forked from tsai/mathnet-numerics
Christoph Ruegg
13 years ago
13 changed files with 299 additions and 365 deletions
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// <copyright file="DiscreteFourierTransform.Options.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
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// files (the "Software"), to deal in the Software without
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// restriction, including without limitation the rights to use,
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
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// copies of the Software, and to permit persons to whom the
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// Software is furnished to do so, subject to the following
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// conditions:
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//
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// The above copyright notice and this permission notice shall be
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// included in all copies or substantial portions of the Software.
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//
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System; |
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namespace MathNet.Numerics.IntegralTransforms |
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{ |
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#if !NOSYSNUMERICS
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using Complex = System.Numerics.Complex; |
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#endif
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/// <summary>
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/// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
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/// </summary>
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public static partial class Fourier |
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{ |
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/// <summary>
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/// Extract the exponent sign to be used in forward transforms according to the
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/// provided convention options.
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/// </summary>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <returns>Fourier series exponent sign.</returns>
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static int SignByOptions(FourierOptions options) |
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{ |
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return (options & FourierOptions.InverseExponent) == FourierOptions.InverseExponent ? 1 : -1; |
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} |
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/// <summary>
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/// Rescale FFT-the resulting vector according to the provided convention options.
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/// </summary>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <param name="samples">Sample Vector.</param>
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static void ForwardScaleByOptions(FourierOptions options, Complex[] samples) |
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{ |
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if ((options & FourierOptions.NoScaling) == FourierOptions.NoScaling || |
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(options & FourierOptions.AsymmetricScaling) == FourierOptions.AsymmetricScaling) |
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{ |
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return; |
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} |
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var scalingFactor = Math.Sqrt(1.0/samples.Length); |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] *= scalingFactor; |
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} |
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} |
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/// <summary>
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/// Rescale the iFFT-resulting vector according to the provided convention options.
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/// </summary>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <param name="samples">Sample Vector.</param>
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static void InverseScaleByOptions(FourierOptions options, Complex[] samples) |
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{ |
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if ((options & FourierOptions.NoScaling) == FourierOptions.NoScaling) |
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{ |
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return; |
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} |
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var scalingFactor = 1.0/samples.Length; |
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if ((options & FourierOptions.AsymmetricScaling) != FourierOptions.AsymmetricScaling) |
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{ |
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scalingFactor = Math.Sqrt(scalingFactor); |
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} |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] *= scalingFactor; |
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} |
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} |
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} |
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} |
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@ -0,0 +1,211 @@ |
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// <copyright file="Fourier.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
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// obtaining a copy of this software and associated documentation
|
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// files (the "Software"), to deal in the Software without
|
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// restriction, including without limitation the rights to use,
|
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// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
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// copies of the Software, and to permit persons to whom the
|
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// Software is furnished to do so, subject to the following
|
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// conditions:
|
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//
|
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// The above copyright notice and this permission notice shall be
|
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// included in all copies or substantial portions of the Software.
|
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//
|
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
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// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
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// OTHER DEALINGS IN THE SOFTWARE.
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// </copyright>
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using System; |
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namespace MathNet.Numerics.IntegralTransforms |
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{ |
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#if !NOSYSNUMERICS
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using System.Numerics; |
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#endif
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/// <summary>
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/// Complex Fast (FFT) Implementation of the Discrete Fourier Transform (DFT).
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/// </summary>
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public static partial class Fourier |
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{ |
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/// <summary>
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/// Applies the forward Fast Fourier Transform (FFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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public static void Forward(Complex[] samples) |
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{ |
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BluesteinForward(samples, FourierOptions.Default); |
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} |
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/// <summary>
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/// Applies the forward Fast Fourier Transform (FFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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public static void Forward(Complex[] samples, FourierOptions options) |
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{ |
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BluesteinForward(samples, options); |
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} |
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/// <summary>
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/// Applies the inverse Fast Fourier Transform (iFFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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public static void Inverse(Complex[] samples) |
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{ |
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BluesteinInverse(samples, FourierOptions.Default); |
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} |
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/// <summary>
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/// Applies the inverse Fast Fourier Transform (iFFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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public static void Inverse(Complex[] samples, FourierOptions options) |
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{ |
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BluesteinInverse(samples, options); |
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} |
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/// <summary>
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/// Naive forward DFT, useful e.g. to verify faster algorithms.
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/// </summary>
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/// <param name="timeSpace">Time-space sample vector.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <returns>Corresponding frequency-space vector.</returns>
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public static Complex[] NaiveForward(Complex[] timeSpace, FourierOptions options) |
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{ |
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var frequencySpace = Naive(timeSpace, SignByOptions(options)); |
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ForwardScaleByOptions(options, frequencySpace); |
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return frequencySpace; |
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} |
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/// <summary>
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/// Naive inverse DFT, useful e.g. to verify faster algorithms.
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/// </summary>
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/// <param name="frequencySpace">Frequency-space sample vector.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <returns>Corresponding time-space vector.</returns>
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public static Complex[] NaiveInverse(Complex[] frequencySpace, FourierOptions options) |
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{ |
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var timeSpace = Naive(frequencySpace, -SignByOptions(options)); |
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InverseScaleByOptions(options, timeSpace); |
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return timeSpace; |
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} |
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/// <summary>
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/// Radix-2 forward FFT for power-of-two sized sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <exception cref="ArgumentException"/>
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public static void Radix2Forward(Complex[] samples, FourierOptions options) |
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{ |
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Radix2Parallel(samples, SignByOptions(options)); |
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ForwardScaleByOptions(options, samples); |
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} |
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/// <summary>
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/// Radix-2 inverse FFT for power-of-two sized sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <exception cref="ArgumentException"/>
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public static void Radix2Inverse(Complex[] samples, FourierOptions options) |
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{ |
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Radix2Parallel(samples, -SignByOptions(options)); |
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InverseScaleByOptions(options, samples); |
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} |
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/// <summary>
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/// Bluestein forward FFT for arbitrary sized sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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public static void BluesteinForward(Complex[] samples, FourierOptions options) |
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{ |
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Bluestein(samples, SignByOptions(options)); |
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ForwardScaleByOptions(options, samples); |
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} |
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/// <summary>
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/// Bluestein inverse FFT for arbitrary sized sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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public static void BluesteinInverse(Complex[] samples, FourierOptions options) |
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{ |
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Bluestein(samples, -SignByOptions(options)); |
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InverseScaleByOptions(options, samples); |
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} |
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/// <summary>
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/// Extract the exponent sign to be used in forward transforms according to the
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/// provided convention options.
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/// </summary>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <returns>Fourier series exponent sign.</returns>
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static int SignByOptions(FourierOptions options) |
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{ |
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return (options & FourierOptions.InverseExponent) == FourierOptions.InverseExponent ? 1 : -1; |
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} |
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/// <summary>
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/// Rescale FFT-the resulting vector according to the provided convention options.
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/// </summary>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <param name="samples">Sample Vector.</param>
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static void ForwardScaleByOptions(FourierOptions options, Complex[] samples) |
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{ |
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if ((options & FourierOptions.NoScaling) == FourierOptions.NoScaling || |
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(options & FourierOptions.AsymmetricScaling) == FourierOptions.AsymmetricScaling) |
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{ |
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return; |
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} |
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var scalingFactor = Math.Sqrt(1.0/samples.Length); |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] *= scalingFactor; |
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} |
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} |
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/// <summary>
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/// Rescale the iFFT-resulting vector according to the provided convention options.
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/// </summary>
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/// <param name="options">Fourier Transform Convention Options.</param>
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/// <param name="samples">Sample Vector.</param>
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static void InverseScaleByOptions(FourierOptions options, Complex[] samples) |
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{ |
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if ((options & FourierOptions.NoScaling) == FourierOptions.NoScaling) |
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{ |
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return; |
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} |
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var scalingFactor = 1.0/samples.Length; |
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if ((options & FourierOptions.AsymmetricScaling) != FourierOptions.AsymmetricScaling) |
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{ |
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scalingFactor = Math.Sqrt(scalingFactor); |
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} |
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for (int i = 0; i < samples.Length; i++) |
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{ |
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samples[i] *= scalingFactor; |
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} |
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} |
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} |
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} |
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@ -1,81 +0,0 @@ |
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// <copyright file="Transform.cs" company="Math.NET">
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// Math.NET Numerics, part of the Math.NET Project
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// http://numerics.mathdotnet.com
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// http://github.com/mathnet/mathnet-numerics
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// http://mathnetnumerics.codeplex.com
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//
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// Copyright (c) 2009-2014 Math.NET
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//
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// Permission is hereby granted, free of charge, to any person
|
|||
// obtaining a copy of this software and associated documentation
|
|||
// files (the "Software"), to deal in the Software without
|
|||
// restriction, including without limitation the rights to use,
|
|||
// copy, modify, merge, publish, distribute, sublicense, and/or sell
|
|||
// copies of the Software, and to permit persons to whom the
|
|||
// Software is furnished to do so, subject to the following
|
|||
// conditions:
|
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//
|
|||
// The above copyright notice and this permission notice shall be
|
|||
// included in all copies or substantial portions of the Software.
|
|||
//
|
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// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
|
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// EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES
|
|||
// OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
|
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// NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT
|
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// HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,
|
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// WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
|
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// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR
|
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// OTHER DEALINGS IN THE SOFTWARE.
|
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// </copyright>
|
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|
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namespace MathNet.Numerics.IntegralTransforms |
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{ |
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#if !NOSYSNUMERICS
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using Complex = System.Numerics.Complex; |
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#endif
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/// <summary>
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/// Integral Transforms (including FFT).
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/// </summary>
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public static class Transform |
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{ |
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/// <summary>
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/// Applies the forward Fast Fourier Transform (FFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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public static void FourierForward(Complex[] samples) |
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{ |
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Fourier.BluesteinForward(samples, FourierOptions.Default); |
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} |
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/// <summary>
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/// Applies the forward Fast Fourier Transform (FFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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public static void FourierForward(Complex[] samples, FourierOptions options) |
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{ |
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Fourier.BluesteinForward(samples, options); |
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} |
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/// <summary>
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/// Applies the inverse Fast Fourier Transform (iFFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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public static void FourierInverse(Complex[] samples) |
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{ |
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Fourier.BluesteinInverse(samples, FourierOptions.Default); |
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} |
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/// <summary>
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/// Applies the inverse Fast Fourier Transform (iFFT) to arbitrary-length sample vectors.
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/// </summary>
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/// <param name="samples">Sample vector, where the FFT is evaluated in place.</param>
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/// <param name="options">Fourier Transform Convention Options.</param>
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public static void FourierInverse(Complex[] samples, FourierOptions options) |
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{ |
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Fourier.BluesteinInverse(samples, options); |
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} |
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} |
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} |
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