# Questions tagged [spectral-analysis]

For questions involving spectral clustering algorithms, frequency domain analysis or correlated subjects. May include Fourier transform and graph theoretic questions.

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### PLS Regression on data with high number of zeros in dependent variable

I want to perform a PLS regression on a data set coming from spectral images (NIRS). My goal is to relate the different spectra to the total amount of a compound. To do this, I have a dataset ...
• 31
20 views

### Interpretation of time series spectral entropy values wrt forecastability by a general neural network

I recently started using spectral entropy to analyze time series (already windowed). I'm having difficulty for interpreting the results, the entropy of the last 25% of a series is 0.19, and the ...
• 51
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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 ...
• 359
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### Singular Spectrum Analysis Decomposition on single input signal using PyTS module

I read this paper and was curious to apply it on a single-channel audio recording of mixed sources. It is about Singular Spectrum Analysis (SSA). The paper mentions that a key component of the ...
15 views

I am performing PCA analysis of NIR spectra for the analysis of the progression of a film coating process I have noticed that one of my components goes up with the film coating process (with upwards ...
460 views

### Hypothesis testing for detecting a (damped) sinusoidal signal in noise

I have a signal in white noise that has the following form: $$r[t_i] = A e^{-t_i/\tau} \sin{(\omega t_i + \phi)} + n[t_i]$$ I would like to test whether the signal (1st ...
• 161
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### Is Fisher transformation appropriate for magnitude squared coherence and phase locking value?

Fisher transformation, or hyperbolic arctangent, is recommend before performing arithmetic on correlation coefficients (e.g., estimating confidence intervals), because it makes their distribution ...
1 vote
91 views

### The logic behind the derivation of the autocovariance generating function?

I am working with complicated sets of time series, where an observed system output is the sum of a number of individual ARMA, error and noise series. I am therefore looking at ways to identify these ...
• 704
1 vote
41 views

### Availability of Linear Grouping Algorithms to Linearly Cluster Datasets

I have been trying to cluster a scatter plot that has a triangular graph, ideally the proper clustering plot should have a linear form, as shown below: I tried using Spectral Clustering: and ...
20 views

### 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
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### Efficient way to encode a set of large covariance matrices

I have a computational model that involves having a set of $K$ covariance matrices, $\{\Sigma_1, ..., \Sigma_K\}$ with each $\Sigma_i \in R^{n \times n}$. Storing all these full covariance matrices is ...
• 1,290
18 views

### How to deal with correlation in spectral data?

Currently I'm tasked with analysing data taken with optical emission spectroscopy (OES). These measurements serve the purpose of identifying regions on the sample rich in certain chemical elements (...
• 175
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### Find spectral density of a process

Let $X_t = C \cos(2πw t) + D \sin(2πwt) + U_t$ where $C, D$ and $U_t$ are Gaussian random variables with unit variance, and where all the variables are independent, and $U_t$ is white noise. Determine ...
• 435
42 views

### 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 ...
• 111
1 vote
60 views

### 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 ...
• 111
291 views

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