The fourier-transform tag has no wiki summary.
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Given samples from multiple normal RVs, how do we recover the histogram of their means?
Let $X_1,...,X_N$ be independent normal random variables. $X_i$ is normal with mean $\mu_i$ and standard deviation $\sigma_i$. Let $x_i$ be a single random sample from $X_i$.
Input: We get all ...
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Discrete Fourier Transform and uneven sampling
In this blog article
an example is given of one can use the DFT to detect frequencies much higher than the sample rate.
In the comments sections I asked how it was done, since DFT normally requires ...
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0answers
32 views
Can the proof of the central limit theorem be expressed as the limit of a convolution with an operator
The central limit theorem, as I understand it (engineer, non-statistician), says that the distribution comprised of means of some other reasonably behaved distributions converges to a normal ...
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1answer
63 views
Unevenly sampled data and the Lomb-Scargle method
I managed to estimate the periodogram of unevenly sampled data using the Lomb-Scargle Method. Analyzing the frequency domain it would be interesting to filter out a frequency band and then apply IFFT ...
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1answer
113 views
Characteristic function and Fourier transform
I understand the definition of characteristic functions used in
probability theory:
For a random Variable X with probability density function $f_X$ the characteristic function is defined as:
...
2
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1answer
73 views
Deconvolution with fourier transform or characteristic function?
Let us consider the following model:
$$Y_j = X_j + \epsilon_j \hspace{15pt} j=1, ..., n$$
Where $Y_j$ is a noisy signal, $\epsilon_j$ is the noise which is independend from the signal $X_j$. We have ...
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2answers
91 views
Separating two complex-valued datasets that have been multiplied together
I have two complex-valued datasets, A and B that can be considered as vectors with the same number of elements.
The datasets are multiplied together using complex point-by-point multiplication, ...
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2answers
152 views
How to test statistical significance of coherence coefficients in spectral analysis?
I would be very thankful for advising me how to test statistical significance of coherence coefficients. I have a statistical software that calculates them for me but it does not test their ...
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1answer
252 views
“Central limit theorem” for weighted sum of correlated random variables
I'm reading a paper which claims that
$$\hat{X}_k=\frac{1}{\sqrt{N}}\sum_{j=0}^{N-1}X_je^{-i2\pi kj/N},$$
(i.e. the Discrete Fourier Transform, DFT) by the C.L.T. tends to a (complex) gaussian random ...
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3answers
336 views
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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1answer
123 views
Finding the instantaneous period of a signal (or calculating period degradation)
I have a signal, of varying amplitude, and after a certain point in time, I expect to see the period of this signal lengthen. I am looking for a way to measure the lengthening of this period.
Is this ...
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132 views
P-value approximation from an underlying unknown distribution
I am calculating a certain statistic(relative entropy) of a certain sequence alignment over DNA sequences. The statistic has a certain distribution in the entire genome of which I only have 1000 ...
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64 views
Clustering the elliptic Fourier series coefficients
What do you think about the best way to perform a search for two discrete group membership in data that consist of four Fourier series coefficients like this:
...
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1answer
176 views
How can one do “two series” Fourier analyses in R?
In Statistica one can do a "two series"/bivariate/cross spectrum Fourier analysis to examine the coherency, gain, and phase spectrum across a pair of signals. It is probably a failing on my part, but ...
3
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1answer
507 views
Analysing periodicity in sparse time series
I am interested in looking for periodicities in a several day long recording of electrical activity. The traces present a very steady baseline over which, from time to time, some short events (300-500 ...
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3answers
658 views
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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1answer
354 views
Fourier transform of distributions
Which distributions are their own Fourier transform besides the normal distribution and the generalized arcsine distribution?
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1answer
336 views
How can I estimate the phase difference between two periodic time-series?
I have 2 daily time-series, each 6 years long. While noisy, they are both clearly periodic (with a frequency of ~1 year), but appear to be out of phase. I would like to estimate the phase difference ...
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101 views
Sine wave with a constant period: what else is constant? [closed]
Which statistic that you can calculate on a window remains constant on a sine wave with a constant period? This is for a window function for a proprietary filter.
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1answer
185 views
Do I use non-normalized or normalized fft output from R to compute phase angle?
Is R's fft() output normalized or not? In other words, do I have to normalize the output first before computing the phase angle using ...
4
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1answer
420 views
Are real and imaginary components of frequency element of fft correlated?
I want to use model-based clustering to classify 1,225 time series (24 periods each). I have decomposed these time series using the fast Fourier transform and selected the harmonics that explain at ...
7
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1answer
238 views
STFT statistical analysis
I am using the evolfft function in the RSEIS R package to do a STFT analysis of a signal.
The signal is one hour long and it ...
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0answers
1k views
Calculate Cross Correlation of two matrices of the 'Values Vs. Time' representation
I have 2 acceleration vectors, each represented by a matrix with its first column corresponding to the magnitude of acceleration and second column corresponding to the time (in ms) They both represent ...
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1answer
263 views
Noise in the Fourier transform
I have a smooth but rather complex curve, sampled with a good frequency. I apply the discrete Fourier transform to it using the fast Fourier transform (FFT) algorithm and get its Fourier image. I need ...
