Python快速變換傅里葉（FFT）過程實例分析

這里做一下記錄，關(guān)于FFT就不做介紹了，直接貼上代碼，有詳細注釋的了：import numpy as npfrom scipy.fftpack import fft,ifftimport matplotlib.pyplot as pltimport seaborn#采樣點選擇1400個，因為設(shè)置的信號頻率分量最高為600赫茲，根據(jù)采樣定理知采樣頻率要大于信號頻率2倍，所以這里設(shè)置采樣頻率為1400赫茲（即一秒內(nèi)有1400個采樣點，一樣意思的）x=np.linspace(0,1,1400) #設(shè)置需要采樣的信號，頻率分量有180，390和600y=7*np.sin(2*np.pi*180*x) + 2.8*np.sin(2*np.pi*390*x)+5.1*np.sin(2*np.pi*600*x)yy=fft(y) #快速傅里葉變換yreal = yy.real # 獲取實數(shù)部分yimag = yy.imag # 獲取虛數(shù)部分yf=abs(fft(y)) # 取絕對值yf1=abs(fft(y))/len(x) #歸一化處理yf2 = yf1[range(int(len(x)/2))] #由于對稱性，只取一半?yún)^(qū)間xf = np.arange(len(y)) # 頻率xf1 = xfxf2 = xf[range(int(len(x)/2))] #取一半?yún)^(qū)間plt.subplot(221)plt.plot(x[0:50],y[0:50]) plt.title('Original wave')plt.subplot(222)plt.plot(xf,yf,'r')plt.title('FFT of Mixed wave(two sides frequency range)',fontsize=7,color='#7A378B') #注意這里的顏色可以查詢顏色代碼表plt.subplot(223)plt.plot(xf1,yf1,'g')plt.title('FFT of Mixed wave(normalization)',fontsize=9,color='r')plt.subplot(224)plt.plot(xf2,yf2,'b')plt.title('FFT of Mixed wave)',fontsize=10,color='#F08080')plt.show()
結(jié)果：

再添加一個簡單的例子

# -*- coding: utf-8 -*-import matplotlib.pyplot as pltimport numpy as npimport seabornFs = 150.0; # sampling rate采樣率Ts = 1.0/Fs; # sampling interval 采樣區(qū)間t = np.arange(0,1,Ts) # time vector,這里Ts也是步長ff = 25; # frequency of the signaly = np.sin(2*np.pi*ff*t)n = len(y) # length of the signalk = np.arange(n)T = n/Fsfrq = k/T # two sides frequency rangefrq1 = frq[range(int(n/2))] # one side frequency rangeYY = np.fft.fft(y) # 未歸一化Y = np.fft.fft(y)/n # fft computing and normalization 歸一化Y1 = Y[range(int(n/2))]fig, ax = plt.subplots(4, 1)ax[0].plot(t,y)ax[0].set_xlabel('Time')ax[0].set_ylabel('Amplitude')ax[1].plot(frq,abs(YY),'r') # plotting the spectrumax[1].set_xlabel('Freq (Hz)')ax[1].set_ylabel('|Y(freq)|')ax[2].plot(frq,abs(Y),'G') # plotting the spectrumax[2].set_xlabel('Freq (Hz)')ax[2].set_ylabel('|Y(freq)|')ax[3].plot(frq1,abs(Y1),'B') # plotting the spectrumax[3].set_xlabel('Freq (Hz)')ax[3].set_ylabel('|Y(freq)|')plt.show()