Discrete Fourier Transform Example (Go + Gonum)

This project demonstrates how to perform a Discrete Fourier Transform (DFT) using the Gonum DSP Fourier package in Go. It generates a composite waveform composed of multiple sine waves, applies a Hanning window to reduce spectral leakage, computes the FFT, and detects the main frequency components.

Overview

This example showcases:

• Generating a composite signal (sum of multiple sine waves).
• Applying a Hanning window to smooth discontinuities at signal edges.
• Computing the Fast Fourier Transform (FFT) using Gonum’s fourier package.
• Identifying the dominant frequencies and their magnitudes.

The program reconstructs the frequencies and amplitudes that make up a mixed signal.

Source: https://www.3blue1brown.com/lessons/fourier-transforms

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Requirements

• Go 1.18+
• Gonum

How It Works

1. Generate Composite Wave

wave := GenerateCompositeWave(freqs, amplitudes, sampleRate, duration)

2. Apply Hanning Window

ApplyHanningWindow(wave)

3. Compute FFT

fft := fourier.NewFFT(fftSize)
spectrum := fft.Coefficients(nil, paddedWave)

4. Compute Magnitude Spectrum

Magnitude is calculated from the complex coefficients and scaled by signal length and window gain.

// Compute magnitude spectrum using original wave length for amplitude scaling
windowGain := 0.5
mag := make([]float64, fftSize/2)
for i := 0; i < fftSize/2; i++ {
    mag[i] = cmplx.Abs(spectrum[i]) * 2 / float64(len(wave)) / windowGain
}

5. Find Main Peaks

peaks := FindMainPeaks(mag, freqRes, neighborhoodHz, threshold)

Parameters

Parameter	Description	Example Value
sampleRate	Sampling rate in Hz	1024
duration	Signal duration in seconds	15.0
freqs	Frequencies of the sine components (Hz)	[50, 120, 300]
amplitudes	Amplitudes of each sine wave	[1.0, 0.5, 0.8]
neighborhoodHz	Range for filtering side lobes (Hz)	3.0
threshold	Minimum magnitude for peak detection	0.05

Example program output

$ go run examples/synthetic/dft_synthetic.go

Detected main frequencies:
Frequency: 50.0 Hz, Magnitude: 1.000
Frequency: 120.0 Hz, Magnitude: 0.500
Frequency: 300.0 Hz, Magnitude: 0.800

Or for an audio file:

$ go run examples/audio_file/dft_audio_file.go \
    -input my_audio_file.mp3 \
    -duration 1 \
    -mmt 0.001 \
    -start 0