Vector Radix FFT Algorithm
Multidimensional rederivation of the 1-D FFT
Divide-and-conquer algorithm
! Operates as a recursive procedure
! Solves problem by dividing it into smaller problems that ar
FIR Filter Design Using Transformations
Objectives
! Reduces M-D FIR design to 1-D FIR design
! Efficient realization of designed filters
Motivation
! M-D designs based on L (Chebyshev) norm are dif
More General DFT
Motivation: The DTFT can be sampled in different ways other than
using a rectangular sampling grid => general DFT!
The rectangular DFT relates a finite-extent rectangular array to
r
IIR Filters
Infinite-length impulse response => cannot use convolution or DFT
to realize filter
IIR filter generally implemented using difference equations and
recursive implementation
General syst
Design of 2D Finite-Impulse-Response (FIR) Filters
2-D FIR Filter Design Problem
Let
I (1 , 2 ): Frequency response of ideal filter
and
i ( n1 , n 2 ) : Impulse response of ideal filter
I (1 , 2 ) =
Computation of The 2D DFT - RC Algorithm
Limited-Storage issues
Assume data stored rowwise on a disk drive or on tape (which is worse
for access time).
time)
Row 0
Row 1
Head must first find the corr
2D Finite-Impulse-Response (FIR) Filters
Introduction
! LSI digital filters are of two main types:
- Finite-duration impulse response (FIR) or nonrecursive filters: impulse response has
finite suppor
The Discrete Cosine Transform (DCT)
Introduction
! The DFT is not the only transform that is widely used in
applications
! Published standards for image and video coding (compression)
make use of the
Motivation For The General Sampling Case
Rectangular sampling is just a straightforward
generalization of the familiar 1-D result but it is actually just
a special case instead of a general one!
Mor