1 files changed, 63 insertions, 0 deletions
diff --git a/exercise04/helpers/ex_4_2.py b/exercise04/helpers/ex_4_2.py
new file mode 100644
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+++ b/exercise04/helpers/ex_4_2.py
@@ -0,0 +1,63 @@
+#!/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
+
+def latex_table(ar):
+    return " & ".join(["$"+str(it)+"$" for it in ar])
+
+x = numpy.array([0.25, 1, -0.5, 0.5, -0.5, -1, -0.5, -0.75])
+print("$x[n]$ & "+latex_table(x))
+
+w = 0.54 - 0.46 * numpy.cos(2*numpy.pi*numpy.array([0,1,2])/2)
+w = numpy.concatenate([w, numpy.zeros(1)])
+print("$w[n]$ & "+latex_table(w))
+
+x_w = x[0:4]*w
+print("$x_w[n]$ & "+latex_table(x_w))
+
+Xft = numpy.fft.fft(x_w)
+Xft_abs = numpy.abs(Xft)
+Xft_phase = numpy.angle(Xft)
+print("$\\underline{X}_w[k]$ & "+latex_table(Xft))
+print("$|\\underline{X}_w[k]|$ & "+latex_table(Xft_abs))
+print("$\\arg\\left(\\underline{X}_w[k]\\right)$ & "+latex_table(Xft_phase))
+
+phi=2*numpy.pi*numpy.array([0,1,2,3])/4
+omega=phi/1e-3
+f=omega/(2*numpy.pi)
+print("$\\phi[k]$ & "+latex_table(phi))
+print("$\\omega[k]$ & "+latex_table(omega))
+print("$f[k]$ & "+latex_table(f))
+