numpy fft example

numpy_fft_example.py

import numpy as np
import matplotlib.pyplot as plt

def fftTest():
    x = np.linspace(0, 2 * np.pi, 100)
    f = -0.1 + np.sin(x) - np.cos(2 * x)  # 元関数
    F = np.fft.rfft(f)  # 実数離散FFT
    for i, Fi in enumerate(F):  # FFT結果の複素数を表示
        print(i, "{:2.2f}".format(Fi))

    fig = plt.figure()
    ax = fig.add_subplot(221)
    ax.plot(x, f, label='$f(x)=-0.1+sin(x)-cos(2x)$')
    ax.plot(x, np.fft.irfft(F), label='$F^{-1}[F[f]](x)$')
    ax.set_xlabel("x")
    ax.set_ylabel("Signal")
    ax.legend()

    ax = fig.add_subplot(222)
    ax.plot(np.abs(F), label='$|F[f](k)|$')
    ax.set_xlabel('Frequency $k$')
    ax.set_ylabel('Abs')
    ax.legend()

    ax = fig.add_subplot(223)
    ax.plot(F.real, label=r'$Re\;F[f](k)$')
    ax.set_xlabel('Frequency $k$')
    ax.set_ylabel('Real')
    ax.legend()

    ax = fig.add_subplot(224)
    ax.plot(F.imag, label=r'$Im\;F[f](k)$')
    ax.set_xlabel('Frequency $k$')
    ax.set_ylabel('Imag')
    ax.legend()
    fig.tight_layout()
    plt.show()


if __name__ == "__main__":
    fftTest()