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 are the same
and then combining answers
Examples of divi
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 difficult
! 1-D designs very well studied and understood
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
rectangular samples of its Fourier transform
! Is there
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 system response defined using z- transform
! Frequency resp
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 ) = i(n1 , n2 )e j1n1 e j2n2
n1
n2
I (1 , 2 ) consists of a
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 correct track containing the desired row and
then the corre
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 support
- Infinite-duration impulse response (IIR) or recursi
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 Discrete Cosine Transform (DCT)
- JPEG
- MPEG
- MPEG2
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!
More general sampling theory needed.
Applications:
1. Hum