From 711fb9f60698bba1d4f7570d34e8cf3fa9a87207 Mon Sep 17 00:00:00 2001 From: Philipp Le Date: Mon, 6 Jul 2020 02:51:38 +0200 Subject: Solution of Exercise 6 --- exercise06/helpers/ex_6_1.py | 69 ++++++++++++++++++++++++++++++++++++++ exercise06/helpers/ex_6_2.py | 80 ++++++++++++++++++++++++++++++++++++++++++++ exercise06/helpers/ex_6_4.py | 75 +++++++++++++++++++++++++++++++++++++++++ 3 files changed, 224 insertions(+) create mode 100644 exercise06/helpers/ex_6_1.py create mode 100644 exercise06/helpers/ex_6_2.py create mode 100644 exercise06/helpers/ex_6_4.py (limited to 'exercise06/helpers') diff --git a/exercise06/helpers/ex_6_1.py b/exercise06/helpers/ex_6_1.py new file mode 100644 index 0000000..2ba7096 --- /dev/null +++ b/exercise06/helpers/ex_6_1.py @@ -0,0 +1,69 @@ +#!/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 +import scipy.signal +import matplotlib.pyplot as plt + +b = [2, -1] +a = [1, -0.5] + +w, h = scipy.signal.freqz(b, a, 8) + +print(scipy.signal.tf2zpk(b,a)) + +w = numpy.round(w*100)/100 +h = numpy.round(h*100)/100 + +print("$\\phi$ in \\si{rad} & $\\left|\\underline{H}\\left(e^{j\\phi}\\right)\\right|$ & $\\arg\\left(\\underline{H}\\left(e^{j\\phi}\\right)\\right)$ in \\si{rad} \\\\") +for n in range(len(w)): + print("$%g$ & $%g$ & $%g$ \\\\" % (w[n], abs(h[n]), (numpy.angle(h[n])))) + +print() + +elems = [] +for n in range(len(w)): + elems.append("(%g, %g)" % (w[n], abs(h[n]))) +print("coordinates {%s}" % " ".join(elems)) + +elems = [] +for n in range(len(w)): + elems.append("(%g, %g)" % (w[n], (numpy.angle(h[n])))) +print("coordinates {%s}" % " ".join(elems)) + +fig = plt.figure() +ax1 = fig.add_subplot(1, 1, 1) +ax1.plot(w, abs(h), 'b') +ax2 = ax1.twinx() +ax2.plot(w, (numpy.angle(h)), 'g') +plt.show() diff --git a/exercise06/helpers/ex_6_2.py b/exercise06/helpers/ex_6_2.py new file mode 100644 index 0000000..dcbfc7a --- /dev/null +++ b/exercise06/helpers/ex_6_2.py @@ -0,0 +1,80 @@ +#!/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 +import scipy.signal +import matplotlib.pyplot as plt + +b = [1, 0.5+1j, 2] +a = [1] + +w, h = scipy.signal.freqz(b, a, 16, whole=True) + +print(scipy.signal.tf2zpk(b,a)) + +w = 1e6*w/numpy.pi + +w = numpy.round(w*100)/100 +h = numpy.round(h*100)/100 + +print("$f$ in \\si{kHz} & $\\left|\\underline{H}\\left(e^{j 2\\pi f T_S}\\right)\\right|$ & $\\arg\\left(\\underline{H}\\left(e^{j 2\\pi f T_S}\\right)\\right)$ in \\si{rad} \\\\") +for n in range(len(w)): + if w[n] <= 1e6: + print("$%g$ & $%g$ & $%g$ \\\\" % (w[n]/1000, abs(h[n]), (numpy.angle(h[n])))) + else: + print("$%g$ & $%g$ & $%g$ \\\\" % (w[n]/1000-2e3, abs(h[n]), (numpy.angle(h[n])))) + +print() + +elems = [] +for n in range(len(w)): + if w[n] <= 1e6: + elems.append("(%g, %g)" % (w[n], abs(h[n]))) + else: + elems.append("(%g, %g)" % (w[n]-2e6, abs(h[n]))) +print("coordinates {%s}" % " ".join(elems)) + +elems = [] +for n in range(len(w)): + if w[n] <= 1e6: + elems.append("(%g, %g)" % (w[n], (numpy.angle(h[n])))) + else: + elems.append("(%g, %g)" % (w[n]-2e6, (numpy.angle(h[n])))) +print("coordinates {%s}" % " ".join(elems)) + +fig = plt.figure() +ax1 = fig.add_subplot(1, 1, 1) +ax1.plot(w, abs(h), 'b') +ax2 = ax1.twinx() +ax2.plot(w, (numpy.angle(h)), 'g') +plt.show() diff --git a/exercise06/helpers/ex_6_4.py b/exercise06/helpers/ex_6_4.py new file mode 100644 index 0000000..0e1bb9e --- /dev/null +++ b/exercise06/helpers/ex_6_4.py @@ -0,0 +1,75 @@ +#!/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) -- cgit v1.1