# Fourier Transform Question - Negative Frequencies?

#### J\$C

When I see a graph of a Fourier Transform, or something in the frequency domain, say band-limited from -$$\Omega$$ to $$\Omega$$, 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?

#### HallsofIvy

Homework Helper
$$e^{-\omega ix}= e^{\omega (-i)x}$$ so negative frequencies are just the complex conjugate of the positive frequencies.

#### Phrak

Hadn't really thought about it. Physically positive/negative frequencies could be interpreted as left/right circularly polarized waves.

### Physics Forums Values

We Value Quality
• Topics based on mainstream science
• Proper English grammar and spelling
We Value Civility
• Positive and compassionate attitudes
• Patience while debating
We Value Productivity
• Disciplined to remain on-topic
• Recognition of own weaknesses
• Solo and co-op problem solving