频谱泄漏

import math
from scipy.fftpack import fft
import scipy.signal as signal
import matplotlib.pyplot as plt

if __name__ == '__main__':
    sample_number = 1024
    fs = 1000
    x = [math.sin(2*math.pi*100*i/fs) for i in range(0, sample_number)]
    # x = x * signal.hanning(1024,sym=0)
    y = fft(x)
    result = abs(y)*2/sample_number
    print(max(result))
    plt.plot(result)
    plt.show()

代码结果为0.7-0.8左右，并不是期望的1，将sample_number增大为2048,4098,8192...并不能减少其发生的频谱泄漏

 这是因为频谱的分辨率为 fs/sample_number= 1000/1024 = 0.9765625Hz，而100Hz并不是0.9765625Hz的整数倍，所以发生泄漏。解决这个问题的办法之一是改变sample_number或者fs的大小，保证m*fs/sample_number = 100,其中m = 0,1,2,3.....