

In [4]:

    
%matplotlib inline
import numpy as np
import matplotlib.pyplot as plt
plt.rcParams['figure.max_open_warning'] = -1
plt.rcParams['font.size'] = 18
import seaborn as sns
import ipywidgets
from scipy.fftpack import fft

Interactive FFT for a time-dependent frequency sinusoid

This is an interactive plot of an FFT for a signal model $$ y(x) = \sin(2\pi(f_0 + \dot{f}_0 x) x)$$ We will show on the left a few periods (not the full extent of the data) and on the right the corresponding FFT. Soem automatic scaling is applied so that relevant information is displayed, most importantly df controls the width of the frequency spectrum window.



In [111]:

    
def plot(f0, f1, df):
    N = int(1e6)
    dT = 1e-4
    f0 = float(f0)
    f1 = float(f1)
    df = float(df)
    f0max = 20.

    x = np.linspace(0.0, N*dT, N)
    f = f0 + f1 * x
    y = np.sin(f * 2.0*np.pi*x)
    yf = fft(y)
    xf = np.linspace(0.0, 1.0/(2.0*dT), N/2)

    fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(10, 3))
    ax1.plot(x, y)
    ax1.set_xlim(0, 5*1/f0max)
    ax1.set_xlabel('$x$')
    
    ax2.plot(xf, 2.0/N * np.abs(yf[0:N/2]))
    ax2.set_xlim(f0 - df, f0 + df)
    ax2.axvline(f0)
    ax2.set_xlabel(r'$\tilde{f}$')
    plt.show()



In [117]:

    
ipywidgets.interact(plot, f0=(8., 12, 0.25), f1=(0.001, 0.05 , 0.001), df=(1., 20, 0.5))