{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

ft-2d.slides.printing

# ft-2d.slides.printing - The 2-D Fourier Transform The 2-D...

This preview shows pages 1–8. Sign up to view the full content.

The 2-D Fourier Transform The 2-D Fourier Transform CS 450: Introduction to Digital Signal and Image Processing Bryan Morse BYU Computer Science

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The 2-D Fourier Transform Introduction Two-Dimensional Continous Fourier Transform Basis functions are product of generalized sinusoids with frequency u in the x direction generalized sinusoids with frequency v in the y direction b ( u , v ) = e i 2 π ux e i 2 π vy = e i 2 π ( ux + vy ) 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 u = 4 , v = 0 u = 0 , v = 5 u = 4 , v = 5 (real parts)
The 2-D Fourier Transform Continuous Transform Two-Dimensional Continous Fourier Transform The transform now becomes: F ( u , v ) = -∞ -∞ f ( x , y ) e - i 2 π ( ux + vy ) dx dy Similar process for the inverse: f ( x , y ) = -∞ -∞ F ( u , v ) e i 2 π ( ux + vy ) du dv

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The 2-D Fourier Transform Examples Example Image Fourier Transform (magnitude)
The 2-D Fourier Transform Examples One-Dimensional Fourier Transform: 1-D Square Pulse

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
The 2-D Fourier Transform Examples Two-Dimensional Fourier Transform: 2-D Square Pulse
The 2-D Fourier Transform Examples Two-Dimensional Fourier Transform: Another Example

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}