How Do I Determine the Frequencies in My FFT Results?

Unlocking the Frequencies in Your FFT Data

Understanding the frequency components within your Fast Fourier Transform (FFT) results is crucial for analyzing signal spectra. This guide explains how to calculate and interpret these frequencies.

Frequency Calculation

The frequency of each FFT bin is determined using this simple formula:

Frequency = Bin Index * (Sampling Rate / FFT Points)

For example, with a 44.1 kHz sampling rate and a 1024-point FFT:

Bin 0: 0 (44100 / 1024) = 0 Hz Bin 1: 1 (44100 / 1024) = 43.1 Hz

Interpreting FFT Output

For real-valued input signals, the FFT's second half (bins N/2 1 to N-1) is redundant. The highest practically useful frequency is found at bin N/2 - 1, representing the Nyquist frequency (half the sampling rate). This is the maximum frequency resolvable by the FFT.

Illustrative Example

Let's examine a 1024-point FFT with a 44.1 kHz sampling rate. The table below shows the frequencies for the first ten bins:

Bin Index	Frequency (Hz)
0	0
1	43.1
2	86.1
3	129.2
4	172.3
5	215.3
6	258.4
7	301.5
8	344.5
9	387.6

By understanding these frequency mappings, you can accurately identify and analyze the spectral components present in your FFT output.

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