(New page: Category:2010 Fall ECE 438 Boutin ---- == Solution to Q1 of Week 14 Quiz Pool == ---- ---- Back to Lab Week 14 Quiz Pool Back to [[ECE438_Lab_Fall_2010|ECE 4...) |
|||
Line 5: | Line 5: | ||
---- | ---- | ||
+ | Using the definition of the CSFT,<br/> | ||
+ | <math> | ||
+ | \begin{align} | ||
+ | F(u,v) &= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)e^{-j2\pi (ux+vy)}dxdy \\ | ||
+ | F(u,0) &= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)e^{-j2\pi (ux)}dxdy \\ | ||
+ | &= \int_{-\infty}^{\infty} \left( \int_{-\infty}^{\infty}f(x,y) dy \right) e^{-j2\pi ux}dx \\ | ||
+ | &= \int_{-\infty}^{\infty} p(x) e^{-j2\pi ux}dx \\ | ||
+ | &= P(u) \\ | ||
+ | \end{align} | ||
+ | </math> | ||
+ | |||
+ | so F(u,0) is the same as P(u) which is the CTFT of the function p(x). | ||
+ | |||
+ | Credit: Prof. Bouman | ||
---- | ---- | ||
Back to [[ECE438_Week14_Quiz|Lab Week 14 Quiz Pool]] | Back to [[ECE438_Week14_Quiz|Lab Week 14 Quiz Pool]] |
Latest revision as of 07:15, 28 November 2010
Solution to Q1 of Week 14 Quiz Pool
Using the definition of the CSFT,
$ \begin{align} F(u,v) &= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)e^{-j2\pi (ux+vy)}dxdy \\ F(u,0) &= \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}f(x,y)e^{-j2\pi (ux)}dxdy \\ &= \int_{-\infty}^{\infty} \left( \int_{-\infty}^{\infty}f(x,y) dy \right) e^{-j2\pi ux}dx \\ &= \int_{-\infty}^{\infty} p(x) e^{-j2\pi ux}dx \\ &= P(u) \\ \end{align} $
so F(u,0) is the same as P(u) which is the CTFT of the function p(x).
Credit: Prof. Bouman
Back to Lab Week 14 Quiz Pool
Back to ECE 438 Fall 2010 Lab Wiki Page
Back to ECE 438 Fall 2010