Why didn't I see a peak at half the frequency in my FFT analysis of two waves?

Click For Summary
SUMMARY

The discussion centers on the unexpected results of FFT analysis when comparing two waves, one resembling a sine wave and the other exhibiting a dip at half the main frequency. The user anticipated a smaller peak at half frequency but concluded that the complexity of the wave resulted in additional higher harmonics instead. The original wave consists of two sine waves in opposite phases, each modulated by a rectangular wave, complicating the expected FFT output. The user seeks clarification on the appearance of the dip and its implications in the frequency domain.

PREREQUISITES
  • Understanding of Fast Fourier Transform (FFT) analysis
  • Knowledge of sine and rectangular waveforms
  • Familiarity with Fourier transforms and their properties
  • Basic concepts of wave modulation and phase relationships
NEXT STEPS
  • Explore the effects of wave modulation on FFT results
  • Learn about the implications of phase differences in waveforms
  • Investigate the relationship between time-domain signals and their frequency-domain representations
  • Study the convolution of signals in the frequency domain
USEFUL FOR

Researchers, signal processing engineers, and students analyzing waveforms and their frequency characteristics through FFT analysis.

Sam Smith
Messages
37
Reaction score
0
I am carrying out FFT analysis to compare two waves. One looks very much like a sine wave the other has an extra dip occurring at half the frequency of the main wave. I have been thinking around how I might expect this to show up in the FFT analysis. At first i was expecting to see a smaller peak at half the main frequency but after a while I thought that it may just result in a few more higher harmonics due to the fact that the wave is becoming more complex. I did the FFT and I didnt see a peak at half frequency. so I guess the second conclusion is correct btu I still can't reconcile why I would expect to see a peak at half frequency of the main peak?
 
Physics news on Phys.org
What does the "dip" look like?
 
Well the original wave is a two sine waves put together each mirroring the other. The dip is in between them so instead of going back to zero the graph dips instead :)
 
OK, so two sine waves mirroring each other have the same frequency but opposite phase. Each of those sine waves is multiplied by a rectangular wave in the time domain, which means that it is convolved with the transform of the rectangular wave in the frequency domain. So you will expect to see a signal that looks much more like the sum of two Fourier transforms of a rectangular wave. Since they are each modulated by the same frequency but opposite phases the resulting sum is not obvious to me. I would expect it to look "complicated".
 
Can you post images? Your description is unclear.
 

Similar threads

Undergrad Please discuss discrete Fourier analysis
  • · Replies 12 ·
Replies
12
Views
2K
Graduate Why do sound waves with slightly different frequencies create beats?
  • · Replies 6 ·
Replies
6
Views
3K
Graduate Fourier Transform : Analysis of 2 different signals
  • · Replies 17 ·
Replies
17
Views
4K
Graduate Understanding gravitational waves (GR)
  • · Replies 43 ·
2
Replies
43
Views
6K
Graduate Understanding Lissajous Curves for Fourier Synthesis
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Resonant Frequencies from Fourier Analysis
  • · Replies 6 ·
Replies
6
Views
2K
Graduate Fourier transform capabilities in reconstructing missing data
  • · Replies 3 ·
Replies
3
Views
5K
Graduate Limits of pitch and time resolution in signal analysis (FFT/SFTF)
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Why should a Fourier transform not be a change of basis?
  • · Replies 43 ·
2
Replies
43
Views
7K
Application and Limitation of Fourier Analysis
  • · Replies 2 ·
Replies
2
Views
2K