A Note on Fast Cyclic Convolution

Convolution Algorithms ∗

can be calculated with the FFT and bring the order of arithmetic operations down to Nlog (N) which can be signi cant for large N . This approach, which is called fast convolutions", is a form of block processing since a whole block or segment of x (n) must be available to calculate even one output value, y (n). So, a time delay of one block length is always required. Another problem is the lter...

6365 April 17 , 2008 Lecture # 26 : Fast Fourier Transforms – I

The Fast Fourier Transform, the FFT, is one of the most widely used algorithms in science and engineering. It is used both in signal processing and for the solution of partial differential equations. For instance, FFTs are used in so–called Fast Poisson solvers. It is also used in combination with cyclic reduction for the FACR (Fourier Analysis Cyclic Reduction) [4] method for Poisson’s equatio...

A note on the comparison between Laplace and Sumudu transforms

Some Historical Notes on Number Theoretic Transform

Modulo arithmetic modulo a prime integer have many interesting properties. Such properties are found in standard books on number theory. Some properties are especially of interest to the signal processing application. It was observed analogy exists between some of them and that cyclic convolution of two sequences modulo a prime integer of two sequences could be computed in integer domain as can...

Fast DCT-based image convolution algorithms and application to image resampling and hologram reconstruction

Convolution and correlation are very basic image processing operations with numerous applications ranging from image restoration to target detection to image resampling and geometrical transformation. In real time applications, the crucial issue is the processing speed, which implies mandatory use of algorithms with the lowest possible computational complexity. Fast image convolution and correl...