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QuickStart Samples

FFT/Fourier Transforms QuickStart Sample (Visual Basic)

Illustrates how to compute the forward and inverse Fourier transform of a real or complex signal using classes in the Extreme.Mathematics.SignalProcessing namespace in Visual Basic.

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Option Infer On

Imports Extreme.Mathematics
' The FFT classes reside in the Extreme.Mathematics.SignalProcessing
' namespace.
Imports Extreme.Mathematics.SignalProcessing

Namespace Extreme.Numerics.QuickStart.VB
    ' Illustrates the use of the FftProvider and Fft classes for computing 
    ' the Fourier transform of real and complex signals.
    Module FourierTransforms

        Sub Main()
            ' This QuickStart sample shows how to compute the Fouier
            ' transform of real and complex signals.

            ' Some vectors to play with:
            Dim r1 = Vector.Create(Of Double)(1000)
            For i As Integer = 0 To r1.Length - 1
                r1(i) = 1.0 / (1 + i)
            Dim c1 = Vector.Create(Of Complex(Of Double))(1000)
            For i As Integer = 0 To c1.Length - 1
                c1(i) = New Complex(Of Double)(Math.Sin(0.03 * i), Math.Cos(0.07 * i))

            Dim r2 = Vector.Create(1.0, 2.0, 3.0, 4.0)
            Dim c2 = Vector.Create(
                New Complex(Of Double)(1, 2),
                New Complex(Of Double)(3, 4),
                New Complex(Of Double)(5, 6),
                New Complex(Of Double)(7, 8))

            ' One-time FFT's

            ' The Vector and ComplexVector classes have static methods to compute FFT's:
            Dim c3 = Vector.FourierTransform(r2)
            Dim r3 = Vector.InverseFourierTransform(c3)
            Console.WriteLine("fft(r2) = {0:F3}", c3)
            Console.WriteLine("ifft(fft(r2)) = {0:F3}", r3)
            ' The ComplexConjugateSignalVector type represents a complex vector
            ' that is the Fourier transform of a real signal. 
            ' It enforces certain symmetry properties:
            Console.WriteLine("c3(i) == conj(c3(N-i)): {0} == conj({1})", c3(1), c3(3))

            ' FFT Providers

            ' FFT's require a fair bit of pre-computation. Using the FftProvider class,
            ' you can get an Fft object that caches these computations.

            ' Here, we create an FFT implementation for a real signal:
            Dim realFft = Fft(Of Double).CreateReal(r1.Length)
            ' For a complex to complex transform:
            Dim complexFft = Fft(Of Double).CreateComplex(c1.Length)

            ' You can set the scale factor for the forward transform.
            ' The default is 1/N.
            realFft.ForwardScaleFactor = 1.0 / Math.Sqrt(c1.Length)
            ' and the backward transform, with default 1:
            realFft.BackwardScaleFactor = realFft.ForwardScaleFactor

            ' The ForwardTransform method performs a forward transform:
            Dim c4 As Vector(Of Complex(Of Double)) = realFft.ForwardTransform(r1)
            Console.WriteLine("First 5 terms of fft(r1):")
            For i As Integer = 0 To 4
                Console.WriteLine("   {0}: {1}", i, c4(i))
            Next i
            c4 = complexFft.ForwardTransform(c1)
            Console.WriteLine("First 5 terms of fft(c1):")
            For i As Integer = 0 To 4
                Console.WriteLine("   {0}: {1}", i, c4(i))
            Next i
            ' ForwardTransform has many overloads for real to complex and
            ' complex to complex transforms.

            ' A one-sided transform returns only the first half of the FFT of
            ' a real signal. The rest can be deduced from the symmetry properties.
            ' Here's how to compute a one-sided FFT:
            Dim halfLength As Integer = r1.Length \ 2 + 1
            Dim c5 = Vector.Create(Of Complex(Of Double))(halfLength)
            realFft.ForwardTransform(r1, c5, RealFftFormat.OneSided)

            ' The BackwardTransform method has a similar set of overloads:
            Dim r4 = Vector.Create(Of Double)(r1.Length)
            realFft.BackwardTransform(c5, r4, RealFftFormat.OneSided)

            ' As the last step, we need to dispose the two FFT implementations.

            ' 2D transforms

            ' 2D transforms are handled in a completely analogous way.
            Dim m = Matrix.Create(Of Double)(36, 56)
            For i As Integer = 0 To m.RowCount - 1
                For j As Integer = 0 To m.ColumnCount - 1
                    m(i, j) = Math.Exp(-0.1 * i) * Math.Sin(0.01 * (i * i + j * j - i * j))
            Dim mFft = Matrix.Create(Of Complex(Of Double))(m.RowCount, m.ColumnCount)

            Dim fft2 = Fft2D(Of Double).CreateReal(m.RowCount, m.ColumnCount)
            fft2.ForwardTransform(m, mFft)

            Console.WriteLine("First few terms of fft(m):")
            For i As Integer = 0 To 3
                Dim comma As String = String.Empty
                For j As Integer = 0 To 3
                    Console.Write("{0}", mFft(i, j).ToString("F4"))
                    comma = ", "

            ' and the backward transform:
            fft2.BackwardTransform(mFft, m)

            ' Once again, we need to dispose the FFT implementation:

            Console.Write("Press Enter key to exit...")

        End Sub

    End Module

End Namespace