public static void Example2() //================[ Basic DFT + Windowing Example ]================
{
// Same Input Signal as Example 1
double amplitude = 1.0; double frequency = 20000;
UInt32 length = 1000;
double samplingRate = 100000;
double[] inputSignal = DSP.Generate.ToneSampling(amplitude, frequency, samplingRate, length);
// Apply window to the Input Data & calculate Scale Factor
double[] wCoefs = DSP.Window.Coefficients(DSP.Window.Type.Hamming, length);
double[] wInputData = DSP.Math.Multiply(inputSignal, wCoefs);
double wScaleFactor = DSP.Window.ScaleFactor.Signal(wCoefs);
// Instantiate & Initialize a new DFT
DSPLib.DFT dft = new DSPLib.DFT();
dft.Inicializar(length);
// Call the DFT and get the scaled spectrum back
Complex[] cSpectrum = dft.Executar(wInputData);
// Convert the complex spectrum to note: Magnitude Format
double[] lmSpectrum = DSP.ConvertComplex.ToMagnitude(cSpectrum);
// Properly scale the spectrum for the added window
lmSpectrum = DSP.Math.Multiply(lmSpectrum, wScaleFactor);
// For plotting on an XY Scatter plot generate the X Axis frequency Span
double[] freqSpan = dft.FrequencySpan(samplingRate);
// At this point a XY Scatter plot can be generated from,
// X axis => freqSpan
// Y axis => lmSpectrum
}
public static void Example9() //================[ Basic DFT Phase Test ]================
{
// Generate a Phase Ramp between two signals
double[] resultPhase = new double[360];
// Instantiate & Initialize a new DFT
DSPLib.DFT dft = new DSPLib.DFT();
dft.Inicializar(2048);
for (Int32 phase = 0; phase < 360; phase++)
{
double[] inputSignalRef = DSP.Generate.ToneCycles(7.0, 128, 2048);
double[] inputSignalPhase = DSP.Generate.ToneCycles(7.0, 128, 2048, phaseDeg: phase);
// Call the DFT and get the scaled spectrum back of a reference and a phase shifted signal.
Complex[] cSpectrumRef = dft.Executar(inputSignalRef);
Complex[] cSpectrumPhase = dft.Executar(inputSignalPhase);
// Magnitude Format - Just as a test point
//double[] lmSpectrumTest = DSPLib.DSP.ConvertComplex.ToMagnitude(cSpectrumRef);
//double[] lmSpectrumTestPhase = DSPLib.DSP.ConvertComplex.ToMagnitude(cSpectrumPhase);
// Extract the phase of bin 128
double[] resultArrayRef = DSP.ConvertComplex.ToPhaseDegrees(cSpectrumRef);
double[] resultArrayPhase = DSP.ConvertComplex.ToPhaseDegrees(cSpectrumPhase);
resultPhase[phase] = resultArrayPhase[128] - resultArrayRef[128];
}
// resultPhase has a linear phase incrementing signal at this point.
// Use UnwrapPhase() to remove phase jumps in output data.
}
public static void Example6() //================[ Basic DFT + Noise Analysis Example ]================
{
// Setup parameters to generate noise test signal of 5 nVrms / rt-Hz
double amplitude = 5.0e-9;
UInt32 length = 1000; double samplingRate = 2000;
// Generate window & calculate Scale Factor for NOISE!
double[] wCoefs = DSP.Window.Coefficients(DSP.Window.Type.Hamming, length);
double wScaleFactor = DSP.Window.ScaleFactor.Noise(wCoefs, samplingRate);
// Instantiate & Initialize a new DFT
DSPLib.DFT dft = new DSPLib.DFT();
dft.Inicializar(length);
// Average the noise 'N' times
Int32 N = 1000;
double[] noiseSum = new double[(length / 2) + 1];
for (Int32 i = 0; i < N; i++)
{
// Generate the noise signal & apply window
double[] inputSignal = DSP.Generate.NoisePsd(amplitude, samplingRate, length);
inputSignal = DSP.Math.Multiply(inputSignal, wCoefs);
// DFT the noise -> Convert -> Sum
Complex[] cSpectrum = dft.Executar(inputSignal);
double[] mag2 = DSP.ConvertComplex.ToMagnitudeSquared(cSpectrum);
if (N == 0)
{
noiseSum = DSP.Math.Add(noiseSum, 0);
}
else
{
noiseSum = DSP.Math.Add(noiseSum, mag2);
}
}
// Calculate Average, convert to magnitude format
// See text for the reasons to use Mag^2 format.
double[] averageNoise = DSP.Math.Divide(noiseSum, N);
double[] lmSpectrum = DSP.ConvertMagnitudeSquared.ToMagnitude(averageNoise);
// Properly scale the spectrum for the added window
lmSpectrum = DSP.Math.Multiply(lmSpectrum, wScaleFactor);
// For plotting on an XY Scatter plot generate the X Axis frequency Span
double[] freqSpan = dft.FrequencySpan(samplingRate);
// At this point a XY Scatter plot can be generated from,
// X axis => freqSpan
// Y axis => lmSpectrum as a Power Spectral Density Value
// Extra Credit - Analyze Plot Data Ignoring the first and last 20 Bins
// Average value should be what we generated = 5.0e-9 Vrms / rt-Hz
double averageValue = DSP.Analyze.FindMean(lmSpectrum, 20, 20);
}
public static void Example8() //================[ Basic DFT + Signal & Noise + Log Magnitude ]================
{
// Same Input Signal as Example 1, except amplitude is 5 Vrms.
double amplitude = 5.0; double frequency = 20000;
UInt32 length = 1000; double samplingRate = 100000;
double[] inputSignal = DSP.Generate.ToneSampling(amplitude, frequency, samplingRate, length);
// Add noise that is about 80 dBc from signal level
// 80 dBc is about the level of noise from a 14 bit ADC
// 1/10,000 down from full scale
double[] inputNoise = DSP.Generate.NoiseRms(amplitude / 10000.0, length);
// Add noise to the signal
double[] compositeInput = DSP.Math.Add(inputSignal, inputNoise);
// Use the BH92 type window - this is a very "Spectrum Analyzer" like window.
// Apply window to the Input Data & calculate Scale Factor
double[] wCoefs = DSP.Window.Coefficients(DSP.Window.Type.BH92, length);
double wScaleFactor = DSP.Window.ScaleFactor.Signal(wCoefs);
double[] wInputData = DSP.Math.Multiply(compositeInput, wCoefs);
// Instantiate & Initialize a new DFT
DSPLib.DFT dft = new DSPLib.DFT();
dft.Inicializar(length);
// Call the DFT and get the scaled spectrum back
Complex[] cSpectrum = dft.Executar(wInputData);
// Convert the complex spectrum to note: Magnitude Format
double[] lmSpectrum = DSP.ConvertComplex.ToMagnitude(cSpectrum);
// Properly scale the spectrum for the added window
lmSpectrum = DSP.Math.Multiply(lmSpectrum, wScaleFactor);
// Convert from linear magnitude to log magnitude format
double[] logMagSpectrum = DSP.ConvertMagnitude.ToMagnitudeDBV(lmSpectrum);
// For plotting on an XY Scatter plot generate the X Axis frequency Span
double[] freqSpan = dft.FrequencySpan(samplingRate);
// At this point a XY Scatter plot can be generated from,
// X axis => freqSpan
// Y axis => logMagSpectrum
// In this example - maximum amplitude of 13.974 dBV is at bin 200 (20,000 Hz)
}
