From 4fd4422b52f6377a82696ea67da9beb13d93e581 Mon Sep 17 00:00:00 2001
From: Nicolas Tobler <nicolas.tobler@ost.ch>
Date: Sun, 15 May 2022 23:15:36 +0200
Subject: draft

---
 buch/papers/ellfilter/python/chebychef.py | 65 +++++++++++++++++++++++++++++++
 1 file changed, 65 insertions(+)
 create mode 100644 buch/papers/ellfilter/python/chebychef.py

(limited to 'buch/papers/ellfilter/python/chebychef.py')

diff --git a/buch/papers/ellfilter/python/chebychef.py b/buch/papers/ellfilter/python/chebychef.py
new file mode 100644
index 0000000..a278989
--- /dev/null
+++ b/buch/papers/ellfilter/python/chebychef.py
@@ -0,0 +1,65 @@
+# %%
+
+import matplotlib.pyplot as plt
+import scipy.signal
+import numpy as np
+
+
+order = 5
+passband_ripple_db = 1
+omega_c = 1000
+
+a, b = scipy.signal.cheby1(
+    order,
+    passband_ripple_db,
+    omega_c,
+    btype='low',
+    analog=True,
+    output='ba',
+    fs=None,
+)
+
+w, mag, phase = scipy.signal.bode((a, b), w=np.linspace(0,2000,256))
+f, axs = plt.subplots(2,1, sharex=True)
+axs[0].plot(w, 10**(mag/20))
+axs[0].set_ylabel("$|H(\omega)| /$ db")
+axs[0].grid(True, "both")
+axs[1].plot(w, phase)
+axs[1].set_ylabel(r"$arg H (\omega) / $ deg")
+axs[1].grid(True, "both")
+axs[1].set_xlim([0, 2000])
+axs[1].set_xlabel("$\omega$")
+plt.show()
+
+
+# %% Cheychev filter F_N plot
+
+w = np.linspace(-1.1,1.1, 1000)
+plt.figure(figsize=(5.5,2))
+for N in [3,6,11]:
+    # F_N = np.cos(N * np.arccos(w))
+    F_N = scipy.special.eval_chebyt(N, w)
+    plt.plot(w, F_N, label=f"$N={N}$")
+plt.xlim([-1.2,1.2])
+plt.ylim([-2,2])
+plt.grid()
+plt.xlabel("$w$")
+plt.ylabel("$C_N(w)$")
+plt.legend()
+plt.savefig("F_N_chebychev2.pdf")
+plt.show()
+
+# %% Build Chebychev polynomials
+
+N = 11
+
+zeros = (np.arange(N)+0.5) * np.pi
+zeros = np.cos(zeros/N)
+
+x = np.linspace(-1.2,1.2,1000)
+y = np.prod(x[:, None] - zeros[None, :], axis=-1)*2**(N-1)
+
+plt.plot(x, y)
+plt.ylim([-1,1])
+plt.grid()
+plt.show()
-- 
cgit v1.2.1


From f4e1f6e84837c77dd49e6ec055efb1b110f7d573 Mon Sep 17 00:00:00 2001
From: Nicolas Tobler <nicolas.tobler@ost.ch>
Date: Mon, 30 May 2022 00:05:03 +0200
Subject: Added content, presentation

---
 buch/papers/ellfilter/python/chebychef.py | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

(limited to 'buch/papers/ellfilter/python/chebychef.py')

diff --git a/buch/papers/ellfilter/python/chebychef.py b/buch/papers/ellfilter/python/chebychef.py
index a278989..254ad4b 100644
--- a/buch/papers/ellfilter/python/chebychef.py
+++ b/buch/papers/ellfilter/python/chebychef.py
@@ -35,7 +35,7 @@ plt.show()
 # %% Cheychev filter F_N plot
 
 w = np.linspace(-1.1,1.1, 1000)
-plt.figure(figsize=(5.5,2))
+plt.figure(figsize=(5.5,2.5))
 for N in [3,6,11]:
     # F_N = np.cos(N * np.arccos(w))
     F_N = scipy.special.eval_chebyt(N, w)
@@ -44,9 +44,10 @@ plt.xlim([-1.2,1.2])
 plt.ylim([-2,2])
 plt.grid()
 plt.xlabel("$w$")
-plt.ylabel("$C_N(w)$")
+plt.ylabel("$T_N(w)$")
 plt.legend()
-plt.savefig("F_N_chebychev2.pdf")
+plt.tight_layout()
+plt.savefig("F_N_chebychev2.pgf")
 plt.show()
 
 # %% Build Chebychev polynomials
-- 
cgit v1.2.1