# Fast Fourier Transform Amplitude Units

• thundgra
In summary, when computing the FFT on a multi year time series of heights in meters and calculating the amplitude as abs(FFT)/N, the resulting units for the amplitude are still in meters. This is because the FFT is simply multiplying the original data by unitless exponentials and dividing by N does not change the units. The zero-frequency bin is also just an average of the original data, so it also has the same units.
thundgra
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

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

## 1. What is the Fast Fourier Transform (FFT)?

The Fast Fourier Transform (FFT) is a mathematical algorithm used to convert a signal from its original time domain into its equivalent representation in the frequency domain. It is used to analyze the frequency components of a signal and is widely used in various fields such as signal processing, image processing, and audio analysis.

## 2. What are amplitude units in FFT?

Amplitude units in FFT refer to the units used to measure the strength or magnitude of the frequency components of a signal. These units depend on the type of signal being analyzed and can range from decibels (dB) for audio signals to meters for seismic signals.

## 3. How are amplitude units related to the FFT output?

The FFT output is a plot of the frequency components of a signal, with the x-axis representing the frequency in Hertz and the y-axis representing the amplitude in the chosen units. The amplitude units are directly related to the FFT output as they determine the scale of the y-axis and the magnitude of each frequency component.

## 4. What is the difference between linear and logarithmic amplitude units?

Linear amplitude units refer to a scale where the amplitude values increase in a linear fashion, while logarithmic units use a logarithmic scale where the amplitude values increase exponentially. Logarithmic units are commonly used in audio signals as they better represent the human perception of sound intensity.

## 5. Can the amplitude units in FFT be converted to other units?

Yes, the amplitude units in FFT can be converted to other units through simple mathematical operations. However, it is important to note that the conversion should be based on the specific type of signal being analyzed to ensure accuracy.

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