Fast Fourier Transforms | Extreme Optimization Numerical Libraries for .NET Professional |

The **Extreme Optimization Numerical Libraries for .NET** provide a set of classes for computing
the Discrete Fourier Transform of real and complex signals.

When only very few Fourier transforms of a given length need to be computed, the Vector

To compute the Fourier transform of a real sequence, use FourierTransform.
This method takes as its only parameter a Vector

The inverse transform is computed using the
InverseFourierTransform method.
This method takes a ComplexVector
and returns a Vector

The following example computes the Fourier transform of a short vector, and then computes the inverse transform. The result is a vector identical to the first one:

DenseVector r1 = Vector.Create(1.0, 2.0, 3.0, 4.0); ComplexVector c1 = Vector.FourierTransform(r1); Vector r2 = Vector.InverseFourierTransform(c1);

For complex signals, the ComplexVector class has a FourierTransform and a InverseFourierTransform method. Each method takes one parameter: a ComplexVector, and also returns a ComplexVector.

In many applications, many Fourier transforms of the same length need to be calculated. To make this process more efficient, you can use Fft objects, that represent the implementation of an FFT of a given length. Fft objects are created through an FftProvider.

The FftProvider is the base class for accessing a specific set of FFT algorithms. Two FFT providers are shipped with the library: a managed provider that uses 100% managed code, and a 'native' provider that uses hand-optimized unmanaged code and is an order of magnitude faster for longer transforms.

In order to use the native provider, the assembly containing the native FFT code for the current processor architecture must be present. This assembly is called Extreme.NativeFft.x86.20.dll on 32 bit systems and Extreme.NativeFft.x64.20.dll on 64 bit systems. If this assembly cannot be found, the managed provider is used instead.

You can access the two providers through the ManagedImplementation and NativeImplementation properties.

The managed provider has two additional properties that indicate when to switch to the native provider (if it is present). The RealManagedThresholdLength property specifies the shortest length of a real FFT for which the native FFT provider will be used. The default is 64. The ComplexManagedThresholdLength property specifies the shortest length of a complex FFT for which the native FFT provider will be used. The default is 32.

Using FFT providers, you can obtain Fft objects for
one-dimensional transforms and Fft2D objects for
two-dimensional transforms.
The Fft and Fft
classes implement System

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