Resolution Enhancement of Raman Spectra of Solids Using True Linear Prediction and Deconvolution

Sievänen, O.-P.

doi:10.1366/0003702991946451

Cited by 6 publications

(5 citation statements)

References 12 publications

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“…This method of determining linear prediction coefficients works best for autoregressive processes to an order less than 0.5N (for real valued signals). 43 This condition simply means that linear prediction depends on the ability of the previous values to model the underlying behavior of the function. Functions with underlying exponential behavior accomplish this well as the Taylor expansion derivatives of an exponential resemble each other.…”

Section: Applicability To Two-dimensional Electronic Spectroscopymentioning

confidence: 99%

“…However, higher power terms in the dephasing rate (such as Gaussian terms) are autoregressive to infinite order and thus are unstable to linear prediction. 43 In spectroscopy, Gaussian lineshapes are common due to inhomogeneous broadening that comes from static inhomogeneity in electronic environments. However, because these signals have successfully been fit to exponential decay previously, it is likely that a) we lack the resolution to see higher order dephasing processes and b) this source of broadening is relatively minimal in comparison to homogenous broadening.…”

Section: Applicability To Two-dimensional Electronic Spectroscopymentioning

confidence: 99%

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Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes

Caram

Engel

2011

Faraday Discuss.

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We present an analysis of dephasing rates for multiple zero-quantum electronic coherences in the Fenna-Matthew-Olson (FMO) pigment-protein complex using two-dimensional electronic spectroscopy. We employ the linear prediction Z-transform to determine both the frequency and decay rates of 8 individually assigned exciton-exciton coherences. Despite congestion in the spectra, we can isolate multiple crosspeaks signals and analyze their dephasing rates. A nontrivial relationship exists between the excitons and the bath determining the lifetimes of different exciton-exciton coherences. We propose that the correlations that protect long-lived electronic coherence may yield microscopic knowledge regarding the structure of the protein bath surrounding the chromophores.

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Section: Applicability To Two-dimensional Electronic Spectroscopymentioning

confidence: 99%

Section: Applicability To Two-dimensional Electronic Spectroscopymentioning

confidence: 99%

Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes

Caram

Engel

2011

Faraday Discuss.

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“…[3][4][5][6][7][8] Among these, digital signal processing technology, such as linear prediction technology, is critical for improving spectral resolution. 9,10 Linear prediction technology improves spectral resolution by making a model of the interference signal and using its autoregressive (AR) model to extrapolate the interference signal to a longer optical path difference. 11 In linear prediction-based spectral resolution enhancement technology, solving the AR model parameters for the interference signal extrapolation is a key step that has a direct effect on the quality of the restored spectrum.…”

Section: Introductionmentioning

confidence: 99%

“…3–8 Among these, digital signal processing technology, such as linear prediction technology, is critical for improving spectral resolution. 9,10…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Spectral Resolution Enhancement Based on Forward–Backward Linear Prediction Total Least Square Method

Qin

Han

et al. 2023

Appl Spectrosc

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In a Fourier transform infrared (IR) spectrometer, the Michelson interference signal extrapolation method based on linear prediction is often used to improve spectral resolution. In this method, an autoregressive (AR) model is established for the Michelson interference signal in the spectrometer. Once the AR model parameters are determined, the AR process is predictable. The interference signal can be used to figure out the AR model's parameters. Based on this, the AR model can be used to extrapolate the interference signal to improve the spectral resolution. In this paper, the forward–backward linear prediction total least squares (FB-TLS) method is proposed to estimate the parameters of the AR model. The parameters that are estimated are used to improve the IR spectral resolution. By simulating different order and signal-to-noise ratio situations, the effects of the Burg, the least square, and the FB-TLS parameter estimation methods on spectral resolution enhancement are studied. The simulation results demonstrate that the FB-TLS parameter estimation method can effectively suppress noise and avoid spurious peaks. The experimental results demonstrate that the FB-TLS parameter estimation method is effective for spectral resolution enhancement technology based on linear prediction. When the FB-TLS method is used to enhance NH3 IR spectral resolution from 2 cm−1 to 1 cm−1, the spectral prediction error in the NH3 characteristic band is only 0.21% compared with the measured NH3 spectrum, whose spectral resolution is 1 cm−1.

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“…When performed naively, deconvolution can tremendously enhance any error and/or noise in the spectra, to the point of losing any practical utility. Several approaches have been devised to obtain a stable solution, giving rise to numerous deconvolution procedures, 6,7,[10][11][12][13][14][15][16] some of which are mathematically equivalent. In Fourier self-deconvolution (FSD), arguably the most common deconvolution method used in infrared spectroscopy, the Fourier transform of the spectrum is divided by an exponential function (equivalent to deconvolving for a Lorentzian broadening) and multiplied by the filter function.…”

Section: Introductionmentioning

confidence: 99%

The Role and Selection of the Filter Function in Fourier Self-Deconvolution Revisited

Lórenz-Fonfrı́a

Padrós

2009

Appl Spectrosc

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Overlapped bands often appear in applications of infrared spectroscopy, for instance in the analysis of the amide I band of proteins. Fourier self-deconvolution (FSD) is a popular band-narrowing mathematical method, allowing for the resolution of overlapped bands. The filter function used in FSD plays a significant role in the factor by which the deconvolved bands are actually narrowed (the effective narrowing), as well as in the final signal-to-noise degradation induced by FSD. Moreover, the filter function determines, to a good extent, the band-shape of the deconvolved bands. For instance, the intensity of the harmful side-lobule oscillations that appear in over-deconvolution depends importantly on the filter function used. In the present paper we characterized the resulting band shape, effective narrowing, and signal-to-noise degradation in infra-, self-, and over-deconvolution conditions for several filter functions: Triangle, Bessel, Hanning, Gaussian, Sinc2, and Triangle2. We also introduced and characterized new filters based on the modification of the Blackmann filter. Our conclusion is that the Bessel filter (in infra-, self-, and mild over-deconvolution), the newly introduced BL3 filter (in self- and mild/moderate over-deconvolution), and the Gaussian filter (in moderate/strong over-deconvolution) are the most suitable filter functions to be used in FSD.

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Resolution Enhancement of Raman Spectra of Solids Using True Linear Prediction and Deconvolution

Cited by 6 publications

References 12 publications

Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes

Extracting dynamics of excitonic coherences in congested spectra of photosynthetic light harvesting antenna complexes

Parameter Estimation in Spectral Resolution Enhancement Based on Forward–Backward Linear Prediction Total Least Square Method

The Role and Selection of the Filter Function in Fourier Self-Deconvolution Revisited

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