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#!/usr/bin/env python3
# SPDX-License-Identifier: BSD-3-Clause
#
# Copyright 2020 Philipp Le
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above copyright
# notice, this list of conditions and the following disclaimer in the
# documentation and/or other materials provided with the distribution.
#
# 3. Neither the name of the copyright holder nor the names of its
# contributors may be used to endorse or promote products derived from
# this software without specific prior written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF
# THE POSSIBILITY OF SUCH DAMAGE.
import numpy
x = numpy.array([-0.5, 1, -2, 2])
print("TEST ================================")
print(numpy.fft.fft(x))
print("a) ==================================")
for k in range(4):
eq_str = "\\underline{X}[%d] = " % (k)
elems = []
res = 0
for n in range(4):
#elems.append("\\underline{x}[%d] \\cdot e^{-j \\frac{2\\pi}{N} %d \\cdot %d}" % (n, k, n))
elems.append("\\underline{x}[%d] \\cdot e^{-j \\frac{\\pi}{2} %d \\cdot %d}" % (n, k, n))
res += x[n] * numpy.exp(-1j*(numpy.pi/2)*n*k)
eq_str += " + ".join(elems)
eq_str += " = " + str(res)
print (eq_str)
print("d) ==================================")
E = numpy.zeros(2)
O = numpy.zeros(2)
for k in range(2):
eq_str = "\\underline{E}[%d] = \\underline{x}[0] + \\underline{w}_2^{%d} \\cdot \\underline{x}[2]" % (k, k)
E[k] = x[0] + numpy.exp(-1j*(numpy.pi)*k) * x[2]
eq_str += " = " + str(E[k])
print (eq_str)
eq_str = "\\underline{O}[%d] = \\underline{x}[1] + \\underline{w}_2^{%d} \\cdot \\underline{x}[3]" % (k, k)
O[k] = x[1] + numpy.exp(-1j*(numpy.pi)*k) * x[3]
eq_str += " = " + str(O[k])
print (eq_str)
for k in range(4):
eq_str = "\\underline{X}[%d] = \\underline{E}[%d] + \\underline{w}_2^{%d} \\cdot \\underline{O}[%d]" % (k, (k%2), k, (k%2))
res = E[k%2] + numpy.exp(-1j*(numpy.pi/2)*k) * O[k%2]
eq_str += " = " + str(res)
print (eq_str)
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