How Do I Determine the Frequencies Corresponding to Bins in an FFT Result?

Understanding FFT Frequency Bins

Interpreting Fast Fourier Transform (FFT) results often requires understanding the frequency associated with each output bin. This is directly related to the sample rate and FFT size.

The first bin (bin 0) always represents the DC component (0 Hz). Subsequent bins correspond to frequencies calculated using the formula: f = n * Fs / N, where 'f' is the frequency, 'n' is the bin number (starting at 0), 'Fs' is the sample rate, and 'N' is the number of FFT points.

For instance, with a 44.1 kHz sample rate and a 1024-point FFT:

• Bin 0: 0 Hz
• Bin 1: 43.066 Hz (approximately 43.1 Hz)
• Bin 2: 86.133 Hz (approximately 86.1 Hz)
• Bin 3: 129.199 Hz (approximately 129.2 Hz)
• and so on...

Important Note: For real-valued input signals, the FFT exhibits Hermitian symmetry. This means the second half of the FFT (bins N/2 to N-1) is a mirrored, complex conjugate of the first half (bins 0 to N/2-1). Therefore, only the first half (up to bin N/2-1) contains unique frequency information. The highest meaningful frequency is the Nyquist frequency (Fs/2).

Using this method, you can accurately map each bin in your FFT output to its corresponding frequency, providing a detailed spectral analysis of your signal.

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