Jet53man: /* Example #2 */

2022-04-19T18:53:26Z

Example #2

Jet53man at 16:59, 19 April 2022

2022-04-19T16:59:03Z

← Older revision		Revision as of 12:59, 19 April 2022
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	The figure/equation pair displayed here, on the right, is an example of a "Fourier expansion for a basic periodic function" that has been presented on p. 464 of the [[~~User:Tohline/~~Appendix/References#CRC\|CRC Standard Mathematical Tables (19th Edition)]]. The following derivation, analysis, and discussion has been motivated by this published CRC example.		The figure/equation pair displayed here, on the right, is an example of a "Fourier expansion for a basic periodic function" that has been presented on p. 464 of the [[Appendix/References#CRC\|CRC Standard Mathematical Tables (19th Edition)]]. The following derivation, analysis, and discussion has been motivated by this published CRC example.

	Referring back to the [[#Standard\|''standard representation'' presented above]], suppose that <math>~f(x)</math> is a square wave (unity amplitude) that extends over the range <math>~\pm c</math>, where, <math>~c < L</math>. (The dashed-black curve in [[#Figure2\|Figure 2]], below, displays one cycle of this function for the specific case of c/L = 1/3.) Replacing <math>~x</math> by the angle,		Referring back to the [[#Standard\|''standard representation'' presented above]], suppose that <math>~f(x)</math> is a square wave (unity amplitude) that extends over the range <math>~\pm c</math>, where, <math>~c < L</math>. (The dashed-black curve in [[#Figure2\|Figure 2]], below, displays one cycle of this function for the specific case of c/L = 1/3.) Replacing <math>~x</math> by the angle,
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	===General Concept===		===General Concept===

	Here we draw from our [[~~User:Tohline/~~Appendix/CGH/ParallelApertures#Utility_of_FFT_Techniques\|accompanying discussion of single-slit apertures]] in the context of computer-generated holography and, for the time being, retain our option to specify a phase angle, <math>~\phi_j</math>, that varies with position across the aperture. Recognizing from that discussion that <math>~D_j \approx L_1[1 - y_1 Y_j/L_1^2]</math>, we have,		Here we draw from our [[Appendix/CGH/ParallelApertures#Utility_of_FFT_Techniques\|accompanying discussion of single-slit apertures]] in the context of computer-generated holography and, for the time being, retain our option to specify a phase angle, <math>~\phi_j</math>, that varies with position across the aperture. Recognizing from that discussion that <math>~D_j \approx L_1[1 - y_1 Y_j/L_1^2]</math>, we have,
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Jet53man: Created page with "FORCETOC =Fourier Series= ==Representations== The following Fourier series r..."

2021-07-25T23:18:32Z

Created page with "__FORCETOC__   =Fourier Series= ==Representations== The following Fourier series r..."

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Jet53man: /* Example #2 */

Jet53man at 16:59, 19 April 2022

Jet53man: Created page with "__FORCETOC__ =Fourier Series= ==Representations== The following Fourier series r..."

Jet53man: Created page with "FORCETOC =Fourier Series= ==Representations== The following Fourier series r..."