Fourier transformation.
The class implements one dimensional and two dimensional Discrete and Fast Fourier Transformation.
        /// <summary>
        ///   Performs the transformation over a double[] array.
        /// </summary>
        public static void FHT(double[] data, FourierTransform.Direction direction)
        {
            int N = data.Length;


            // Forward operation
            if (direction == FourierTransform.Direction.Forward)
            {
                // Copy the input to a complex array which can be processed
                //  in the complex domain by the FFT
                var cdata = new Complex[N];
                for (int i = 0; i < N; i++)
                {
                    cdata[i].Re = data[i];
                }

                // Perform FFT
                FourierTransform.FFT(cdata, FourierTransform.Direction.Forward);

                //double positive frequencies
                for (int i = 1; i < (N / 2); i++)
                {
                    cdata[i].Re *= 2.0;
                    cdata[i].Im *= 2.0;
                }

                // zero out negative frequencies
                //  (leaving out the dc component)
                for (int i = (N / 2) + 1; i < N; i++)
                {
                    cdata[i].Re = 0.0;
                    cdata[i].Im = 0.0;
                }

                // Reverse the FFT
                FourierTransform.FFT(cdata, FourierTransform.Direction.Backward);

                // Convert back to our initial double array
                for (int i = 0; i < N; i++)
                {
                    data[i] = cdata[i].Im;
                }
            }

            else // Backward operation
            {
                // The inverse Hilbert can be calculated by
                //  negating the transform and reapplying the
                //  transformation.
                //
                // H^–1{h(t)} = –H{h(t)}

                FHT(data, FourierTransform.Direction.Forward);

                for (int i = 0; i < data.Length; i++)
                {
                    data[i] = -data[i];
                }
            }
        }
Exemplo n.º 2
0
        /// <summary>
        ///   Performs the Fast Hilbert Transform over a complex[] array.
        /// </summary>
        ///
        public static void FHT(Complex[] data, FourierTransform.Direction direction)
        {
            int N = data.Length;

            // Forward operation
            if (direction == FourierTransform.Direction.Forward)
            {
                // Makes a copy of the data so we don't lose the
                //  original information to build our final signal
                Complex[] shift = (Complex[])data.Clone();

                // Perform FFT
                FourierTransform.FFT(shift, FourierTransform.Direction.Backward);
                TransformArray(shift);

                // Reverse the FFT
                FourierTransform.FFT(shift, FourierTransform.Direction.Forward);

                // Put the Hilbert transform in the Imaginary part
                //  of the input signal, creating a Analytic Signal
                for (int i = 0; i < N; i++)
                {
                    data[i] = new Complex(data[i].Real, shift[i].Imaginary);
                }
            }

            else // Backward operation
            {
                // Just discard the imaginary part
                for (int i = 0; i < data.Length; i++)
                {
                    data[i] = new Complex(data[i].Real, 0.0);
                }
            }
        }
Exemplo n.º 3
0
        /// <summary>
        /// Two dimensional Fast Fourier Transform.
        /// </summary>
        ///
        /// <param name="data">Data to transform.</param>
        /// <param name="direction">Transformation direction.</param>
        ///
        /// <remarks><para><note>The method accepts <paramref name="data"/> array of 2<sup>n</sup> size
        /// only in each dimension, where <b>n</b> may vary in the [1, 14] range. For example, 16x16 array
        /// is valid, but 15x15 is not.</note></para></remarks>
        ///
        /// <exception cref="ArgumentException">Incorrect data length.</exception>
        ///
        public static void FFT2(Complex[,] data, Direction direction)
        {
            int k = data.GetLength(0);
            int n = data.GetLength(1);

            // check data size
            if (!Tools.IsPowerOf2(k) || !Tools.IsPowerOf2(n))
            {
                throw new ArgumentException("The matrix rows and columns must be a power of 2.");
            }

            if (k < minLength || k > maxLength || n < minLength || n > maxLength)
            {
                throw new ArgumentException("Incorrect data length.");
            }

            // process rows
            var row = new Complex[n];

            for (int i = 0; i < k; i++)
            {
                // copy row
                for (int j = 0; j < row.Length; j++)
                {
                    row[j] = data[i, j];
                }

                // transform it
                FourierTransform.FFT(row, direction);

                // copy back
                for (int j = 0; j < row.Length; j++)
                {
                    data[i, j] = row[j];
                }
            }

            // process columns
            var col = new Complex[k];

            for (int j = 0; j < n; j++)
            {
                // copy column
                for (int i = 0; i < k; i++)
                {
                    col[i] = data[i, j];
                }

                // transform it
                FourierTransform.FFT(col, direction);

                // copy back
                for (int i = 0; i < k; i++)
                {
                    data[i, j] = col[i];
                }
            }
        }
        /// <summary>
        ///   Performs the transformation over a complex[] array.
        /// </summary>
        public static void FHT(Complex[] data, FourierTransform.Direction direction)
        {
            int N = data.Length;

            // Forward operation
            if (direction == FourierTransform.Direction.Forward)
            {
                // Makes a copy of the data so we don't lose the
                //  original information to build our final signal
                var shift = (Complex[])data.Clone();

                // Perform FFT
                FourierTransform.FFT(shift, FourierTransform.Direction.Backward);

                //double positive frequencies
                for (int i = 1; i < (N / 2); i++)
                {
                    shift[i].Re *= 2.0;
                    shift[i].Im *= 2.0;
                }
                // zero out negative frequencies
                //  (leaving out the dc component)
                for (int i = (N / 2) + 1; i < N; i++)
                {
                    shift[i].Re = 0.0;
                    shift[i].Im = 0.0;
                }

                // Reverse the FFT
                FourierTransform.FFT(shift, FourierTransform.Direction.Forward);

                // Put the Hilbert transform in the Imaginary part
                //  of the input signal, creating a Analytic Signal
                for (int i = 0; i < N; i++)
                {
                    data[i].Im = shift[i].Im;
                }
            }

            else // Backward operation
            {
                // Just discard the imaginary part
                for (int i = 0; i < data.Length; i++)
                {
                    data[i].Im = 0.0;
                }
            }
        }
Exemplo n.º 5
0
        /// <summary>
        ///   Performs the Fast Hilbert Transform over a double[] array.
        /// </summary>
        ///
        public static void FHT(double[] data, FourierTransform.Direction direction)
        {
            int N = data.Length;

            // Forward operation
            if (direction == FourierTransform.Direction.Forward)
            {
                // Copy the input to a complex array which can be processed
                //  in the complex domain by the FFT
                Complex[] cdata = new Complex[N];
                for (int i = 0; i < N; i++)
                {
                    cdata[i] = new Complex(data[i], 0.0);
                }

                // Perform FFT
                FourierTransform.FFT(cdata, FourierTransform.Direction.Forward);
                TransformArray(cdata);

                // Reverse the FFT
                FourierTransform.FFT(cdata, FourierTransform.Direction.Backward);

                // Convert back to our initial double array
                for (int i = 0; i < N; i++)
                {
                    data[i] = cdata[i].Imaginary;
                }
            }

            else // Backward operation
            {
                // The inverse Hilbert can be calculated by
                //  negating the transform and reapplying the
                //  transformation.
                //
                // H^–1{h(t)} = –H{h(t)}

                FHT(data, FourierTransform.Direction.Forward);

                for (int i = 0; i < data.Length; i++)
                {
                    data[i] = -data[i];
                }
            }
        }
Exemplo n.º 6
0
        /// <summary>
        /// One dimensional Fast Fourier Transform.
        /// </summary>
        ///
        /// <param name="data">Data to transform.</param>
        /// <param name="direction">Transformation direction.</param>
        ///
        /// <remarks><para><note>The method accepts <paramref name="data"/> array of 2<sup>n</sup> size
        /// only, where <b>n</b> may vary in the [1, 14] range.</note></para></remarks>
        ///
        /// <exception cref="ArgumentException">Incorrect data length.</exception>
        ///
        public static void FFT(Complex[] data, Direction direction)
        {
            int n = data.Length;
            int m = Tools.Log2(n);

            // reorder data first
            ReorderData(data);

            // compute FFT
            int tn = 1, tm;

            for (int k = 1; k <= m; k++)
            {
                Complex[] rotation = FourierTransform.GetComplexRotation(k, direction);

                tm   = tn;
                tn <<= 1;

                for (int i = 0; i < tm; i++)
                {
                    Complex t = rotation[i];

                    for (int even = i; even < n; even += tn)
                    {
                        int     odd = even + tm;
                        Complex ce  = data[even];
                        Complex co  = data[odd];

                        double tr = co.Real * t.Real - co.Imaginary * t.Imaginary;
                        double ti = co.Real * t.Imaginary + co.Imaginary * t.Real;

                        data[even] += new Complex(tr, ti);
                        data[odd]   = new Complex(ce.Real - tr, ce.Imaginary - ti);
                    }
                }
            }

            if (direction == Direction.Forward)
            {
                for (int i = 0; i < data.Length; i++)
                {
                    data[i] /= (double)n;
                }
            }
        }