Question

我正在尝试获取fft幅度以匹配输入时域信号的幅度比例。

对于这个问题，我已经尝试了很多“答案”，但似乎没有一个对我有用。所以我写了一个实验程序。

这需要一段音频（来自文件或-您可以使用加性合成来创建波形）。

然后我可以选择将信号填充为零（选择数量和要分析的步数）。

我没有网站发布我创建的绘图的图像-但是，如果您在底部（Python 3.x）剪切并发布程序，您将很快看到它们！

该程序的一小部分在下面。

代码的相关部分（下面的plot_pad_stats（））是：

    for p in np.arange(start,end,step):
        s1 = pad(s,int(p))

        ftp = np.fft.fft(s1,norm=norma)
        ft = norm_fft(s1,norm)

        if real:
            ftp = ftp.real
            ft = ft.real
        else:
            ftp = np.sqrt(ftp.real**2 + ftp.imag**2)
            ft = np.sqrt(ft.real**2 + ft.imag**2)
        if absolute:
            ftp = abs(ftp)      
            ft = abs(ft)      
        if active:
            ftp = [(f+abs(f))/2 for f in ftp]
            ft = [(f+abs(f))/2 for f in ft]

        minft[p1] = min(ftp)
        maxft[p1] = max(ftp)
        meanft[p1] = np.mean(ftp)
        lenft[p1] = int(p)

        minnft[p1] = min(ft)
        maxnft[p1] = max(ft)
        meannft[p1] = np.mean(ft)
        lennft[p1] = int(p)

我怀疑与相位有关-但不知道如何获得fft幅度标度以匹配正在分析的时域信号...

不仅增加了填充的变化很有趣，而且随着信号从单个正弦波变为更复杂的波而变化！

任何帮助表示感谢：-tony.fdlr@gmail.com

arrays = plot_pad_stats：只调用无参数即可绘制440hz信号全幅值

使用

   additativeSignal(hza=[1],aa=None,ap=[0],n=88200,sr=44100,verbose=True):
    '''
    hza = herz array
    aa = amplitude array
    ap = phase array
    n = number samples to return
    sr = sampling frequency
    verbose = sanity check
    '''

to create additative synthesised signals eg

    signal = additativeSignal([440,880,1320],[0.6,0.3,0.2],[0,0,0])
    signal = additativeSignal([440,550,600],[0.6,0.5,0.3],[0,50,100])

然后

    plot_pad_stats(signal)

使用

    plot_signal(s,start,end) to plot the signal (or a section thereof)

注意=相位值是在样本中而不是度数或弧度！

或获得更多乐趣：

锯齿波：

        f = 100
        a = 0.8
        ph = 0
        noFqs = 20

        signal = additativeSignal(
         [f * i for i in range(1,noFqs+1)],
         [am/i for i in range(1,noFqs+1)],
         [0 for i in range(1,noFqs+1)])   

        plot_signal(signal[0:1000])

        arrs = plot_pad_stats(signal,maxpad=1000,steps=1000,absolute=False)

与其他参数一起玩，尽您所能！

请注意，可能需要一些时间来绘制！

以下是供您使用的代码（python 3.x）

import numpy as np
import matplotlib.pyplot as plt 

def pad(s,n):
    '''
    pad signal to make length n
    '''
    ls = len(s)
    #print('Pad request: sig len: {}, new len: {}'.format(ls,n))
    if n <= ls:
        return s
    s2 = np.zeros(n)
    try:
        s2[:ls] = s
    except:
        #print('Pad exception: sig len: {}, new len: {}'.format(ls,n))            
        return s
    return s2

def norm_fft(s,norm=True):
    '''
    See plot_pad_stats below for explanation    
    '''
    if norm:
        norma = 'ortho'
    else:
        norma = None
    n = len(s)

    ft = np.fft.fft(s,norm=norma) / n
    ft = ft[range(int(n / 2))]

    return ft

def additativeSignal(hza=[1],aa=None,ap=[0],n=88200,sr=44100,verbose=True):
    '''
    hza = herz array
    aa = amplitude array
    ap = phase array
    n = number samples to return
    sr = sampling frequency
    verbose = sanity check
    '''
    xa = np.arange(0,n)
    s = np.zeros(n)
    a = 0
    apl = len(ap)
    if apl < len(hza):
        apl = np.zeros(len(hza))
    if not (isinstance(aa,(np.ndarray,list))):
        aa = np.ones(len(hza))
    if not (isinstance(ap,(np.ndarray,list))):
        aa = np.ones(len(hza))
    for hz in hza:
        amp=aa[a]
        phase = ap[a]
        if verbose:
            print("freq %d, amp = %f, phase: %d" % (hz,amp,phase))
        if hz != 0:
            s += (np.sin(2*np.pi*(xa+phase)/(sr/hz))*amp)
        a += 1
    return s

def plot_pad_stats(s=None,
                  sr=44100,
                  minpad = 0,
                  maxpad = 300,
                  steps = 300,
                  real = True,
                  norm = None,
                  absolute = True,
                  active = False
                  ):
    '''
    s = signal (audio etc)
    sr = sample rate
    minpad - minimum number of zeroed samples to append
    maxpad - maximum number of zeroed samples to append
    steps - number of ffts to calculate
    real - use only real values otherwise take sqrt(real**2 + imag**2)
    norm - np.fft.fft norm arg
    absolute - make fft results absolute (ie >0)
    active - standard activation function - any negative values changed to zero
    '''

    if norm:
        norma = 'ortho'
    else:
        norma = None
    minpad = int(minpad)

    # Create 1 sec 4450 herz full volume audio signal at 44100 hz sampling frequency
    if type(s) == type(None):
        s = additativeSignal([440],[1],[0],44100,44100,True)

    start = len(s) + minpad
    end = start + maxpad
    prange = maxpad

    #Arrays of fft results:

    # length fft
    lenft = [0 for p in range(steps)]
    # max fft val
    maxft = [0 for p in range(steps)]
    # min fft val
    minft = [0 for p in range(steps)]
    # mean fft val
    meanft = [0 for p in range(steps)]

    # same arrays using the above normalised function
    lennft = [0 for p in range(steps)]
    maxnft = [0 for p in range(steps)]
    minnft = [0 for p in range(steps)]
    meannft = [0 for p in range(steps)]

    p1 = 0
    step = prange/steps
    print('fft len sig {} step {}'.format(len(s),step))

    for p in np.arange(start,end,step):
        #print('fft {} len sig {} padded len {}'.format(p1,len(s),int(p))) 
        s1 = pad(s,int(p))

        ftp = np.fft.fft(s1,norm=norma)
        ft = norm_fft(s1,norm)

        if real:
            ftp = ftp.real
            ft = ft.real
        else:
            ftp = np.sqrt(ftp.real**2 + ftp.imag**2)
            ft = np.sqrt(ft.real**2 + ft.imag**2)
        if absolute:
            ftp = abs(ftp)      
            ft = abs(ft)      
        if active:
            ftp = [(f+abs(f))/2 for f in ftp]
            ft = [(f+abs(f))/2 for f in ft]

        minft[p1] = min(ftp)
        maxft[p1] = max(ftp)
        meanft[p1] = np.mean(ftp)
        lenft[p1] = int(p)

        minnft[p1] = min(ft)
        maxnft[p1] = max(ft)
        meannft[p1] = np.mean(ft)
        lennft[p1] = int(p)

        p1 += 1
        #:22.8f
    plt.subplot(211)
    plt.title("FFT stats. Sig Len {} with {} - {} appended zeros".format(len(s),minpad,maxpad+minpad))
    plt.xlabel("signal + pad length {} - {}".format(start,end))
    plt.ylabel("max {:f} - {:f} and\nmin {:f} - {:f}\nand mean {:f} - {:f}\nffta  values (abs/real)".format(min(maxft),max(maxft),min(minft),max(minft),min(meanft),max(meanft)))
    plt.plot(lenft,maxft,'bo')
    plt.plot(lenft,minft,'r+')
    plt.plot(lenft,meanft,'g*')

    plt.subplot(212)
    plt.title("\nNormalised FFT stats. Sig Len {} with {} - {} appended zeros".format(len(s),minpad,maxpad+minpad))
    plt.xlabel("signal + pad length\n{} - {}".format(start,end))
    plt.ylabel("max {:22.8f} - {:22.8f} and\nmin {:22.8f} - {:22.8f}\nand mean {:22.8f} - {:22.8f}\nffta  values (abs/real)".format(min(maxnft),max(maxnft),min(minnft),max(minnft),min(meannft),max(meannft)))
    plt.plot(lennft,maxnft,'bo')
    plt.plot(lennft,minnft,'r+')
    plt.plot(lennft,meannft,'g*')

    plt.show()

    return maxft,minft,lenft

def plot_signal(s,start=0,end=None):
    plt.title("Signal")
    plt.xlabel("samples")
    plt.ylabel("amplitude")
    if end == None:
        plt.plot(s)
    else:
        plt.plot(s[start:end])
    plt.show()

致谢

托尼

Answer 1

如果我理解的正确，您希望在频谱域中看到时间信号的正确幅度。在下面的示例中，我添加了两个振幅分别为1和0.5的正弦波。在右边的频谱中，您可以看到振幅似乎减半了，这是由于复杂的FFT在负和正频率之间分配了功率。

import numpy as np
import matplotlib.pyplot as p
%matplotlib inline

T=3 # secs
d=0.04 # secs
n=int(T/d)
print(n)
t=np.arange(0,T,d)  
fr=1 # Hz
y1= np.sin(2*np.pi*fr*t) 
y2= 1/2*np.sin(2*np.pi*3*fr*t+0.5) 
y=y1+y2 
f=np.fft.fftshift(np.fft.fft(y))
freq=np.fft.fftshift(np.fft.fftfreq(n,d))
p.figure(figsize=(12,5))
p.subplot(121)
p.plot(t,y1,'.-',color='red', lw=0.5, ms=1)  
p.plot(t,y2,'.-',color='blue', lw=0.5,ms=1) 
p.plot(t,y,'.-',color='green', lw=4, ms=4, alpha=0.3) 
p.xlabel('time (sec)')
p.ylabel('amplitude (Volt)')
p.subplot(122)
p.plot(freq,np.abs(f)/n)
p.xlabel(' freq (Hz)')
p.ylabel('amplitude (Volt)');

获取fft幅度以匹配输入时域信号幅度比例（numpy.fft）

1 个答案: