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Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.

Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 14EQ
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Numerical methods 

using taylor's series 

Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.
Transcribed Image Text:Near-infrared spectroscopy (NIRS) is an analytical method that uses electromagnetic spectrum from 780 nm to 2500 nm in various non-destructive measurement applications. The measured signal of five wavelengths are tabulated in the Table 1. To improve the quality of the NIRS signals, the rate of change can be computed to eliminate unwanted signals. Table 1 Wavelength, x (nm) Measured Signal, E(x) (unit) 750 900 950 1000 1150 12.34 87.23 332.12 455.74 429.41 By applying all appropriate numerical first order derivative methods to the following questions: (i) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 50 nm. (ii) Estimate the rate of change of the signal when the wavelength was 950 nm using an interval of 200 nm. (iii) Identify the best method in estimating the rate of change of the signals with a concise justification if the exact solution is 2.4566.
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