/* * Example program using the Complex FFT server class. */ // Include the header file for complex FFT server class: #include <rw/cfft.h> // Header files for complex vectors: #include <rw/math/mathvec.h> #include <math.h> #include <iostream> int main() { // Set series length: unsigned npts = 12; // Allocate a server: DComplexFFTServer server; /* * Create two series, one a cosine series, the * other a sine series. This is done by first * using a constructor for an RWMathVec<double> with * increasing elements, taking the cosine (or * sine) of this vector, then constructing a * complex vector from that. */ // One cycle: RWMathVec<DComplex> a = cos( RWMathVec<double>(npts,0,2.0*M_PI/npts) ); // Two cycles: RWMathVec<DComplex> a2 = sin( RWMathVec<double>(npts,0,4.0*M_PI/npts) ); /* * Calculate the superposition of the two. Note that we * are adding two complex vectors here with one * simple statement. */ RWMathVec<DComplex> asum = a + a2; // Output the vectors: std::cout << "a:\n" << a << "\n"; std::cout << "a2:\n" << a2 << "\n"; std::cout << "asum:\n" << asum << "\n"; /* * Print out the transforms, normalized by the * number of points. */ std::cout << "\nTransform of a:\n"; std::cout << server.fourier(a)/DComplex(npts); std::cout << "\nTransform of a2:\n"; std::cout << server.fourier(a2)/DComplex(npts); RWMathVec<DComplex> asumFFT = server.fourier(asum); std::cout << "\nTransform of asum:\n"; std::cout << asumFFT/DComplex(npts); /* * Check Parseval's Theorem. First, calculate the * variance of the series asum, using the global * function variance(). */ std::cout << "\nOriginal Variance: " << variance(asum) << "\n"; /* * Next, calculate the spectral variance of the Fourier * transformed series, using the global function * spectralVariance(). */ double var = spectralVariance(asumFFT/DComplex(npts)); std::cout << "Spectral Variance: " << var << "\n\n"; /* * Print out the normalized back transform of * asumFFT; this should equal the original asum. */ std::cout << "\nBack Transform of asum:\n" <<server.ifourier(asumFFT)/DComplex(npts); }

Sample Input:

None required.

Sample Output:

See file example3.out in the examples directory for the complete sample output. Note that the exact numbers depend on machine precision.

a: [ ( 1, 0) ( 0.866, 0) ( 0.5, 0) ( 0, 0) ... ] a2: [ ( 0, 0) ( 0.866, 0) ( 0.866, 0) ( 0, 0) ... ] asum: [ ( 1, 0) ( 1.732, 0) ( 1.366, 0) ( 0, 0) ... ] Transform of a: [ ( 0, 0) ( 0.5, 0) ( 0, 0) ... ] Transform of a2: [ ( 0, 0) ( 0, 0) ( 0, -0.5) ... Transform of asum: [ ( 0, 0) ( 0.5, 0) ( 0, -0.5) ... ] Original variance: 1 Spectral variance: 1 Back transform of asum: [ ( 1, 0) ( 1.732, 0) ( 1.366, 0) ( 0, 0) ... ]