All Questions
Tagged with fourier-transform signal-processing
25 questions
0
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23
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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 ...
- 53
2
votes
0
answers
141
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Calculating convolution in R [closed]
I am struggling to get the correct answer for the simple calculation of convolution in R.
The convolution of $f(t) = e^{-t}$ and $g(t) = \sin(t)$ is:
$$
(f * g)(t) = 1/2 \left( e^{-t} + \sin(t) - \cos(...
- 705
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0
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46
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Can you decompose a wave approximately?
I have data which looks like composition of sine waves.
I need to decompose it to fewest possible sine waves that would give me tolerable error.
The picture is of a half-period. Each half-period ...
- 159
1
vote
0
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85
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The length of spectral density is longer than the data using spectrum() in R
I'm using spectrum(method = "pgram") in R to calculate the spectral density in my time series.
spectrum() returns the spectral density for each frequency(from 1/n, 2/n to 1/2, n is the time ...
- 41
0
votes
1
answer
103
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Finding autocorrelation coefficients given PSD values at 2 frequencies
Assuming that $S_X(w)$ denotes powers spectral density function at
frequency $w$, we are given
$$S_X\left(\frac{\pi}{4}\right)=10+3\sqrt{2},\quad
S_X\left(\frac{\pi}{6}\right)=11+3\sqrt{3}.$$ We also ...
- 105
2
votes
0
answers
109
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Uncertainty principle in probability theory
In probability theory, there is the covariance inequality
$$\operatorname{Var}(Y) \geq \frac{\operatorname{Cov}(Y,X)^{2}}{\operatorname {Var} (X)}.$$
In signal processing, there is a similar ...
- 538
0
votes
1
answer
39
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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 ...
- 171
1
vote
1
answer
71
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How to discard the first spike after auto-correlation and handle sloping auto-correlation output [closed]
Disclaimer: I am not very mathematically inclined and am mostly looking to be pointed in the right direction.
I have various signals that I am putting through an auto-correlation function that uses ...
1
vote
0
answers
221
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How to search for irregular signals: Fourier, DWT or k-means?
See my notebook here
I want to search for irregular time signals in a data set of ~3 500 000 time signals. I can't give a clear definition of irregular signal, but it must fulfil the criteria of: not ...
- 121
1
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0
answers
23
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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), ...
2
votes
1
answer
4k
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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 ...
- 223
1
vote
0
answers
1k
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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 ...
- 341
3
votes
1
answer
352
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Compressed Sensing: Missing Fourier Coefficients?
This question is regarding the problem of reconstructing a signal given only a subset of the Fourier coefficients are observed:
$$\min_x \|x\|_1 \text{ subject to } y = Ax$$
where $x = (x_1,x_2,\...
- 1,322
1
vote
1
answer
622
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Statistical analysis of fourier transform of a 2D image (freaking AMAZING)
I'm a statistics grad student, and I just started getting into Digital-Image-Processing (an analogy for processing super-large contingency tables). In the book "Digital Image Processing" by Gonzalez ...
- 530
3
votes
1
answer
1k
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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 ...
- 5,146
1
vote
0
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69
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Significance of coherence frequncies
I have used the spectrum package in R to find the coherence between two time series. I can currently find a significance level using the $c=\sqrt {1-\alpha^{(\frac{1}{n-1})}}$ for each individual ...
- 11
5
votes
1
answer
672
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Testing data for regular oscillations
This is a little hard to explain, but I would like to test data for periodic oscillations, but not necessarily oscillations of the same amplitude. for example (crudely!):
So basically I want to test ...
- 183
7
votes
2
answers
6k
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What is the Fourier Transform of a brownian motion?
I looked into this article http://en.wikipedia.org/wiki/Brownian_noise and it says that:
If we have a brownian motion $W(t) = \int _{0}^{t} dW(s)$, then given that the spectral density of white noise ...
- 325
12
votes
3
answers
23k
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How to prove that the Fourier Transform of white noise is flat?
If we take $X_n$ a series a random vector with its components each having a probability distribution with zero mean and finite variance, and are statistically independent. How do we prove that the ...
- 325
5
votes
1
answer
2k
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time-series analysis Vs statistical signal processing
Is there a way to identify when to use time series analysis or signal processing.
Time series data analysis can be divided to signal processing and normal time series analysis.
In signal processing ...
3
votes
1
answer
1k
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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 ...
- 3,506
1
vote
2
answers
2k
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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 ...
- 11
5
votes
1
answer
1k
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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 ...
- 185
5
votes
1
answer
4k
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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 ...
- 4,591
1
vote
1
answer
728
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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 ...
- 3,925