Sources of information on time-frequency domain transformation

[korni]

Hello PF members

I am a very new member to your forum
and very new to time-frequency transformation.

Over the summer I will be doing some research on vibration signals
and for now I want to start understanding some basic things
upon the time and frequency domain
and transformation between the two
using Fourier Series and Fourier Transform.

What I am looking for is sources of information (preferably books to get from library)
around this subject
and hopefully some that will be relevant to the field of vibrations.

Do you have any knowledge upon which books can I start from?

I am really glad I found this forum cause there is a lot information on my subject
and a lot of questions I myself have. I will be visiting often :D

Regards
korni

 

[korni]

Anybody who could help guys?
I am trapped!

I started of with:
Fundamentals of signal processing for sound and vibration engineers (by Wiley) (too much maths)

and with Dynamics of structures by Clough and Penzien
but am still struggling.

something for the noob? :)

 

[olivermsun]

There is a book by T. W. Korner called "Fourier Analysis" which I found interesting reading, although it may depend what level of mathematics you are looking for.

If you want something with a more engineering-oriented approach suitable for DSP applications, you might look for Oppenheimer, "Discrete-Time Signal Processing."

There are many resources on the web which are quite helpful for understanding the basics of Fourier Analysis (including Wikipedia, which is always a quick and easy place to get a table of transform pairs).

 

[korni]

Thank you very much for taking the time to reply to my question.

I am mainly looking an engineering approach
but something that will explain in that context the relations between time domain and frequency domain
comment on the use of each and advantages disadvantages etc.

I will take a look on what you proposed.

Thanks again!

PS. I have been reading over wiki, but can't say I can feel reliable to it

 

[paulfr]

The time domain is the time signal you would see on an oscilliscope being fed from some transducer that converts the physical phenomena into an electrical signal.

The frequency domain is what you see from a Spectrum Analyzer. What this does is create filters that measure the amount of energy at that frequency. It then changes the frequency band of the filter to measure at another frequency and continues to do this until the entire frequency band of interest is plotted. This is called sweeping.

You need to understand Fourier Series and Fourier Analysis to understand that all periodic signals [signals that repeat the same time domain shape again and again] are equivalent to an infinite sum of sine and cosine waves of different magnitudes and harmonically related frequencies.

My favorite book on the subject is by Ronald Bracewell former professor at Stanford U.

The math does look involved but the general idea is simple.

Here is a video that is fairly basic.
http://www.youtube.com/watch?v=fofJkOWW8GM&feature=related

You can see that integration is needed to do the transformation from time to frequency domain.

 

[korni]

Hi paulfr

I started reading the following book

Dynamics of Structures - By Clough and Penzien
which seems alright up to now.
I have understood a lot of stuff
and it binds up together the maths I read before

I don't mind the maths
and I am familiar with Fourier Series
it is just that the books I was finding in the beginning had to do only with the maths
and not the engineering side of the aspect.

I will definitely look at the book you are proposing
( is it Bracewell, R.N., The Fourier Transform and Its Applications ? )

And thank you very much for writting down these stuff

Kind regards

 

[paulfr]

Yes, you have the correct book and title.
It is quite heavy in Math but covers a wide range of applications for frequency domain transformations.
Basically, looking at the frequency domain gives one another view of the system under consideration which allows deeper understanding and analysis.

 

[korni]

I think this is exactly what I was looking for.
I'll be getting the book tomorrow.

Thanks again!