spkit.ffrft

spkit.ffrft(x, alpha)

Fast Fractional Fourier Transform

Fast Fractional Fourier Transform

• perfect reconstruction with iffrft

Parameters:

x: real signal

alpha: value

Returns:

Y: complex signal

See also

frft

Fractional Fourier Transform

ifrft

Inverse Fractional Fourier Transform

iffrft

Inverse Fast Fractional Fourier Transform

Notes

• FRFT frft Fractional Fourier Transform, is classic and more accepted approach. Compared to FFRFT, ffrft

References

• wikipedia -

Examples

#sp.ffrft
import numpy as np
import matplotlib.pyplot as plt
import spkit as sp
t = np.linspace(0,2,500)
x = np.cos(2*np.pi*5*t)
xf = sp.ffrft(x,alpha=0.5)
plt.figure(figsize=(10,5))
plt.subplot(211)
plt.plot(t,x,label='x: input signal')
plt.xlim([t[0],t[-1]])
plt.xlabel('time (s)')
plt.ylabel('x')
plt.legend(loc='upper right')
plt.subplot(212)
plt.plot(t,xf.real,label='xf.real',alpha=0.9)
plt.plot(t,xf.imag,label='xf.imag',alpha=0.9)
plt.plot(t,np.abs(xf),label='|xf|',alpha=0.9)
plt.xlim([t[0],t[-1]])
plt.ylabel(r'xf: FFRFT(x) $\alpha=0.5$')
plt.legend(loc='upper right')
plt.tight_layout()
plt.show()