我正在尝试计算以下高斯的傅立叶变换:

# sample spacing 
dx = 1.0 / 1000.0 
 
# Points 
x1 = -5 
x2 = 5 
 
x = np.arange(x1, x2, dx) 
 
def light_intensity(): 
    return 10*sp.stats.norm.pdf(x, 0, 1)+0.1*np.random.randn(x.size) 
 
fig, ax = plt.subplots() 
ax.plot(x,light_intensity())

我在空间频域中创建一个新数组(高斯的傅立叶变换是高斯变换，因此这些值应该相似)。我绘制并得到这个:

fig, ax = plt.subplots() 
 
xf = np.arange(x1,x2,dx) 
yf= np.fft.fftshift(light_intensity()) 
ax.plot(xf,np.abs(yf))

为什么它 split 成两个峰？

请您参考如下方法:

建议:

使用np.fft.fft
fft 从 0 Hz 开始
规范化/重新缩放

完整示例:

import numpy as np 
import matplotlib.pyplot as plt 
from scipy.stats import norm 
 
def norm_fft(y, T, max_freq=None): 
    N = y.shape[0] 
    Nf = N // 2 if max_freq is None else int(max_freq * T) 
    xf = np.linspace(0.0, 0.5 * N / T, N // 2) 
    yf = 2.0 / N * np.fft.fft(y) 
    return xf[:Nf], yf[:Nf] 
 
def generate_signal(x, signal_gain=10.0, noise_gain=0.0): 
    signal = norm.pdf(x, 0, 1) 
    noise = np.random.randn(x.size) 
    return signal_gain * signal + noise_gain * noise 
 
# Signal parameters 
x1 = 0.0 
x2 = 5.0 
N = 10000 
T = x2 - x1 
 
# Generate signal data 
x = np.linspace(x1, x2, N) 
y = generate_signal(x) 
 
# Apply FFT 
xf, yf = norm_fft(y, T, T / np.pi) 
 
# Plot 
fig, ax = plt.subplots(2) 
ax[0].plot(x, y) 
ax[1].plot(xf, np.abs(yf)) 
plt.show()

或者，有噪声:

对称图

或者，如果您想享受频域中的对称性:

import numpy as np 
import matplotlib.pyplot as plt 
from scipy.stats import norm 
 
def norm_sym_fft(y, T, max_freq=None): 
    N = y.shape[0] 
    b = N if max_freq is None else int(max_freq * T + N // 2) 
    a = N - b 
    xf = np.linspace(-0.5 * N / T, 0.5 * N / T, N) 
    yf = 2.0 / N * np.fft.fftshift(np.fft.fft(y)) 
    return xf[a:b], yf[a:b] 
 
def generate_signal(x, signal_gain=10.0, noise_gain=0.0): 
    signal = norm.pdf(x, 0, 1) 
    noise = np.random.randn(x.size) 
    return signal_gain * signal + noise_gain * noise 
 
# Signal parameters 
x1 = -10.0 
x2 = 10.0 
N = 10000 
T = x2 - x1 
 
# Generate signal data 
x = np.linspace(x1, x2, N) 
y = generate_signal(x) 
 
# Apply FFT 
xf, yf = norm_sym_fft(y, T, 4 / np.pi) 
 
# Plot 
fig, ax = plt.subplots(2) 
ax[0].plot(x, y) 
ax[1].plot(xf, np.abs(yf)) 
plt.show()

或者，有噪声:

python之使用 Numpy 进行傅立叶变换

对称图