added simple fft

lib/simple_fft/fft.h

@@ -0,0 +1,100 @@
+/*
+ * ----------------------------------------------------------------------------
+ * "THE BEER-WARE LICENSE" (Revision 42):
+ * Dmitry Ivanov <dm.vl.ivanov@gmail.com> wrote this file. As long as you retain
+ * this notice you can do whatever you want with this stuff. If we meet some day,
+ * and you think this stuff is worth it, you can buy me a beer in return.
+ * ----------------------------------------------------------------------------
+ */
+
+#ifndef __SIMPLE_FFT__FFT_H__
+#define __SIMPLE_FFT__FFT_H__
+
+#include <cstddef>
+
+using std::size_t;
+
+/// The public API
+namespace simple_fft {
+
+/// FFT and IFFT functions
+
+// in-place, complex, forward
+template <class TComplexArray1D>
+bool FFT(TComplexArray1D & data, const size_t size, const char *& error_description);
+
+template <class TComplexArray2D>
+bool FFT(TComplexArray2D & data, const size_t size1, const size_t size2,
+         const char *& error_description);
+
+template <class TComplexArray3D>
+bool FFT(TComplexArray3D & data, const size_t size1, const size_t size2, const size_t size3,
+         const char *& error_description);
+
+// in-place, complex, inverse
+template <class TComplexArray1D>
+bool IFFT(TComplexArray1D & data, const size_t size, const char *& error_description);
+
+template <class TComplexArray2D>
+bool IFFT(TComplexArray2D & data, const size_t size1, const size_t size2,
+          const char *& error_description);
+
+template <class TComplexArray3D>
+bool IFFT(TComplexArray3D & data, const size_t size1, const size_t size2, const size_t size3,
+          const char *& error_description);
+
+// not-in-place, complex, forward
+template <class TComplexArray1D>
+bool FFT(const TComplexArray1D & data_in, TComplexArray1D & data_out,
+         const size_t size, const char *& error_description);
+
+template <class TComplexArray2D>
+bool FFT(const TComplexArray2D & data_in, TComplexArray2D & data_out,
+         const size_t size1, const size_t size2, const char *& error_description);
+
+template <class TComplexArray3D>
+bool FFT(const TComplexArray3D & data_in, TComplexArray3D & data_out,
+         const size_t size1, const size_t size2, const size_t size3,
+         const char *& error_description);
+
+// not-in-place, complex, inverse
+template <class TComplexArray1D>
+bool IFFT(const TComplexArray1D & data_in, TComplexArray1D & data_out,
+          const size_t size, const char *& error_description);
+
+template <class TComplexArray2D>
+bool IFFT(const TComplexArray2D & data_in, TComplexArray2D & data_out,
+          const size_t size1, const size_t size2, const char *& error_description);
+
+template <class TComplexArray3D>
+bool IFFT(const TComplexArray3D & data_in, TComplexArray3D & data_out,
+          const size_t size1, const size_t size2, const size_t size3,
+          const char *& error_description);
+
+// not-in-place, real, forward
+template <class TRealArray1D, class TComplexArray1D>
+bool FFT(const TRealArray1D & data_in, TComplexArray1D & data_out,
+         const size_t size, const char *& error_description);
+
+template <class TRealArray2D, class TComplexArray2D>
+bool FFT(const TRealArray2D & data_in, TComplexArray2D & data_out,
+         const size_t size1, const size_t size2, const char *& error_description);
+
+template <class TRealArray3D, class TComplexArray3D>
+bool FFT(const TRealArray3D & data_in, TComplexArray3D & data_out,
+         const size_t size1, const size_t size2, const size_t size3,
+         const char *& error_description);
+
+// NOTE: There is no inverse transform from complex spectrum to real signal
+// because round-off errors during computation of inverse FFT lead to the appearance
+// of signal imaginary components even though they are small by absolute value.
+// These can be ignored but the author of this file thinks adding such an function
+// would be wrong methodogically: looking at complex result, you can estimate
+// the value of spurious imaginary part. Otherwise you may never know that IFFT
+// provides too large imaginary values due to too small grid size, for example.
+
+} // namespace simple_fft
+
+#endif // __SIMPLE_FFT__FFT_H__
+
+#include "fft.hpp"