CS430 - S'05
Lecture 06 : 2/1/05

Reading Assignment: 4 Gonzalez/Woods

Today's Topics

• Frequency Concepts
• 1D Fourier Transform
• 1D Spectrum
• 2D Fourier Transform
• 2D Spectrum

What Spectrum Would This Image Produce? answer

Image Enhancement in the Frequency Domain

Function Summation

• Example Summation
• 1D Frequency Spectrum
• sin(x)
• sin(3x)
• sin(5x)
• sin(1x) + 1/3*sin(3x)
• sin(1x)+1/3*sin(3x)+1/5*sin(5x)+1/7*sin(7x)
• sin(1x)+1/3*sin(3x)+...+1/41*sin(41x)
• What happens if you don't multiply by 1/factor on each term.

Fourier Transform

• Transform Figure
• Transform Notation
• Important Note
• Spectrum Definition
• Spectrum Details
• Power Spectrum
• Filtering
• Examples
• Vertical Line
• Vertical Line Shifted
• 45 Degree Line
• Small Dot
• Small Dot Shifted
• Small Dot In Lower Left
• Larger Dot
• Larger Fuzzy Dot
• Two Dots
• Horizontal line
• Vertical line
• Checker Board 4x4
• Checker Board 8x8
• Checker Board 32x32
• Big Circle
• 32 Cosine Wave Horizontal
• 32 Cosine Wave Vertical
• 64 Cosine Wave Horizontal
• 64 Cosine Wave Vertical
• 128 Cosine Wave Horizontal
• 128 Cosine Wave Vertical
• 64 Square Wave Horizontal
• 64 Square Wave Vertical
• 10 Target (cosine)
• 20 Target (cosine)
• 40 Target (cosine)
• 80 Target (cosine)