Question

我正在编写一个脚本来模拟随机白噪声，以研究其转变为信号形式时的行为。

下面是我遇到的问题：

def white_noise(n: int, N: int, slope: int = grad):
    """
    - Creates a data set of white noise with size n, N;
    - Filters this dataset with the corresponding slope;
        This slope is usually equal to -5/3 or -2/3
    - Makes sure the slope is equal to the requested slope in the double log scale.

    @param n: size of random array
    @param N: number of random arrays
    @param slope: slope of the gradient
    @return: white_noise, filtered white_noise and the original signal
    """
    x = np.linspace(0, 1, n)
    slope_loglog = (10 ** (slope * np.log10(x) + 1))

    white_noise = rnd.rand(n, N) ** 2 # squaring the white noise to retrieve the power spectrum
    white_noise_filtered = []
    white_noise_signal = []
    white_noise_retransformed = []

    for k in range(N):
        white_noise_filtered.append(white_noise[:,k] * slope_loglog)
        white_noise_signal.append(fft.ifft(white_noise[:,k] * slope_loglog))

    white_noise_filtered, white_noise_signal, white_noise_retransformed = \
        np.asarray((white_noise_filtered, white_noise_signal, white_noise_retransformed))

    white_noise_filtered = white_noise_filtered.transpose()
    white_noise_signal = white_noise_signal.transpose().imag


    return white_noise, white_noise_filtered, white_noise_signal, white_noise_retransformed, slope_loglog

在我应用快速傅里叶逆变换（1D）的步骤中，我的模拟噪声生成了一个复杂的数组（在处理傅里叶变换时可以预料到）。我不明白的是为什么所有复杂值的实数部分等于“ Inf”。这些应该具有有限的值，那么我在做什么错了？

（注意：slope_loglog与梯度为-5/3的对数-对数转换数据有关。）

由于我需要先安装ift，然后再使用fft才能再次获得原始噪声（或偏移），所以我需要了解为什么我的脚本会这样做。仅采用阵列“ white_noise_signal”的虚部不会产生原始噪声。

Answer 1

这与FFT / IFFT无关

np.log10(0) = -np.inf

和

10 ** np.inf = np.inf

因此，如果您使用负斜率，即slope = -1

10 ** (slope * np.log10(0)) = np.inf

将其乘以 any 信号，您将得到inf。

此外，如果您跳过以下列表之间的列表，则可以显着简化代码：

def white_noise(n: int, N: int, slope: int = -5/3):
    """
    - Creates a data set of white noise with size n, N;
    - Filters this dataset with the corresponding slope;
        This slope is usually equal to -5/3 or -2/3
    - Makes sure the slope is equal to the requested slope in the double log scale.

    @param n: size of random array
    @param N: number of random arrays
    @param slope: slope of the gradient
    @return: white_noise, filtered white_noise and the original signal
    """

    x = np.linspace(0, 1, n)
    slope_loglog = (10 ** (slope * np.log10(x) + 1))

    white_noise = np.random.rand(n, N) ** 2 # cubing the white noise to retrieve the power spectrum

    white_noise_filtered = (white_noise * slope_loglog).T
    white_noise_signal = (np.fft.ifft(white_noise, axis=-1) * slope_loglog).T.imag

    return white_noise, white_noise_filtered, white_noise_signal, slope_loglog

为什么我的ifft导致复数的实部是无限的？

1 个答案: