Downconverting band-limited real-valued signal is a mess I don't have time to clean up. :-)

real_downconvert.py

#!/usr/bin/env python

import numpy
import scipy.fftpack

import matplotlib.pyplot as plt

def plot_time_domain_of(items):
	for t, samples, label in items:
		plt.plot(t, samples, label=label)
	plt.legend()
	plt.show()

def plot_spectrum_of(items):
	for t, samples, label in items:
		f = scipy.fftpack.fft(samples) / len(samples)
		f_mag = numpy.absolute(f)
		f_db = numpy.log10(f_mag) * 20
		plt.plot(f_db, label=label)
	plt.legend()
	plt.show()

sampling_rate = 137.5e6
intermediate_frequency = 35e6
target_center_frequency = 20e6

frequency_shift = target_center_frequency - intermediate_frequency

sample_count = 200
test_signal_frequency = 20e6

n = numpy.arange(0, sample_count, dtype=numpy.float64)
t = n / sampling_rate

w = t * 2 * numpy.pi

signal = numpy.cos(w * test_signal_frequency)
sinusoid = numpy.cos(w * frequency_shift)

output = signal * sinusoid

signals = (
	(t, signal, 'signal'),
	(t, sinusoid, 'mix'),
	(t, output, 'out'),
)

plot_time_domain_of(signals)
plot_spectrum_of(signals)