FftSharp

FftSharp is a collection of Fast Fourier Transform (FFT) tools for .NET. FftSharp is provided under the permissive MIT license so it is suitable for use in commercial applications. FftSharp targets .NET Standard and has no dependencies so it can be easily used in cross-platform .NET Framework and .NET Core applications.

Quickstart

// Begin with an array containing sample data
double[] signal = FftSharp.SampleData.SampleAudio1();

// Shape the signal using a Hanning window
var window = new FftSharp.Windows.Hanning();
window.ApplyInPlace(signal);

// Calculate the FFT as an array of complex numbers
System.Numerics.Complex[] spectrum = FftSharp.FFT.Forward(signal);

// or get the magnitude (units²) or power (dB) as real numbers
double[] magnitude = FftSharp.FFT.Magnitude(spectrum);
double[] power = FftSharp.FFT.Power(spectrum);

Signal	Windowed Signal	FFT

Sample Data

// sample audio with tones at 2, 10, and 20 kHz plus white noise
double[] signal = FftSharp.SampleData.SampleAudio1();
int sampleRate = 48_000;
double samplePeriod = sampleRate / 1000.0;

// plot the sample audio
ScottPlot.Plot plt = new();
plt.Add.Signal(signal, samplePeriod);
plt.YLabel("Amplitude");
plt.SavePng("time-series.png", 500, 200);

Spectral Magnitude and Power Density

Most people performing FFT operations are interested in calculating magnitude or power of their signal with respect to frequency. Magnitude units are the square of the original units, and power is in decibels.

Frequency of each point is a linear range between zero and half the sample rage (Nyquist frequency). A helper function makes it easy to get an array of frequencies (Hz units) to match the FFT that was generated.

// sample audio with tones at 2, 10, and 20 kHz plus white noise
double[] signal = FftSharp.SampleData.SampleAudio1();
int sampleRate = 48_000;

// calculate the power spectral density using FFT
System.Numerics.Complex[] spectrum = FftSharp.FFT.Forward(signal);
double[] psd = FftSharp.FFT.Power(spectrum);
double[] freq = FftSharp.FFT.FrequencyScale(psd.Length, sampleRate);

// plot the sample audio
ScottPlot.Plot plt = new();
plt.Add.ScatterLine(freq, psd);
plt.YLabel("Power (dB)");
plt.XLabel("Frequency (Hz)");
plt.SavePng("periodogram.png", 500, 200);

FFT using Complex Numbers

If you are writing a performance application or just enjoy working with real and imaginary components of complex numbers, you can build your own complex array perform FFT operations on it in place:

System.Numerics.Complex[] buffer =
{
    new(real: 42, imaginary: 12),
    new(real: 96, imaginary: 34),
    new(real: 13, imaginary: 56),
    new(real: 99, imaginary: 78),
};

FftSharp.FFT.Forward(buffer);

Filtering

The FftSharp.Filter module has methods to apply low-pass, high-pass, band-pass, and band-stop filtering. This works by converting signals to the frequency domain (using FFT), zeroing-out the desired ranges, performing the inverse FFT (iFFT), and returning the result.

double[] audio = FftSharp.SampleData.SampleAudio1();
double[] filtered = FftSharp.Filter.LowPass(audio, sampleRate: 48000, maxFrequency: 2000);

Windowing

Signals are often windowed prior to FFT analysis. Windowing is essentially multiplying the waveform by a bell-shaped curve prior to analysis, improving the frequency resolution of the FFT output.

The Hanning window is the most common window function for general-purpose FFT analysis. Other window functions may have different scallop loss or spectral leakage properties. For more information review window functions on Wikipedia.

double[] signal = FftSharp.SampleData.SampleAudio1();

var window = new FftSharp.Windows.Hanning();
double[] windowed = window.Apply(signal);

Hanning Window	Power Spectral Density

Windowing signals prior to calculating the FFT improves signal-to-noise ratio at lower frequencies, making power spectrum peaks easier to resolve.

No Window	Power Spectral Density

Window Functions

This chart (adapted from Understanding FFT Windows) summarizes windows commonly used for FFT analysis.

Window	Use Case	Frequency Resolution	Spectral Leakage	Amplitude Accuracy
Barlett	Random	Good	Fair	Fair
Blackman	Random	Poor	Best	Good
Cosine	Random	Fair	Fair	Fair
Flat Top	Sine waves	Poor	Good	Best
Hanning	Random	Good	Good	Fair
Hamming	Random	Good	Fair	Fair
Kaiser	Random	Fair	Good	Good
Rectangular	Transient	Best	Poor	Poor
Tukey	Transient	Good	Poor	Poor
Welch	Random	Good	Good	Fair

Demo Application

A sample application is included with this project that interactively displays an audio signal next to its FFT using different windowing functions.

Microphone Demo

One of the demos included is a FFT microphone analyzer which continuously monitors a sound card input device and calculates the FFT and displays it in real time.

Spectrogram

A spectrogram is a visual representation of the spectrum of frequencies of a signal as it varies with time. Spectrograms are created by computing power spectral density of a small window of an audio signal, moving the window forward in time, and repeating until the end of the signal is reached. In a spectrogram the horizontal axis represents time, the vertical axis represents frequency, and the pixel intensity represents spectral magnitude or power.

Spectrogram is a .NET library for creating spectrograms.