Understanding Fourier Transforms: Solving Confusion with Even Functions

In summary, The problem was finding the Fourier Transform of a given function f(t). The integral was evaluated and the correct answer was obtained. The confusion arose when trying to use the Fourier cosine transform for an even function, and the resulting answer was different. The solution attempted was using the formula Fcosine = 2*int (1-t) cos (wt) dt from 0 to 1. However, the reason for the discrepancy is unknown.
  • #1
engcon
12
0
Hi, I got a problem in which I have to find the Fourier Transform of a function f(t) defined:

f(t) = { 1 - |t|, |t| < 1
0, |t| > 1 }

Well , I found the Fourier transform by working out the integral f(t)e^(-iwt) with the limits being -inf to +inf (and I got the right answer).

Now, since f(t) is an even function, does that mean I can use the Fourier cosine transform?

I tried to work it out and got a different answer, and basically I'm confused? :frown:

Any help is appreciated, thanks!
 
Mathematics news on Phys.org
  • #2
yeah i have the same problem here!
 
  • #3
Yes, the function is even, and so you can use the Fourier cosine transform. However, since you've not posted your solution, I can't see why you're getting a different answer.

eng_pro said:
yeah i have the same problem here!

Your user-name is very similar to the OP's. Coincidence?
 
  • #4
yes i did it

i used: Fcosine = 2*int (1-t) cos (wt) dt from 0 to1
 
  • #5
yep it is coincidence..i don't know the OP's username k
 

1. What is the Fourier Transform and how is it used?

The Fourier Transform is a mathematical operation used to decompose a function into its constituent frequencies. It is commonly used in signal processing, image processing, and data analysis to analyze the frequency components of a signal or data set.

2. What is the difference between the Fourier Transform and the Inverse Fourier Transform?

The Fourier Transform is used to convert a signal from the time domain to the frequency domain, while the Inverse Fourier Transform is used to convert a signal from the frequency domain back to the time domain. In other words, the Fourier Transform tells us what frequencies make up a signal, while the Inverse Fourier Transform tells us how much of each frequency is present in the signal.

3. Why is the Fourier Transform sometimes confusing to understand?

The concept of the Fourier Transform can be difficult to grasp because it involves complex mathematical concepts such as integration and complex numbers. Additionally, the visualization of the Fourier Transform can be challenging for some people to conceptualize.

4. How is the Fourier Transform related to other transforms, such as the Laplace Transform?

The Fourier Transform is a special case of the more general Laplace Transform. While the Fourier Transform is used for signals that are periodic or have a finite duration, the Laplace Transform can be used for signals that are non-periodic and have an infinite duration.

5. Can the Fourier Transform be applied to any type of data?

The Fourier Transform can be applied to any data that can be represented as a function, as long as it follows certain conditions such as being integrable and having a finite energy. This means that it can be applied to a wide range of data types, including signals, images, and even non-physical data such as stock prices or weather patterns.

Similar threads

A Memory issues in numerical integration of oscillatory function
    • General Math
Replies
3
Views
417
B How to calculate the Fourier transform of sin(a*t)*exp(-t/b) ?
    • General Math
Replies
7
Views
2K
MHB Property of real-valued Fourier transformation
    • General Math
Replies
1
Views
1K
MHB Fourier Series involving Hyperbolic Functions
    • General Math
Replies
9
Views
2K
MHB Aidan's question via email about Fourier Transforms (2)
    • General Math
Replies
1
Views
10K
I Get the time axis right in an inverse Fast Fourier Transform
    • General Math
Replies
2
Views
2K
Fourier Transform - Solutions Error?
    • Calculus and Beyond Homework Help
Replies
5
Views
328
I Fourier transform of a beat
    • Topology and Analysis
Replies
7
Views
2K
MHB Fourier Transform of Periodic Functions
    • General Math
Replies
5
Views
3K
A Polar Fourier transform of derivatives
    • Differential Equations
Replies
4
Views
2K

Hot Threads

Recent Insights

Back
Top