Different Domains
Here integral transforms are defined for functions on the real numbers, but they can be defined more generally for functions on a group.
- If instead one uses functions on the circle (periodic functions), integration kernels are then biperiodic functions; convolution by functions on the circle yields circular convolution.
- If one uses functions on the cyclic group of order n ( or ), one obtains n × n matrices as integration kernels; convolution corresponds to circulant matrices.
Read more about this topic: Integral Transform
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