DFT: Properties

Building the Cantata Workspace

1. Create a centered white rectangle on a black background using the operators Constant and Pad . Display it.
2. Take the forward Fourier transform using FFT and display it.
3. Rotate the object using the operator Rotate . Take its DFT and display it.
4. Add the centered rectangle and the rotated rectangle using the operator Blend , then take the forward DFT and display the result.
5. Translate the object using the operator Translate .
6. Expand the original image by a factor of two using the operators: Expand , Impulse and Multiply .

Exercises

• Translate the DFT by half of the image dimension using the translation property, by multiplying the image by (-1)**(x+y).
  Hint: use operators Piecewise Linear , Add and AND .
• Create a small 8x8 pattern and replicated it to generate a 256x256 image using the expansion property.