Fast Fourier Transform Amplitude Units

Click For Summary
SUMMARY

The Fast Fourier Transform (FFT) applied to a time series of heights in meters retains the original units of meters for the amplitude calculation. When computing the amplitude using the formula abs(FFT)/N, where N is the number of samples, the units remain unchanged. This is because the FFT process involves multiplying by unitless exponentials and summing, and dividing by N simply averages the data without altering its units.

PREREQUISITES
  • Understanding of Fast Fourier Transform (FFT) principles
  • Basic knowledge of time series analysis
  • Familiarity with amplitude calculations
  • Concept of unit consistency in mathematical operations
NEXT STEPS
  • Research the mathematical foundations of Fast Fourier Transform (FFT)
  • Explore time series analysis techniques for height data
  • Learn about amplitude and frequency domain representations
  • Investigate unit consistency in signal processing
USEFUL FOR

Data scientists, signal processing engineers, and researchers working with time series data who need to understand the implications of FFT on unit measurements.

thundgra
Messages
1
Reaction score
0
Hi there,

So I have a multi year time series of of heights in meters that I am working on. If I compute the FFT on the data and then calculate the amplitude as: abs(FFT)/N where N is the number of samples what units do I end up with for the amplitude? Is it still in meters?
Cheers
 
Physics news on Phys.org
Yes, it is still in meters. The FFT is just taking the original data, multiplying it by exponentials (which are unitless), and summing. Dividing by N does not change the units - indeed, for the zero-frequency bin you are just averaging the original data, so it has the same units.

jason
 

Similar threads

Graduate Memory issues in numerical integration of oscillatory function
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Fourier transform, same frequencies, different amplitudes
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Fourier transform of rectangular pulses
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad The Relationship Between Angular and Cyclic Frequency in Fourier Transform
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad The domain of the Fourier transform
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Can an FFT be used to extract individual sinusoids from a set of data points?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Ambiguous Results for two Fourier transform techniques
  • · Replies 7 ·
Replies
7
Views
3K
Undergrad Magnitude and phase of the Fourier transform
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Motivation for Fourier series/transform
  • · Replies 8 ·
Replies
8
Views
5K
Undergrad What Is the Amplitude of a Harmonic Load in the Frequency Domain?
  • · Replies 2 ·
Replies
2
Views
1K