Signal and Image Processing in Different Representations
Abstract
One of the fundamental and powerful ideas of signal processing is that of a system function and input-output relations. Traditionally input-output relations are formulated in the time domain or, equivalently, in the spectral domain. However, over the last sixty years it has been found that many natural and man made signals are nonstationary, and the standard formulation does not fully describe what is happening, and therefore is not effective. We have shown that an immense simplification occurs, both conceptually and technically, when input-output relations are formulated in the combined time-frequency plane. We have developed an approach for formulating time-frequency/input-output systems for both the deterministic and random case. Using our approach we have solved a number of hitherto unsolved problems. In particular, we have been able to obtain the exact time-dependent solution of the Wiener process, the exact solution to the gliding tone problem, and the full exact solution to the RC circuit driven by white noise, among other problems. In addition, using our formulation we have clarified the issues with the ABC algorithm proposed by A. Noga, and we have also been able to formulate nonstationary noise so that it produces images that are similar to real clouds.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2008
- Accession Number
- ADA477410
Entities
People
- Leon Cohen
Organizations
- Hunter College