What is Spectral analysis: Definition and 31 Discussions

Least-squares spectral analysis (LSSA) is a method of estimating a frequency spectrum, based on a least squares fit of sinusoids to data samples, similar to Fourier analysis. Fourier analysis, the most used spectral method in science, generally boosts long-periodic noise in long gapped records; LSSA mitigates such problems.LSSA is also known as the Vaníček method after Petr Vaníček, and as the Lomb method (or the Lomb periodogram) and the Lomb–Scargle method (or Lomb–Scargle periodogram), based on the contributions of Nicholas R. Lomb and, independently, Jeffrey D. Scargle. Closely related methods have been developed by Michael Korenberg and by Scott Chen and David Donoho.

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  1. starryexplorer

    I Obtaining Transit Spectrum for Celestial Bodies Using JWST NIRSPEC

    I've recently been tasked with obtaining transit spectrum data for some fascinating celestial bodies, including Ceres, Enceladus, Ganymede, Io, and Titan. The goal is to compare their transit spectra with that of Earth. However, I'm facing a bit of a challenge when it comes to using the Github...
  2. V

    A Extracting Color from a Spectral Date

    Hello everybody, I would love some help on the following; I have a spectral date (As image 1 below) formed by the wavelength, refraction index and the absorption coefficient. Is there any way to relate this spectral date to a dominant wavelength? or in a few words extract the color from this...
  3. A

    How much does the equivalent width of a line change by the introduction of 5% scattered light?

    How much does the equivalent width of a line change by the introduction of 5% scattered light? We know the equivalent width is defined as We know the equivalent width is defined as $$W = \int_{-\infty}^{\infty} \bigg(\frac{1-F_{\nu}}{F_c}\bigg) \, d\nu$$ where ##F_{\nu}## represents the flux in...
  4. Leonardo Machado

    A Improper boundary in non-linear ODE (pseudospectral methods)

    Hello, I am trying to compute some non-linear equations with pseudospectral/collocation methods. Basically I am expanding the solution as $$ y(x)=\sum_{n=0}^{N-1} a_n T_n(x), $$ Being the basis an Chebyshev polynomial with the mapping x in [0,inf]. Then we put this into a general...
  5. Leonardo Machado

    A Boundary conditions in the time evolution of Spectral Method in PDE

    Hi everyone! I am studying spectral methods to solve PDEs having in mind to solve a heat equation in 2D, but now i am struggling with the time evolution with boundary conditions even in 1D. For example, $$ u_t=k u_{xx}, $$ $$ u(t,-1)=\alpha, $$ $$ u(t,1)=\beta, $$ $$ u(0,x)=f(x), $$ $$...
  6. tworitdash

    A Spectral domain double integral with singularities

    The integral looks like Y_{mut, mn} = -j^{m+n}nm \int_{-\infty}^{\infty}\int_{-\infty}^{\infty} \frac{2 ab (k^2 - k_x^2) \sin^2(\frac{k_yb}{2}) \cos^2(\frac{k_xa}{2})}{\omega \mu k_z (\frac{k_yb}{2})^2 [(n\pi)^2 - (k_xa)^2][(m\pi)^2 - (k_xa)^2]} dk_x dk_y Here, k_z = -1j \sqrt{(-(k_0^2 -...
  7. Leonardo Machado

    A Rational Chebyshev Collocation Method For Damped Harmonic Oscilator

    Hello everyone. I'm currently trying to solve the damped harmonic oscillator with a pseudospectral method using a Rational Chebyshev basis $$ \frac{d^2x}{dt^2}+3\frac{dx}{dt}+x=0, \\ x(t)=\sum_{n=0}^N TL_n(t), \\ x(0)=3, \\ \frac{dx}{dt}=0. $$ I'm using for reference the book "Chebyshev and...
  8. Andrew Church

    I Composition of the Sun: How We Know via Spectral Absorption Lines

    The question “how do we know the composition of the sun” falls shorts everywhere I look. 1. There is the spectral absorption lines. Explanations given how that works, indicate how we know the elements, but fails to tell us how we know about the preponderance of Hydrogen and Helium...
  9. SMBH

    I How to check if stellar/galactic spectrum extraction went well?

    I've been doing some spectrum extractions in IRAF, stellar and galactic, and I was wondering if anyone here had any ideas on how to tell if the extraction/calibration/etc went well? I have a bunch of finished projects but I'm not sure about how to tell if they're any good or not. Let me know if...
  10. J

    A Subtract Radiated from Background Spectrum to Analyze Absorption Spectrum

    Hi everyone, I have an absorption spectrum that I obtained from a sample after radiation and I need to use the background sample as a reference, how can I do that using excel? what I did is subtract the radiated from the background spectrum then plot it, is that right? Thanks.
  11. boneh3ad

    A Interpreting a paper on spectral analysis

    I do a fair bit of spectral analysis of time series in my research, but to date my experience in the topic is almost exclusively from an engineering perspective rather than the more statistical approach. Of course I am aware that ultimately they are equivalent, but it means that my familiarity...
  12. Wrichik Basu

    B Obtaining spectrum of Sodium from Sodium Vapour Lamp

    I learned that two lines in the emission spectrum of Sodium, namely ## D_1 ## and ## D_2 ##, are on the visible region of the spectrum. Can I obtain these lines from a Sodium vapour lamp? I want to use a prism to separate out the individual wavelengths, a no then use a photographic film to...
  13. ISamson

    I How to Perform Spectral Analysis at Home: Tips and Tricks

    What can spectra tell us? They can tell us the speed of the object, its temperature, size and some more, but how can we do this at home with a glass prism? Do you know?
  14. phy_optics

    Halogen Lamp Spectrum 12V, 50W MR16: A vs B

    12V, 50W, MR16 halogen lamp spectrum is measured as shown ('B') with our newly developed mini-spectrometer having resolution ~1nm. But in internet it was similar to 'A' (We don't know how much resolution spectrometer they've used). Could anybody let me know what exactly the spectrum look like...
  15. KennethK

    Calculate the spectrum of a linear operator

    <mod note: moved to homework> Calculate the spectrum of the linear operator ##T## on ##B(\ell^1)##. $$T(x_1,x_2,x_3,\dots)=(\sum_{n=2}^\infty x_n, x_1, x_2, x_3, \dots)$$I think the way to do it is to find the point spectrums of ##T## and its adjoint ##T^*##. But I don't know how to calculate...
  16. W

    I Spectral representation of an incompressible flow

    Hi PH. Let ##u_i(\mathbf{x},t)## be the velocity field in a periodic box of linear size ##2\pi##. The spectral representation of ##u_i(\mathbf{x},t)## is then $$u_i(\mathbf{x},t) = \sum_{\mathbf{k}\in\mathbb{Z}^3}\hat{u}_i(\mathbf{k},t)e^{\iota k_jx_j}$$ where ι denotes the usual imaginary...
  17. D

    Lower Bound on Weighted Sum of Auto Correlation

    Homework Statement Given ##v = {\left\{ {v}_{i} \right\}}_{i = 1}^{\infty}## and defining ## {v}_{n}^{\left( k \right)} = {v}_{n - k} ## (Shifting Operator). Prove that there exist ## \alpha > 0 ## such that $$ \sum_{k = - \infty}^{\infty} {2}^{- \left| k \right|} \left \langle {v}^{\left (...
  18. Likith D

    B What type of spectrum is a rainbow?

    maybe it is emission spectrum of the sun but, seems continuous... unlike few distinct lines of the hydrogen emission spectrum...few images i just checked about it are similar to absorption spectrum...then maybe difraction could have made emission spectrum seem so or maybe not... Well I am very...
  19. Elvis 123456789

    Photons emitted by Hydrogen and helium atoms

    Homework Statement An excited hydrogen atom can emit photons of various wavelengths. a) What is the maximum wavelength of the Balmer series (in nm) (5pt) b) What is the minimum wavelength of the Balmer series (in nm) (5pt) c) Corresponding to part b), what is the kinetic energy of the recoil...
  20. P

    I How can larger dips in absorption line give more element

    So I just learned that in a spectrum like this one: (For now, let's concentrate on the graph given below.) The longer the dip is in the graph, the more the corresponding element is present. However, if each individual color corresponds to a different element, then how can a larger dip mean...
  21. Ma Xie Er

    A Basic Spectral Analysis proof help

    I'm reading "Time Series Analysis and Its Applications with R examples", 3rd edition, by Shumway and Stoffer, and I don't really understand a proof. This is not for homework, just my own edification. It goes like this: Σt=1n cos2(2πtj/n) = ¼ ∑t=1n (e2πitj/n - e2πitj/n)2 = ¼∑t=1ne4πtj/n + 1 + 1...
  22. A

    Singular spectral analysis of periodic series with period L

    Let's have a time series with a period=L. Suppose we arbitrarily choose the window length of the trajectory matrix to be equal to L which is also equal to the period of a time series. Then the second column of the matrix will also start with the same entry as the first column, because all...
  23. M

    Black-body radiation spectral analysis

    Why is it that we observe a continuous spectrum in black-body radiation not discrete spectral lines dependent on the composition of the black-body? A niave understanding is that it relates to the complexity of the atomic structure of the black-body as well as thermal motion of its constiuent...
  24. D

    Spectral Analysis of Gas Atoms: Temperature Calculation

    Hello Homework Statement A gas of atoms, each of mass m, is maintained in a box at temperature T. The atoms emit light which passes (in the x-direction) through a window in the box and can be observed as a spectral line in a spectroscope. A stationary atom would emit light at the sharply...
  25. R

    Spectral Analysis Applied to Ocean Waves

    [b]1. I am currently looking at the area of spectral analysis applied to ocean waves. I have a set of "raw" recorded data of wave height, direction, frequency etc. I understand that spectral analysis is used to validate/process wave data recorded by instruments. [b]2. Have I more or less...
  26. R

    Spectral Analysis applied to ocean waves

    Hi all, I would appreciate your guidance on the following: I am currently looking at the area of spectral analysis applied to ocean waves. I have a set of "raw" recorded data of wave height, direction, frequency etc. I understand that spectral analysis is used to validate/process wave data...
  27. M

    Proton NMR spectral analysis

    Homework Statement Which isomer with formula C6H12O2 has the following NMR spectrum? http://aceorganic.pearsoncmg.com/epoch-plugin/tempfiles/1869_4119.jpg [b]3. The Attempt at a Solution It's hard (and probably unhelpful) to list all the tries I've had at this.
  28. P

    Measuring Power Spectral Analysis in dBvolts vs Frequency: Tips and Techniques

    when looking at a power spectral analysis dBvolts vs frequency (Hz), how can you measure the area under the curve of a specific frequency range using the width at half height? any ideas?
  29. R

    Spectral analysis and displacement law

    He everyone first of all, I am not quite sure, if I put this post in the correct topic, so sorry if that's the case. The things is, altough I don't go to school anymore I recently stumbled upon some theories and wanted to check them myself using the formulas that I could find on the net. I...
  30. Cyrus

    MATLAB MATLAB Spectral Analysis Code - Help Needed

    Does someone have a code that would let me do a spectral analysis in MATLAB on a curve? I tried using fft but I can't get it to work.
  31. W

    Spectral Analysis: alternatives to Fourier Transforms?

    hi, Could someone point me to some good material that relates to problems of (computational) spectral analysis? I understand FFT well enough, and although I'm not very good with math I'm willing to chew. What I'm seeking is some alternative approach to Fourier transformation (ie. from...
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