Дискретна Фуријеова трансформација — разлика између измена

F(\omega_1 = 2\pi ) = \sum_{j=0}^{N-1=9} e^{ -\mathrm{i} \cdot 2\pi \cdot t_j } \cdot f(t_j ) = \ldots = 0 -3.5\mathrm{i} = y_1 = {\hat c}_1

F(\omega_2 = 4\pi ) = \sum_{j=0}^{N-1=9} e^{ -\mathrm{i} \cdot 4\pi \cdot t_j } \cdot f(t_j ) = \ldots = 15 +0\mathrm{i} = y_2 = {\hat c}_2

F(\omega_3 = 6\pi ) = 2.5 - 3\mathrm{i} = y_3 = {\hat c}_3

F(\omega_4 = 8\pi ) = 6.7586e-14 + 2.8240e-14i = y_4 = {\hat c}_4

double my_function ( double t )

return 5 + 10 * cos( ugaona_brzina * t) + 15 * cos( 2 * ( ugaona_brzina * t ) )

+ 20 * sin ( 3 * ( ugaona_brzina * t ) );

complex double get_fourier_coef ( double omega_n, double* t, double* f )

for ( k = 0; k < N; k ++ )

coeff += cexp ( - I * omega_n * t[k] ) * f[ k ] ;

f[0] = my_function ( t[0] );

for ( n = 1; n < N; n ++ )

omega[n] = 2 * pi * n / ( N * T );

f[n] = my_function ( t[n] );

for ( n = 0; n < N/2+1; n ++ )

coeff[n] = get_fourier_coef ( omega[n], t, f );

if ( cabs(coeff[n]) > 0.1 ){

printf ( "# Koeficijent %d: %e * e^i*%e\n", n, cabs(coeff[n]), carg(coeff[n]) );

a[0] = cabs(coeff[0] ) / N;

for ( n = 1; n < N/2+1; n++ )

if ( cabs( coeff[n] ) > 0.1 )

// c = 1/2 ( a + ib ), zato a = 2 * |c|, b == 0

a[n] = 2 * cabs( coeff[n] ) / N;

if ( abs ( carg(coeff[n]) ) > 0.001 )

printf ( "Nasa rekonstrukcija:\n f ( t ) = %e", a[0] );

for ( n = 1; n < N/2+1; n++ )

if ( a[n] )

if ( phi[n] )

printf ( " + %e * cos ( %d * ( 2 * pi * t + %e ) )", a[n], n, phi[n] );

printf ( "+ %e * cos ( %d * 2 * pi * t )", a[n], n );

printf ( "\n" );