How Do I Calculate Frequencies from FFT Results?

Understanding FFT Frequency Outputs

Analyzing the frequency components of a signal using the Fast Fourier Transform (FFT) requires understanding how to map FFT output bins to actual frequencies. This involves using the sample rate and FFT size.

Frequency Calculation

The frequency (f) of the nth bin in an FFT's output is calculated as:

<code>f = n * Fs / N</code>

where:

• n is the bin index (starting from 0)
• Fs is the sampling rate of the input signal
• N is the size of the FFT (number of points)

Illustrative Example

Let's say we have an FFT with a sampling rate (Fs) of 44.1 kHz and an FFT size (N) of 1024. The first bin (n = 0) represents DC (0 Hz). The second bin (n = 1) represents a frequency of approximately 43.07 Hz (1 * 44100 / 1024). Each subsequent bin represents a progressively higher frequency.

Important Note: Real Signals

For real-valued input signals, the FFT output exhibits Hermitian symmetry. This means the second half of the FFT results (bins N/2 to N-1) are redundant, being complex conjugates of the first half (bins 0 to N/2-1). Therefore, only the first half (up to and including bin N/2 -1) contains unique frequency information. The highest frequency represented is Fs/2 (the Nyquist frequency).

In Summary

Using the simple formula above, we can accurately determine the frequency associated with each bin in an FFT's output. This is a crucial step in various signal processing applications, allowing for detailed frequency analysis and interpretation.

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