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Many tricks and techniques have been developed to speed up the computation of FFTs. Significant reductions in computation time result from table lookup of twiddle factors, compiler-friendly or assembly-language programming, special hardware, and FFT algorithms for real-valued data.Higher-radix algorithms, fast bit-reversal, and special butterflies yield more modest but worthwhile savings.

The use of FFT algorithms such as the radix-2 decimation-in-time or decimation-in-frequency methods result in tremendous savings in computations when computing the discrete Fourier transform . While most of the speed-up of FFTs comes from this,careful implementation can provide additional savings ranging from a few percent to several-fold increases in program speed.

Precompute twiddle factors

The twiddle factor , or W N k 2 k N , termsthat multiply the intermediate data in the FFT algorithms consist of cosines and sines that each take the equivalent of several multiplies to compute.However, at most N unique twiddle factors can appear in any FFT or DFT algorithm.(For example, in the radix-2 decimation-in-time FFT , only N 2 twiddle factors k k 0 1 2 N 2 1 W N k are used.) These twiddle factors can be precomputed once and storedin an array in computer memory, and accessed in the FFT algorithm by table lookup . This simple technique yields very substantial savings andis almost always used in practice.

Compiler-friendly programming

On most computers, only some of the total computation time of an FFT is spent performing the FFT butterfly computations;determining indices, loading and storing data, computing loop parameters and other operations consume the majorityof cycles. Careful programming that allows the compiler to generateefficient code can make a several-fold improvement in the run-time of an FFT.The best choice of radix in terms of program speed may depend more on characteristics of the hardware (such as the number of CPU registers) orcompiler than on the exact number of computations. Very often the manufacturer's library codes are carefullycrafted by experts who know intimately both the hardware and compiler architecture and how to get the most performanceout of them, so use of well-written FFT libraries is generally recommended.Certain freely available programs and libraries are also very good.Perhaps the best current general-purpose library is the FFTW package; information can be found at (External Link) . A paper by Frigo and Johnson describes many of the key issues in developing compiler-friendly code.

Program in assembly language

While compilers continue to improve, FFT programs written directly in the assembly language of a specific machine are oftenseveral times faster than the best compiled code. This is particularly true for DSP microprocessors, which havespecial instructions for accelerating FFTs that compilers don't use. (I have myself seen differences of up to 26 to 1 in favor of assembly!)Very often, FFTs in the manufacturer's or high-performance third-party libraries are hand-coded in assembly.For DSP microprocessors, the codes developed by Meyer, Schuessler, and Schwarz are perhaps the best ever developed; while the particular processors are now obsolete, the techniquesremain equally relevant today. Most DSP processors provide special instructions and ahardware design favoring the radix-2 decimation-in-time algorithm, which is thus generally fastest on these machines.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
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Source:  OpenStax, The dft, fft, and practical spectral analysis. OpenStax CNX. Feb 22, 2007 Download for free at http://cnx.org/content/col10281/1.2
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