Proof-of-concept TDR measurements

Software/PC_Application/Traces/fftcomplex.cpp

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+/*
+ * Free FFT and convolution (C++)
+ *
+ * Copyright (c) 2020 Project Nayuki. (MIT License)
+ * https://www.nayuki.io/page/free-small-fft-in-multiple-languages
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a copy of
+ * this software and associated documentation files (the "Software"), to deal in
+ * the Software without restriction, including without limitation the rights to
+ * use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
+ * the Software, and to permit persons to whom the Software is furnished to do so,
+ * subject to the following conditions:
+ * - The above copyright notice and this permission notice shall be included in
+ *   all copies or substantial portions of the Software.
+ * - The Software is provided "as is", without warranty of any kind, express or
+ *   implied, including but not limited to the warranties of merchantability,
+ *   fitness for a particular purpose and noninfringement. In no event shall the
+ *   authors or copyright holders be liable for any claim, damages or other
+ *   liability, whether in an action of contract, tort or otherwise, arising from,
+ *   out of or in connection with the Software or the use or other dealings in the
+ *   Software.
+ */
+
+#include <cstddef>
+#include <cstdint>
+#include <stdexcept>
+#include <utility>
+#include "fftcomplex.h"
+
+using std::complex;
+using std::size_t;
+using std::uintmax_t;
+using std::vector;
+
+
+// Private function prototypes
+static size_t reverseBits(size_t val, int width);
+
+
+void Fft::transform(vector<complex<double> > &vec, bool inverse) {
+    size_t n = vec.size();
+    if (n == 0)
+        return;
+    else if ((n & (n - 1)) == 0)  // Is power of 2
+        transformRadix2(vec, inverse);
+    else  // More complicated algorithm for arbitrary sizes
+        transformBluestein(vec, inverse);
+}
+
+
+void Fft::transformRadix2(vector<complex<double> > &vec, bool inverse) {
+    // Length variables
+    size_t n = vec.size();
+    int levels = 0;  // Compute levels = floor(log2(n))
+    for (size_t temp = n; temp > 1U; temp >>= 1)
+        levels++;
+    if (static_cast<size_t>(1U) << levels != n)
+        throw std::domain_error("Length is not a power of 2");
+
+    // Trigonometric table
+    vector<complex<double> > expTable(n / 2);
+    for (size_t i = 0; i < n / 2; i++)
+        expTable[i] = std::polar(1.0, (inverse ? 2 : -2) * M_PI * i / n);
+
+    // Bit-reversed addressing permutation
+    for (size_t i = 0; i < n; i++) {
+        size_t j = reverseBits(i, levels);
+        if (j > i)
+            std::swap(vec[i], vec[j]);
+    }
+
+    // Cooley-Tukey decimation-in-time radix-2 FFT
+    for (size_t size = 2; size <= n; size *= 2) {
+        size_t halfsize = size / 2;
+        size_t tablestep = n / size;
+        for (size_t i = 0; i < n; i += size) {
+            for (size_t j = i, k = 0; j < i + halfsize; j++, k += tablestep) {
+                complex<double> temp = vec[j + halfsize] * expTable[k];
+                vec[j + halfsize] = vec[j] - temp;
+                vec[j] += temp;
+            }
+        }
+        if (size == n)  // Prevent overflow in 'size *= 2'
+            break;
+    }
+}
+
+
+void Fft::transformBluestein(vector<complex<double> > &vec, bool inverse) {
+    // Find a power-of-2 convolution length m such that m >= n * 2 + 1
+    size_t n = vec.size();
+    size_t m = 1;
+    while (m / 2 <= n) {
+        if (m > SIZE_MAX / 2)
+            throw std::length_error("Vector too large");
+        m *= 2;
+    }
+
+    // Trigonometric table
+    vector<complex<double> > expTable(n);
+    for (size_t i = 0; i < n; i++) {
+        uintmax_t temp = static_cast<uintmax_t>(i) * i;
+        temp %= static_cast<uintmax_t>(n) * 2;
+        double angle = (inverse ? M_PI : -M_PI) * temp / n;
+        expTable[i] = std::polar(1.0, angle);
+    }
+
+    // Temporary vectors and preprocessing
+    vector<complex<double> > avec(m);
+    for (size_t i = 0; i < n; i++)
+        avec[i] = vec[i] * expTable[i];
+    vector<complex<double> > bvec(m);
+    bvec[0] = expTable[0];
+    for (size_t i = 1; i < n; i++)
+        bvec[i] = bvec[m - i] = std::conj(expTable[i]);
+
+    // Convolution
+    vector<complex<double> > cvec(m);
+    convolve(avec, bvec, cvec);
+
+    // Postprocessing
+    for (size_t i = 0; i < n; i++)
+        vec[i] = cvec[i] * expTable[i];
+}
+
+
+void Fft::convolve(
+        const vector<complex<double> > &xvec,
+        const vector<complex<double> > &yvec,
+        vector<complex<double> > &outvec) {
+
+    size_t n = xvec.size();
+    if (n != yvec.size() || n != outvec.size())
+        throw std::domain_error("Mismatched lengths");
+    vector<complex<double> > xv = xvec;
+    vector<complex<double> > yv = yvec;
+    transform(xv, false);
+    transform(yv, false);
+    for (size_t i = 0; i < n; i++)
+        xv[i] *= yv[i];
+    transform(xv, true);
+    for (size_t i = 0; i < n; i++)  // Scaling (because this FFT implementation omits it)
+        outvec[i] = xv[i] / static_cast<double>(n);
+}
+
+
+static size_t reverseBits(size_t val, int width) {
+    size_t result = 0;
+    for (int i = 0; i < width; i++, val >>= 1)
+        result = (result << 1) | (val & 1U);
+    return result;
+}