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qa_fft.py
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#!/usr/bin/env python
#
# Copyright 2008,2010,2012 Free Software Foundation, Inc.
#
# This file is part of GNU Radio
#
# GNU Radio is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 3, or (at your option)
# any later version.
#
# GNU Radio is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License along
# with this program; if not, write to the Free Software Foundation, Inc.,
# 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA.
#
from gnuradio import gr, gr_unittest, fft, blocks
# Note: Octave code to verify these results:
# primes = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167,
# 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311]
# src_data = primes(1:2:end) + primes(2:2:end)*i
# forward = fft(src_data(:))
# reverse = ifft(forward(:))
# windowed = fft(src_data(:).*hamming(32))
# reverse_window_shift = ifft(fftshift(forward.*hamming(32)))
primes = (2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53,
59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131,
137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223,
227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311)
primes_transformed = ((4377 + 4516j),
(-1706.1268310546875 + 1638.4256591796875j),
(-915.2083740234375 + 660.69427490234375j),
(-660.370361328125 + 381.59600830078125j),
(-499.96044921875 + 238.41630554199219j),
(-462.26748657226562 + 152.88948059082031j),
(-377.98440551757812 + 77.5928955078125j),
(-346.85821533203125 + 47.152004241943359j),
(-295 + 20j),
(-286.33609008789062 - 22.257017135620117j),
(-271.52999877929688 - 33.081821441650391j),
(-224.6358642578125 - 67.019538879394531j),
(-244.24473571777344 - 91.524826049804688j),
(-203.09068298339844 - 108.54627227783203j),
(-198.45195007324219 - 115.90768432617188j),
(-182.97744750976562 - 128.12318420410156j),
(-167 - 180j),
(-130.33688354492188 - 173.83778381347656j),
(-141.19784545898438 - 190.28807067871094j),
(-111.09677124023438 - 214.48896789550781j),
(-70.039543151855469 - 242.41630554199219j),
(-68.960540771484375 - 228.30015563964844j),
(-53.049201965332031 - 291.47097778320312j),
(-28.695289611816406 - 317.64553833007812j),
(57 - 300j),
(45.301143646240234 - 335.69509887695312j),
(91.936195373535156 - 373.32437133789062j),
(172.09465026855469 - 439.275146484375j),
(242.24473571777344 - 504.47515869140625j),
(387.81732177734375 - 666.6788330078125j),
(689.48553466796875 - 918.2142333984375j),
(1646.539306640625 - 1694.1956787109375j))
class test_fft(gr_unittest.TestCase):
def setUp(self):
self.tb = gr.top_block()
self.fft_size = 32
def tearDown(self):
pass
def assert_fft_ok2(self, expected_result, result_data):
expected_result = expected_result[:len(result_data)]
self.assertComplexTuplesAlmostEqual2(expected_result, result_data,
abs_eps=1e-9, rel_eps=4e-4)
def test_forward(self):
src_data = tuple([complex(primes[2 * i], primes[2 * i + 1]) for i in range(self.fft_size)])
expected_result = primes_transformed
src = blocks.vector_source_c(src_data)
s2v = blocks.stream_to_vector(gr.sizeof_gr_complex, self.fft_size)
op = fft.fft_vcc(self.fft_size, True, [], False)
v2s = blocks.vector_to_stream(gr.sizeof_gr_complex, self.fft_size)
dst = blocks.vector_sink_c()
self.tb.connect(src, s2v, op, v2s, dst)
self.tb.run()
result_data = dst.data()
self.assert_fft_ok2(expected_result, result_data)
def test_reverse(self):
src_data = tuple([x / self.fft_size for x in primes_transformed])
expected_result = tuple([complex(primes[2 * i], primes[2 * i + 1]) for i in range(self.fft_size)])
src = blocks.vector_source_c(src_data)
s2v = blocks.stream_to_vector(gr.sizeof_gr_complex, self.fft_size)
op = fft.fft_vcc(self.fft_size, False, [], False)
v2s = blocks.vector_to_stream(gr.sizeof_gr_complex, self.fft_size)
dst = blocks.vector_sink_c()
self.tb.connect(src, s2v, op, v2s, dst)
self.tb.run()
result_data = dst.data()
self.assert_fft_ok2(expected_result, result_data)
def test_multithreaded(self):
# Same test as above, only use 2 threads
src_data = tuple([x / self.fft_size for x in primes_transformed])
expected_result = tuple([complex(primes[2 * i], primes[2 * i + 1]) for i in range(self.fft_size)])
nthreads = 2
src = blocks.vector_source_c(src_data)
s2v = blocks.stream_to_vector(gr.sizeof_gr_complex, self.fft_size)
op = fft.fft_vcc(self.fft_size, False, [], False, nthreads)
v2s = blocks.vector_to_stream(gr.sizeof_gr_complex, self.fft_size)
dst = blocks.vector_sink_c()
self.tb.connect(src, s2v, op, v2s, dst)
self.tb.run()
result_data = dst.data()
self.assert_fft_ok2(expected_result, result_data)
def test_window(self):
src_data = tuple([complex(primes[2 * i], primes[2 * i + 1]) for i in range(self.fft_size)])
expected_result = ((2238.9174 + 2310.4750j),
(-1603.7416 - 466.7420j),
(116.7449 - 70.8553j),
(-13.9157 + 19.0855j),
(-4.8283 + 16.7025j),
(-43.7425 + 16.9871j),
(-16.1904 + 1.7494j),
(-32.3797 + 6.9964j),
(-13.5283 + 7.7721j),
(-24.3276 - 7.5378j),
(-29.2711 + 4.5709j),
(-2.7124 - 6.6307j),
(-33.5486 - 8.3485j),
(-8.3016 - 9.9534j),
(-18.8590 - 8.3501j),
(-13.9092 - 1.1396j),
(-17.7626 - 26.9281j),
(0.0182 - 8.9000j),
(-19.9143 - 14.1320j),
(-10.3073 - 15.5759j),
(3.5800 - 29.1835j),
(-7.5263 - 1.5900j),
(-3.0392 - 31.7445j),
(-15.1355 - 33.6158j),
(28.2345 - 11.4373j),
(-6.0055 - 27.0418j),
(5.2074 - 21.2431j),
(23.1617 - 31.8610j),
(13.6494 - 11.1982j),
(14.7145 - 14.4113j),
(-60.0053 + 114.7418j),
(-440.1561 - 1632.9807j))
window = fft.window_hamming(ntaps=self.fft_size)
src = blocks.vector_source_c(src_data)
s2v = blocks.stream_to_vector(gr.sizeof_gr_complex, self.fft_size)
op = fft.fft_vcc(self.fft_size, True, window, False)
v2s = blocks.vector_to_stream(gr.sizeof_gr_complex, self.fft_size)
dst = blocks.vector_sink_c()
self.tb.connect(src, s2v, op, v2s, dst)
self.tb.run()
result_data = dst.data()
self.assert_fft_ok2(expected_result, result_data)
def test_reverse_window_shift(self):
src_data = tuple([x / self.fft_size for x in primes_transformed])
expected_result = ((-74.8629 - 63.2502j),
(-3.5446 - 2.0365j),
(2.9231 + 1.6827j),
(-2.7852 - 0.8613j),
(2.4763 + 2.7881j),
(-2.7457 - 3.2602j),
(4.7748 + 2.4145j),
(-2.8807 - 4.5313j),
(5.9949 + 4.1976j),
(-6.1095 - 6.0681j),
(5.2248 + 5.7743j),
(-6.0436 - 6.3773j),
(9.7184 + 9.2482j),
(-8.2791 - 8.6507j),
(6.3273 + 6.1560j),
(-12.2841 - 12.4692j),
(10.5816 + 10.0241j),
(-13.0312 - 11.9451j),
(12.2983 + 13.3644j),
(-13.0372 - 14.0795j),
(14.4682 + 13.3079j),
(-16.7673 - 16.7287j),
(14.3946 + 11.5916j),
(-16.8368 - 21.3156j),
(20.4528 + 16.8499j),
(-18.4075 - 18.2446j),
(17.7507 + 19.2109j),
(-21.5207 - 20.7159j),
(22.2183 + 19.8012j),
(-22.2144 - 20.0343j),
(17.0359 + 17.6910j),
(-91.8955 - 103.1093j))
window = fft.window_hamming(ntaps=self.fft_size)
src = blocks.vector_source_c(src_data)
s2v = blocks.stream_to_vector(gr.sizeof_gr_complex, self.fft_size)
op = fft.fft_vcc(self.fft_size, False, window, True)
v2s = blocks.vector_to_stream(gr.sizeof_gr_complex, self.fft_size)
dst = blocks.vector_sink_c()
self.tb.connect(src, s2v, op, v2s, dst)
self.tb.run()
result_data = dst.data()
self.assert_fft_ok2(expected_result, result_data)
if __name__ == '__main__':
gr_unittest.run(test_fft, "test_fft.xml")