EECS20N: Signals and Systems

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Week 10

• FS coefficients
• Negative freq.
• Transfer function
• Filtering
• Filtering sounds
• Filtering images
• Cascade
• Freq response
• Commutativity
• Feedback
• Freq response

Filtering Images

Below is an original image, the same image after lowpass filtering, and the same image after highpass filtering:

  

Lowpass filtering in images has the effect of blurring the image. In fact, optical lenses that blur an image can be modeled as LTI lowpass filters. Highpass filtering has a rather strange effect on an image. Notice that solid blocks of color are replaced with a middle gray. This is because solid blocks of color correspond to low spatial frequencies, which are removed by highpass filtering. Edges correspond to high spatial frequencies, so the regions near the edges are relatively enhanced. Patterns, such as that in Helen's suit above, are largely preserved, since they consist primarily of high spatial frequencies.