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a. Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: i. Dirac delta function f(x) = = 8(x) ii. Shifted Dirac delta function f(x) i=+n = - - 8(x – x0) iii. Comb function f(x)= Σ 8(x − ix) i=-n iv. Rectangular function f(x) = sqr(x/W) i=+inf v. Square wave f(x) = Σ_sqr((x - ix)/W) i=-inf (hint: For the square wave, use convolution properties) b. Sketch the following 2-D spatial Fourier transform pairs: i. a line (1D slit) ii. a circular aperture iii. a rectangular function (2D aperture) iv. a linear grating [i.e. a 2D grid.] (hint: you can separate these 2-D shapes into Cartesian or cylindrical 1-D functions with known transforms and use the separation of variables property of the spatial FT) 2. Using the Gwyddion software: a. Generate the 2-D spatial FFT of all the patterns including circular aperture, stripe aperture, and linear grating [see below for the images] using Gwyddion. Compare to your sketches in problem 1, and explain any discrepancies. b. Generate the 2-D spatial FFTs of the smiley image and find a mask that removes the stripes in the image. Explain how this works. i. Circular Aperture ii. Stripe Aperture iii. Linear Grating iv. Sector star V. Smiley Image IIII

a. Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: i. Dirac delta function f(x) = = 8(x) ii. Shifted Dirac delta function f(x) i=+n = - - 8(x – x0) iii. Comb function f(x)= Σ 8(x − ix) i=-n iv. Rectangular function f(x) = sqr(x/W) i=+inf v. Square wave f(x) = Σ_sqr((x - ix)/W) i=-inf (hint: For the square wave, use convolution properties) b. Sketch the following 2-D spatial Fourier transform pairs: i. a line (1D slit) ii. a circular aperture iii. a rectangular function (2D aperture) iv. a linear grating [i.e. a 2D grid.] (hint: you can separate these 2-D shapes into Cartesian or cylindrical 1-D functions with known transforms and use the separation of variables property of the spatial FT) 2. Using the Gwyddion software: a. Generate the 2-D spatial FFT of all the patterns including circular aperture, stripe aperture, and linear grating [see below for the images] using Gwyddion. Compare to your sketches in problem 1, and explain any discrepancies. b. Generate the 2-D spatial FFTs of the smiley image and find a mask that removes the stripes in the image. Explain how this works. i. Circular Aperture ii. Stripe Aperture iii. Linear Grating iv. Sector star V. Smiley Image IIII

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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please do problem 2!!!! explain all of your ansswers and always provide a sketch for each. i through iv. also no chatgpt or ai answer please

a. Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: i. Dirac delta function f(x) = = 8(x) ii. Shifted Dirac delta function f(x) i=+n = - - 8(x – x0) iii. Comb function f(x)= Σ 8(x − ix) i=-n iv. Rectangular function f(x) = sqr(x/W) i=+inf v. Square wave f(x) = Σ_sqr((x - ix)/W) i=-inf (hint: For the square wave, use convolution properties) b. Sketch the following 2-D spatial Fourier transform pairs: i. a line (1D slit) ii. a circular aperture iii. a rectangular function (2D aperture) iv. a linear grating [i.e. a 2D grid.] (hint: you can separate these 2-D shapes into Cartesian or cylindrical 1-D functions with known transforms and use the separation of variables property of the spatial FT) 2. Using the Gwyddion software: a. Generate the 2-D spatial FFT of all the patterns including circular aperture, stripe aperture, and linear grating [see below for the images] using Gwyddion. Compare to your sketches in problem 1, and explain any discrepancies. b. Generate the 2-D spatial FFTs of the smiley image and find a mask that removes the stripes in the image. Explain how this works.
Transcribed Image Text:a. Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: Sketch (no need to derive unless it is helpful to you) the spatial 1-D Fourier transform pairs of the following functions: i. Dirac delta function f(x) = = 8(x) ii. Shifted Dirac delta function f(x) i=+n = - - 8(x – x0) iii. Comb function f(x)= Σ 8(x − ix) i=-n iv. Rectangular function f(x) = sqr(x/W) i=+inf v. Square wave f(x) = Σ_sqr((x - ix)/W) i=-inf (hint: For the square wave, use convolution properties) b. Sketch the following 2-D spatial Fourier transform pairs: i. a line (1D slit) ii. a circular aperture iii. a rectangular function (2D aperture) iv. a linear grating [i.e. a 2D grid.] (hint: you can separate these 2-D shapes into Cartesian or cylindrical 1-D functions with known transforms and use the separation of variables property of the spatial FT) 2. Using the Gwyddion software: a. Generate the 2-D spatial FFT of all the patterns including circular aperture, stripe aperture, and linear grating [see below for the images] using Gwyddion. Compare to your sketches in problem 1, and explain any discrepancies. b. Generate the 2-D spatial FFTs of the smiley image and find a mask that removes the stripes in the image. Explain how this works.
i. Circular Aperture ii. Stripe Aperture iii. Linear Grating iv. Sector star V. Smiley Image IIII
Transcribed Image Text:i. Circular Aperture ii. Stripe Aperture iii. Linear Grating iv. Sector star V. Smiley Image IIII
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