频谱泄漏和hann窗

相关文档： 频域信号处理

对于8kHz取样频率的200Hz 300Hz的叠加波形进行512点FFT计算其频谱，比较矩形窗和hann窗的频谱泄漏。

# -*- coding: utf-8 -*-
#用hann窗降低频谱泄漏
#
import numpy as np
import pylab as pl
import scipy.signal as signal

sampling_rate = 8000
fft_size = 512
t = np.arange(0, 1.0, 1.0/sampling_rate)
x = np.sin(2*np.pi*200*t)  + 2*np.sin(2*np.pi*300*t)

xs = x[:fft_size] 
ys = xs * signal.hann(fft_size, sym=0)

xf = np.fft.rfft(xs)/fft_size
yf = np.fft.rfft(ys)/fft_size
freqs = np.linspace(0, sampling_rate/2, fft_size/2+1)
xfp = 20*np.log10(np.clip(np.abs(xf), 1e-20, 1e100))
yfp = 20*np.log10(np.clip(np.abs(yf), 1e-20, 1e100))
pl.figure(figsize=(8,4))
pl.title(u"200Hz和300Hz的波形和频谱")
pl.plot(freqs, xfp, label=u"矩形窗")
pl.plot(freqs, yfp, label=u"hann窗")
pl.legend()
pl.xlabel(u"频率(Hz)")

a = pl.axes([.4, .2, .4, .4])
a.plot(freqs, xfp, label=u"矩形窗")
a.plot(freqs, yfp, label=u"hann窗")
a.set_xlim(100, 400)
a.set_ylim(-40, 0)
pl.show()