Fourier Transform Question - Negative Frequencies?

In summary, the conversation discusses the confusion surrounding the interpretation of negative frequencies in a Fourier Transform or frequency domain graph. It is noted that while physically, frequencies are typically seen as positive, mathematically the FT allows for negative frequencies. It is clarified that negative frequencies are simply the complex conjugate of positive frequencies. The concept of positive and negative frequencies being interpreted as left and right circularly polarized waves is also mentioned.
  • #1
J$C
15
0
When I see a graph of a Fourier Transform, or something in the frequency domain, say band-limited from -[tex]\Omega[/tex] to [tex]\Omega[/tex], I'm confused to what the interpretation is of the negative frequencies. Physically it would seem as though something considered in cycles/second for example, should be positive but mathematically the FT will allow for negative frequencies.

Can somebody clarify this for me?
 
Physics news on Phys.org
  • #2
[tex]e^{-\omega ix}= e^{\omega (-i)x}[/tex] so negative frequencies are just the complex conjugate of the positive frequencies.
 
  • #3
Hadn't really thought about it. Physically positive/negative frequencies could be interpreted as left/right circularly polarized waves.
 

FAQ: Fourier Transform Question - Negative Frequencies?

What is a Fourier transform?

A Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies. It is used to analyze signals and systems in various fields, including mathematics, physics, and engineering.

What are negative frequencies in a Fourier transform?

Negative frequencies in a Fourier transform refer to frequencies that have a negative sign in their representation. These frequencies are also known as imaginary or complex frequencies and are used to represent oscillations that are out of phase with the original signal.

Why do we need to consider negative frequencies in a Fourier transform?

Negative frequencies are essential in a Fourier transform because they provide a complete representation of a signal. By including negative frequencies, we can accurately analyze signals that have both positive and negative frequencies, such as real-world signals that are non-symmetric.

How are negative frequencies represented in a Fourier transform?

Negative frequencies are typically represented using complex numbers in a Fourier transform. The real part of the complex number represents the positive frequency, while the imaginary part represents the negative frequency. Together, they form a complete representation of the original signal.

Can negative frequencies have physical significance?

No, negative frequencies do not have physical significance. They are simply a mathematical tool used to analyze signals and systems. In the real world, signals and oscillations cannot have negative frequencies, but they are useful in the mathematical representation of these phenomena.

Similar threads

I The Relationship Between Angular and Cyclic Frequency in Fourier Transform
Replies
2
Views
2K
How do I know "what Fourier transform" to use?
Replies
3
Views
1K
Fourier Transform of a sin(2pi*x)
Replies
7
Views
13K
I New frequency generation in AM signal
2
Replies
47
Views
3K
I Motivation for Fourier series/transform
Replies
8
Views
4K
What does the fourier transform do
Replies
1
Views
2K
Intuition for imaginary part of Fourier Transformation?
Replies
3
Views
3K
Fourier Transforms is Inflicting Pain
Replies
6
Views
2K
Fourier transform: duality property and convolution
Replies
1
Views
1K
Compact summary of Fourier series equations
Replies
11
Views
1K

Hot Threads

Recent Insights

Back
Top