Which is the variable for amplitude in fourier transform equation?

Posted on 2013-02-04
Medium Priority
Last Modified: 2013-11-25
In this Sinusoidual signal equation: Equation

I know that A_0 is to shift the signal up or down, and the A_n is for the amplitude. What I don't understand however is when this equation is transformed into Fourier transform equation, the variable for the amplitude goes missing?

This is the fourier transform equation: Fourier Transform Equation
Both a_n and b_n are variables for the phase. What about the variable for the amplitude?
Question by:xenonn
LVL 27

Accepted Solution

aburr earned 1000 total points
ID: 38851892
The a_n and b_n are the amplitudes of the sin and cos part of the final answer.
They combine to give the amplitude (and phase) of the periodic wave
a cos (wt) + b sine(wt) = c sin(wt + p)
c = (a^2 + b^2)^0.5            p = arctan(b/a)         b = c cos(p)      a = c sin(p)
LVL 15

Assisted Solution

yuk99 earned 1000 total points
ID: 38852216
The answer provided by aburr is exactly right. I just get late a bit. :)

Since you put your question also to MATLAB zone let me give you some code to illustrate the function behavior depending on a_n and b_n;

x = linspace(-pi*2,pi*2,100);
n = 3;
hold on
for a = 2:n
for a = 2:n
for a = 1:n
hold off

Open in new window

On the resulting plot you will see red lines for a>b, blue - for a<b and green - for a==b. You can see that if a==b, the greater the coefficients, the greater the amplitude. And the greater the difference, the greater the phase shift.

Featured Post

A proven path to a career in data science

At Springboard, we know how to get you a job in data science. With Springboard’s Data Science Career Track, you’ll master data science  with a curriculum built by industry experts. You’ll work on real projects, and get 1-on-1 mentorship from a data scientist.

Question has a verified solution.

Are you are experiencing a similar issue? Get a personalized answer when you ask a related question.

Have a better answer? Share it in a comment.

Join & Write a Comment

This month, Experts Exchange’s free Course of the Month is focused on CompTIA IT Fundamentals.
If you try to migrate from Elastix to Issabel, you will face a lot of issues. These problems are inevitable but fortunately, you can fix them. In the guide below, I will explain how I performed the migration while keeping all data and successfully t…
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
In a recent question (https://www.experts-exchange.com/questions/29004105/Run-AutoHotkey-script-directly-from-Notepad.html) here at Experts Exchange, a member asked how to run an AutoHotkey script (.AHK) directly from Notepad++ (aka NPP). This video…

624 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question