Title :
Nested quadratic arithmetic for efficient convolution of complex sequences with Quadratic Modified Fermat Number Transforms
Author :
Radhakrishnan, C. ; Jenkins, W.K.
Author_Institution :
Dept. of Electr. Eng., Pennsylvania State Univ., University Park, PA, USA
Abstract :
Recently the Modified Fermat Number Transform (MFNT) was extended to a Quadratic MFNT (QMFNT) by combining Right Circular Convolution (RCC) and Left Circular Convolution (LCC) to produce a quadratic representation of the convolution output. This paper investigates nesting of two distinct quadratic number representations, the first associated with quadratic coding of complex input sequences, and the second associated with QMFNT block processing. Quadratic coding of complex sequences combined with QMFNT block processing eliminates cross-products in the complex multiplication. Finally, a generalized form of the QMFNT (GMFNT) is introduced and then extended into two dimensions.
Keywords :
convolution; transforms; QMFNT block processing; RCC; complex multiplication; complex sequences convolution; left circular convolution; nested quadratic arithmetic; quadratic MFNT; quadratic coding; quadratic modified Fermat number transforms; quadratic number representation; right circular convolution; Convolution; Equations; Fault tolerance; Fault tolerant systems; Modulation; Transforms; 2-D MFNT; Fermat Number Transforms (FNT); efficient 2-D block processing; fast 2-D convolution; modified FNT (MFNT); quadratic MFNT (QMFNT);
Conference_Titel :
Signals, Systems and Computers (ASILOMAR), 2011 Conference Record of the Forty Fifth Asilomar Conference on
Conference_Location :
Pacific Grove, CA
Print_ISBN :
978-1-4673-0321-7
DOI :
10.1109/ACSSC.2011.6189974
