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Lecture 1 - The Fourier Transforms and its Applications

Folder Name. Folder Description. Satellite imaging. Earth observing sensors.

Image processing. Infrared imaging.

An optical Fourier transform coprocessor with direct phase determination

Phase shifts. Imaging systems. Data modeling. Digital image processing.

Course Description

Infrared radiation. Show All Keywords. Even the "exact" FFT algorithms have errors when finite-precision floating-point arithmetic is used, but these errors are typically quite small; most FFT algorithms, e. Cooley-Tukey, have excellent numerical properties. These results, however, are very sensitive to the accuracy of the twiddle factors used in the FFT i.

Fast Fourier Transform and Its Applications -

Moreover, even achieving this accuracy requires careful attention to scaling in order to minimize the loss of precision, and fixed-point FFT algorithms involve rescaling at each intermediate stage of decompositions like Cooley-Tukey. This compositional viewpoint immediately provides the simplest and most common multidimensional DFT algorithm, known as the row-column algorithm after the two-dimensional case, below.

In more than two dimensions, it is often advantageous for cache locality to group the dimensions recursively. Yet another variation is to perform matrix transpositions in between transforming subsequent dimensions, so that the transforms operate on contiguous data; this is especially important for out-of-core and distributed memory situations where accessing non-contiguous data is extremely time-consuming.

The Discrete Fourier Transform and the Fast Fourier Transform

This may also have cache benefits. The simplest case of vector-radix is where all of the radices are equal e.

Vector radix with only a single non-unit radix at a time, i. Other, more complicated, methods include polynomial transform algorithms due to Nussbaumer , which view the transform in terms of convolutions and polynomials products.

Signal Decomposition, Time and Frequency domains

See Duhamel and Vetterli for more information and references. From Prime-Wiki. Jump to: navigation , search.

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