Solved

Which is the variable for amplitude in fourier transform equation?

Posted on 2013-02-04
2
634 Views
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?
0
Comment
Question by:xenonn
2 Comments
 
LVL 27

Accepted Solution

by:
aburr earned 250 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)
where
c = (a^2 + b^2)^0.5            p = arctan(b/a)         b = c cos(p)      a = c sin(p)
0
 
LVL 15

Assisted Solution

by:yuk99
yuk99 earned 250 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);
clf
n = 3;
hold on
for a = 2:n
    plot(x,a*sin(x)+cos(x),'color','r')
end
for a = 2:n
    plot(x,sin(x)+a*cos(x),'color','b')
end
for a = 1:n
    plot(x,a*sin(x)+a*cos(x),'color','g')
end
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.
0

Featured Post

How your wiki can always stay up-to-date

Quip doubles as a “living” wiki and a project management tool that evolves with your organization. As you finish projects in Quip, the work remains, easily accessible to all team members, new and old.
- Increase transparency
- Onboard new hires faster
- Access from mobile/offline

Join & Write a Comment

Suggested Solutions

Title # Comments Views Activity
nmap scanner? 7 82
Copy a file to a share on a Domain 3 57
VMware NSX version 6.2.2 upgrade 6.2.4 6 50
Server Room Hardware 5 49
This is an article about my experiences with remote access to my clients (so that I may serve them) and eventually to my home office system via Radmin Remote Control. I have been using remote access for over 10 years and have been improving my metho…
When it comes to security, there are always trade-offs between security and convenience/ease of administration. This article examines some of the main pros and cons of using key authentication vs password authentication for hosting an SFTP server.
Viewers will learn how to connect to a wireless network using the network security key. They will also learn how to access the IP address and DNS server for connections that must be done manually. After setting up a router, find the network security…
The goal of the video will be to teach the user the concept of local variables and scope. An example of a locally defined variable will be given as well as an explanation of what scope is in C++. The local variable and concept of scope will be relat…

760 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

Need Help in Real-Time?

Connect with top rated Experts

16 Experts available now in Live!

Get 1:1 Help Now