<< Chapter < Page
  Digital signal processing - dsp     Page 2 / 14
Chapter >> Page >

There are several different FFT algorithms in common use. In addition, there are many sites on the web where you can find explanations of themechanics of FFT algorithm. I won't replicate those explanations. Rather, I will explain the underlying concepts that make the FFT possible andillustrate those concepts using a simple program. Hopefully, once you understand the underlying concepts, one or more of the explanations of themechanics that you find on other sites will make sense to you.

A general-purpose transform

The Fourier transform is most commonly associated with its use in transforming time-domain data into frequency-domain data. However, it isimportant to understand that there is nothing inherent in the Fourier transform regarding either the time domain or the frequency domain. Rather,the Fourier transform is a general-purpose transform that is used to transform a set of complex data in one domain into a different set ofcomplex data in another domain. It is purely happenstance that it happens to be so valuable in describing the relationship between the time domain andthe frequency domain.

Transforming from space domain to wave number domain

For example, my first job after earning a BSEE degree in 1962 was in the Seismic Research Department of Texas Instruments. That is where I had myfirst encounter with Digital Signal Processing (DSP) . In that job, I did a lot of work with Fourier transforms involving the time domain and the frequencydomain. I also did a lot of work with Fourier transforms involving the space domain and the wave-number domain.

Wave number is the name given to the reciprocal of wavelength for compression and shear waves propagating through a medium such as an ironbar, earth, water, or air, and also for electromagnetic waves such as radio and radar propagating through space.

(Those familiar with the subject will know that while compression waves will propagate through water and air, those media won't supportshear waves.)

Two-dimensional Fourier transforms

For example, one of the things that we did was to compute two-dimensional Fourier transforms on diagrams representing weighted points intwo-dimensional space. We would transform the weighted points in the space domain into points in the wave-number domain.

The weighted points in the space domain represented the locations and amplifications of seismometers in a two-dimensional array on the surface ofthe earth. Each seismometer was amplified by a different gain factor and polarity. The amplified outputs of the seismometers were added together invarious and complex ways intended to enhance signals and suppress noise.

Wave-number response to seismic waves

In this case, the wave number was the reciprocal of the wave length of seismic waves propagating across the array. By plotting the results of thetransformation in the wave-number domain, we could estimate which seismic waves would be enhanced and which seismic waves would be suppressed by theprocessing being applied to the seismometer outputs.

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Digital signal processing - dsp. OpenStax CNX. Jan 06, 2016 Download for free at https://legacy.cnx.org/content/col11642/1.38
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Digital signal processing - dsp' conversation and receive update notifications?

Ask