DiscreteFourierTransform.cc
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#include "DiscreteFourierTransform.hh"
#include <bits/stdc++.h>
template <class T, class E>
DiscreteFourierTransform<T, E>::DiscreteFourierTransform(vector<T> signal_, double sampleSpacing_)
{
signal = signal_;
sampleSpacing = sampleSpacing_;
}
template <class T, class E>
void DiscreteFourierTransform<T, E>::compute(bool computeFFT)
{
if (computeFFT)
{
const int N = signal.size();
const int powerOf2 = DiscreteFourierTransform<T, E>::highestPowerof2(N);
// Zero padding is a simple concept; it simply refers to adding zeros to end of a time-domain signal to increase its length to reach power of 2.
while (signal.size() < powerOf2)
signal.push_back((T)0);
phasors = DiscreteFourierTransform<T, E>::fft(signal);
}
else
phasors = DiscreteFourierTransform<T, E>::dft(signal);
}
template <class T, class E>
std::vector<E> DiscreteFourierTransform<T, E>::createTestPoints(int N, double sampleSpacing)
{
std::vector<E> out;
const E t = (E)sampleSpacing;
for (int i = 0; i < N; i++)
{
out.push_back((E)t * i);
}
return out;
}
template <class T, class E>
std::vector<E> DiscreteFourierTransform<T, E>::createTestFunction(std::vector<E> x)
{
const int N = x.size();
std::vector<E> out;
for (int i = 0; i < N; i++)
{
const E val = (E)sin(50.0 * 2.0 * M_PI * x[i]) + 0.5 * sin(80.0 * 2.0 * M_PI * x[i]);
out.push_back(val);
}
return out;
}
/**
* @brief We use Cooley-Tukey FFT Algorithm if the size of the signal is a power of 2 otherwise you should DFT brut. In The future we will use bluestein algorithm instead of DFT.
* Cooley-Tukey FFT Algorithms: http://people.scs.carleton.ca/~maheshwa/courses/5703COMP/16Fall/FFT_Report.pdf
*
* @tparam T template type of input data
* @tparam E template type of output data
* @param sig the signal as an input
* @return std::vector<std::complex<E>> the phasors (array of complex number)
*/
template <class T, class E>
std::vector<std::complex<E>> DiscreteFourierTransform<T, E>::fft(std::vector<T> sig)
{
const int N = sig.size();
if (N == 1)
{
std::vector<std::complex<E>> out;
const std::complex<E> temp((E)sig[0], (E)0);
out.push_back(temp);
return out;
}
const std::complex<E> WN = (complex<E>)std::polar(1.0, 2 * M_PI / N);
std::complex<E> W((E)1, (E)0);
// divide and conquer:
// Recurse: all even samples
std::vector<std::complex<E>>
x_evens = fft(getEven(sig));
// Recurse: all odd samples
std::vector<std::complex<E>> x_odds = fft(getOdd(sig));
// Now, combine and perform N/2 operations!
std::complex<E> zeroComplex((E)0, (E)0);
std::vector<std::complex<E>> x(N, zeroComplex);
for (int k = 0; k < N / 2; k++)
{
x[k] = x_evens[k] + W * x_odds[k];
x[k + (N / 2)] = x_evens[k] - W * x_odds[k];
W = W * WN;
}
return x;
}
template <class T, class E>
std::vector<std::complex<E>> DiscreteFourierTransform<T, E>::dft(std::vector<T> x)
{
const int N = x.size();
std::complex<E> zeroComplex((E)0, (E)0);
std::vector<std::complex<E>> out(N, zeroComplex);
for (int k = 0; k < N; k++)
{
for (int n = 0; n < N; n++)
{
const std::complex<E> expVal = (complex<E>)std::polar(1.0, -2 * k * n * M_PI / N);
out[k] += ((E)x[n]) * expVal;
}
}
return out;
}
template <class T, class E>
std::vector<E> DiscreteFourierTransform<T, E>::computeDSP(std::vector<std::complex<E>> x, double /*frequency_*/)
{
const int N = x.size();
std::vector<E> out;
for (int k = 1; k < N / 2; k++)
{
const E magnitudePower2 = (E)pow(abs(x[k]), 2);
// const E dsp = (E)(2.0 / (N * frequency_)) * magnitudePower2;
out.push_back(magnitudePower2);
}
return out;
}
template <class T, class E>
std::vector<E> DiscreteFourierTransform<T, E>::getFreq(std::vector<std::complex<E>> x, double frequency_)
{
const int N = x.size();
std::vector<E> out;
for (int k = 1; k < N / 2; k++)
{
const E freq = (E)k * frequency_ / N;
out.push_back(freq);
}
return out;
}
template <class T, class E>
std::vector<E> DiscreteFourierTransform<T, E>::getPeriods(std::vector<std::complex<E>> x, double frequency_)
{
const int N = x.size();
std::vector<E> out;
for (int k = 1; k < N / 2; k++)
{
const E period = N / ((E)k * frequency_);
out.push_back(period);
}
return out;
}
template <class T, class E>
std::vector<T> DiscreteFourierTransform<T, E>::getOdd(std::vector<T> x)
{
std::vector<T> odd;
for (int i = 0; i < x.size(); i++)
{
if (i % 2 != 0)
odd.push_back(x[i]);
}
return odd;
}
template <class T, class E>
std::vector<T> DiscreteFourierTransform<T, E>::getEven(std::vector<T> x)
{
std::vector<T> even;
for (int i = 0; i < x.size(); i++)
{
if (i % 2 == 0)
even.push_back(x[i]);
}
return even;
}
template <class T, class E>
bool DiscreteFourierTransform<T, E>::isPowerOfTwo(int N)
{
return (N & (N - 1)) == 0;
}
template <class T, class E>
int DiscreteFourierTransform<T, E>::highestPowerof2(int n)
{
int p = n;
while (!DiscreteFourierTransform<T, E>::isPowerOfTwo(p))
{
p += 1;
}
return p;
}