lecture06: 2D filters, and Linear systems
This lecture introduces block diagrams for representing and
building filters. It also considers filtering in 2D and one of its
applications: tomography, where we also see the Radon transform.
Topics covered
- How to draw filters
- Block diagrams of FIR filters
- Block diagrams of IIR filters
- Block diagrams and Z-transforms
- Block diagram of ARMA
- Abstracting the blocks
- Connecting the blocks
- Transposed Block diagram of ARMA
- Connecting the blocks
- Filtering in the real world
- Upsampling again
- Upsampling example
- Upsampling block diagram
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- Upsampling block diagram
- Downsampling
- Resampling
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- Digital to Analogue
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- Filter Design
- Convolution in 2D
- Filters in 2D
- Edge detection
- Sobel Edge detection
- Filters in 2D
- Prewitt filters
- Roberts filters
- Laplacian
- Filters in 2D
- Embossing an image
- Applications: tomography
- Computed Aided Tomography
- An example: Radon transform
- Fourier transform of the cut
- Fourier slice theorem
- Notional algorithm
- Back-projection filtering algorithm
- Sampling of Fourier Domain
- Examples