by H.O. Bartelt, et. al.
An optical signal (image etc.) can be described by its complex amplitude u (x,y), or by its spatial frequency spectrum. Both descriptions are complete and also equivalent, because one can be derived from the other by a Fourier transformation. Neither the complex amplitude nor the spatial frequency spectrum is suitable for answering a question like "what is the spatial frequency in a certain part of the image?". Here the term "local spectrum" is adequate. A rigorous definition of the "local spectrum" can be based on the Wigner distribution function. We developed optical methods for producing this "local spectrum" and we applied these methods to the investigation of sound patterns.
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