@Janith (1) I think your comment (repeated below), indicates that your seem to have not thoroughly understood two things: (a) the meanings of "time domain" and "frequency domain", (b) the general operation procedure/pattern of "transform".

Let me first repeat you comment in your edited question, which is in two parts: (i) I think both amplitude spectrum and phase spectrum can be plotted using complex form of Fourier series. (ii) But,in general form of Fourier series I can't find the phase in that.

I would suggest to use the following article for reference to our coming discussion on your question about "... I can't find the phase in that. It would be nice if your would read it quickly before you would give any comments related to you question.

Now the article:

Nothing in a hurry. I would suggest you to read the article, think about it in your leisure time (me too) and come back later.

I mean in general form of fourier series , which indicates phase ?

I think you can find the answer to your question in the article I am referring.

(1) The Elster's MR article is very short, so I think you can get the answer in less than 30 seconds (me 3 sec!), (2) This paper is actually part of my (locked) answer to your question of FFT apps: Using FFT in MRI. Happy reading and learning.

I understand a little bit more from it. Fourier series is a method which can be used to express any periodic function as a series of sinusoids.But,Fourier transform is a mathematical procedure for converting a signal in time domain to a complex number in frequency domain . So, in spectrum , the complex function(y) is plotted against frequency(x) .And General form of Fourier series is a simplification of Fourier series.

I will edit my question back.

However, you still need to polish and reword your statements a bit, otherwise you will mislead the teacher or examiner that you only know 90% of the stuff. Let me suggest some rewording. (1) Fourier series, by definition, is NOT a "method", though you can say it is a "representation". You might try again. (2) "Spectrum" is misleading, perhaps you should say "Spectrum Analysis" (SA). You might guess why SA is not mentioned in FFT theory, but only in FFT application.

Ah, locking down jogging/supper time. See you later.