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inc/FFT.h

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+/**
+ * @file      FFT.h
+ * @brief     Fast Fourier Transform
+ * @details   fft() transforms time domain to frequency domain and
+ *            ifft() transforms frequency to time domain domain
+ * @version   TI-RSLK MAX v1.1
+ * @author    Daniel Valvano and Jonathan Valvano
+ * @copyright Copyright 2020 by Jonathan W. Valvano, valvano@mail.utexas.edu,
+ * @warning   AS-IS
+ * @note      For more information see  http://users.ece.utexas.edu/~valvano/
+ * @date      July 13, 2020
+ ******************************************************************************/
+
+/* Factored discrete Fourier transform, or FFT, and its inverse iFFT */
+// Derived from 
+// http://www.math.wustl.edu/~victor/mfmm/index.html#mfmm-software
+// Mathematics for Multimedia, ISBN 978-0-8176-4879-4, was formerly managed by Elsevier/Academic Press.
+// MSP432 available RAM limits size to N=2048 points
+#include <math.h>
+#include <stdlib.h>
+/*!
+ * @defgroup Math
+ * @brief
+ * @{*/
+
+/*!
+ * @brief a complex number has a real and imaginary part
+ */
+struct complex{
+  float Real; 
+  float Imag;
+}; 
+typedef struct complex complex_t;
+
+/**
+ * \brief PI is ratio of circumference to diameter of a circle
+ */
+#ifndef PI
+#define PI	3.14159265358979323846264338327950288
+#endif
+
+/**
+ * discrete Fast Fourier Transform,
+ * Converts time to frequency domain                             <br>
+ * Assume the input is real data sampled at fs                   <br>
+ * Place n measurements into the real part of array v            <br>
+ * Set the imaginary part of array v to 0                        <br>
+ * Call fft() and the results are returned back in array v       <br>
+ * If the input is real only, then the transform will contain    <br>
+ *   Index 0 <= k < n/2 complex components of frequency f=k/fs   <br>
+ *   E.g., k=0 represents the DC component of the input          <br>
+ *   Index n/2 <= k < n are complex conjugates of the first half <br>
+ * @param v array of input data in complex form
+ * @param n size of the two arrays 2, 4, 8, ..., 2048
+ * @param tmp temporary array of data in complex form
+ * @return none
+ * @note n is a power of two from 2 to 2048
+ * @brief fft
+ */
+void fft(complex_t *v, int n, complex_t *tmp);
+
+
+/**
+ * discrete Inverse Fast Fourier Transform,
+ * Converts frequency to time domain                                        <br>
+ * Assume the input is complex data with components k=0 to n-1              <br>
+ * Index 0 <= k < n-1 complex components of frequency f=k/fs                <br>
+ *   E.g., k=0 represents the DC component of the input                     <br>
+ * Place n complex values into the array v                                  <br>
+ * Typically the index n/2 <= k < n are complex conjugates of the first half<br>
+ * Call ifft() and the results are returned back in array v                 <br>
+ * If the input is real only, then the transform will contain               <br>
+ * @param v array of input data in complex form
+ * @param n size of the two arrays 2, 4, 8, ..., 2048
+ * @param tmp temporary array of data in complex form
+ * @return none
+ * @note n is a power of two from 2 to 2048
+ * @brief Inverse fft
+ */
+void ifft(complex_t *v, int n, complex_t *tmp);
+
+