Skip to content

Instantly share code, notes, and snippets.

@lebedov lebedov/
Last active Jun 7, 2020

What would you like to do?
Frequency shift a signal using SSB modulation.
#!/usr/bin/env python
Frequency shift a signal using SSB modulation.
import numpy as np
import scipy as sp
import scipy.signal
import matplotlib.pyplot as plt
def nextpow2(x):
"""Return the first integer N such that 2**N >= abs(x)"""
return int(np.ceil(np.log2(np.abs(x))))
def freq_shift(x, f_shift, dt):
Shift the specified signal by the specified frequency.
# Pad the signal with zeros to prevent the FFT invoked by the transform from
# slowing down the computation:
N_orig = len(x)
N_padded = 2**nextpow2(N_orig)
t = np.arange(0, N_padded)
return (scipy.signal.hilbert(np.hstack((x, np.zeros(N_padded-N_orig, x.dtype))))*np.exp(2j*np.pi*f_shift*dt*t))[:N_orig].real
dt = 1e-3
fs = 1/dt
T = 1.0
t = np.arange(0, T, dt)
N = len(t)
# Construct original signal:
x = 3*np.cos(2*np.pi*t)+np.cos(2*np.pi*3*t)+2*np.cos(2*np.pi*5*t)
# Uncomment the code below to construct a more interesting signal:
# N_taps = 2500
# np.random.seed(1)
# b = sp.signal.remez(N_taps, [0.0, 14.5/fs, 15.5/fs, 19.5/fs, 20.5/fs, 0.5], [0, 1, 0])
# x = sp.signal.lfilter(b, 1.0, np.random.rand(len(t)))
# Frequency shift:
f_shift = 10.0
# Shift signal's frequency components by using the Hilbert transform
# to perform SSB modulation:
x_shift = freq_shift(x, f_shift, dt)
# Plot results:
f = np.fft.fftfreq(N, dt)
xf = np.fft.fft(x).real
xf_shift = np.fft.fft(x_shift).real
start = 0
stop = int((25.0/(fs/2.0))*(N/2.0))
plt.subplot2grid((2, 3), (0, 0), rowspan=2, colspan=2)
plt.plot(t, x, 'b', t, x_shift, 'r-')
plt.xlabel('t (s)')
plt.legend(('original', 'shifted'))
plt.subplot2grid((2, 3), (0, 2))
plt.stem(f[start:stop], xf[start:stop])
plt.subplot2grid((2, 3), (1, 2))
plt.stem(f[start:stop], xf_shift[start:stop])
plt.xlabel('F (Hz)')
plt.suptitle('Frequency Shifting Using SSB Modulation')
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment
You can’t perform that action at this time.