squares of the absolute values of $x_k$. Can I then use discrete integration ...
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1 vote
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### FFT: zero-padding and mean subtraction

When computing FFT of a finite-time discrete sample with a non-zero mean, I get two different results depending on the order of operations: whether I zero-pad and then subtract the mean or subtract ...
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### Why can weekends cause harmony?

The following plot shows power spectra (periodograms) of a sample from $X_t \sim \operatorname{Poisson}(1)$ along with that same sample where: Weekends were set to zero Sundays were set to zero ...
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1 vote
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### Non-stationary Random Fourier Features

Random Fourier Features (RFFs) were introduced by A. Rahimi and B. Recht in their 2007 publication Random Features for Large-Scale Kernel Machines. RFFs are based on Bochner's theorem, which applies ...
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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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