O’ZBEKISTON RESPUBLIKASI AXBOROT TEXNOLOGIYALARI VA KOMMUNIKATSIYALARINI RIVOJLANTIRISH VAZIRLIGI
Muhammad Al-Xorazmiy nomidagi Toshkent Axborot Texnologiyalari Universiteti
Algoritmlarni loyihalash
Topshirdi: Baxtiyorov Asilbek
Tekshirdi:Ravshanov Anvar
Toshkent-2024
MISOL
Mavzu:Funksiyalarni Furye qatoriga yoyish
DASTURI:
const pi =3.14;
// Function f(x) = x + 5π
function f($x) {
return $x + 5 * pi;
}
// Numerical integration using the trapezoidal rule
function integrate($func, $a, $b, $n = 1000) {
$h = ($b - $a) / $n;
$sum = 0.5 * ($func($a) + $func($b));
for ($i = 1; $i < $n; $i++) {
$sum += $func($a + $i * $h);
}
return $sum * $h;
}
// Function to calculate an and bn coefficients
function fourierCoefficients($n, $a = -pi, $b = pi, $numIntervals = 1000) {
// an coefficient
$an_func = function($x) use ($n) {
return f($x) * cos($n * $x);
};
// bn coefficient
$bn_func = function($x) use ($n) {
return f($x) * sin($n * $x);
};
$a_n = integrate($an_func, $a, $b, $numIntervals) / pi;
$b_n = integrate($bn_func, $a, $b, $numIntervals) / pi;
return [$a_n, $b_n];
}
// Function to compute Fourier series
function fourierSeries($x, $terms = 10) {
$pi = pi;
// Compute a0
$a0_func = function($x) {
return f($x);
};
$a0 = integrate($a0_func, -$pi, $pi) / (2 * $pi);
// Fourier Series Initialization
$sum = $a0;
// Calculate Fourier Series up to the specified number of terms
for ($n = 1; $n <= $terms; $n++) {
list($a_n, $b_n) = fourierCoefficients($n);
$sum += $a_n * cos($n * $x) + $b_n * sin($n * $x);
}
return $sum;
}
// Example usage:
$x = 1.0; // You can set this to any value within the interval [-pi, pi]
$a_values = [];
for ($n = 0; $n <= 10; $n++) {
$a_values[$n] = fourierCoefficients($n)[0];
}
print_r($a_values);
?>
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