Merge pull request #21 from Yuto-Yamamoto01/yyamamoto/chapter03

3章を追加

Author: taishi-n

yyamamoto/chapter03/q01.py

@@ -0,0 +1,10 @@
+import numpy as np
+
+def linear_conv(x, h):
+    N = x.size
+    z = np.zeros(2*N-1, dtype=complex)
+    k = np.arange(N)
+    h_addzeros = np.hstack([h, np.zeros(N)])
+    for n in range(2*N-1):
+        z[n] = np.sum(x[k] * h_addzeros[n-k])
+    return z

yyamamoto/chapter03/q02.py

@@ -0,0 +1,9 @@
+import numpy as np
+
+def circular_conv(x, h):
+    N = x.size
+    z = np.zeros(N, dtype=complex)
+    k = np.arange(N)
+    for n in range(N):
+        z[n] = np.sum(x[k] * h[(n-k) % N])
+    return z

yyamamoto/chapter03/q03.py

@@ -0,0 +1,10 @@
+import numpy as np
+
+def linear_conv2(x, h):
+    N = x.size
+    z = np.zeros(N, dtype=complex)
+    k = np.arange(N)
+    h_addzeros = np.hstack([h, np.zeros(N)])
+    for n in range(N):
+        z[n] = np.sum(x[k] * h_addzeros[n-k])
+    return z

yyamamoto/chapter03/q04.py

@@ -0,0 +1,25 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from q01 import linear_conv
+from q02 import circular_conv
+from q03 import linear_conv2
+
+x = np.array([4,3,2,1])
+y = np.array([1,0,-1,0])
+
+z1 = linear_conv(x, y)
+z2 = circular_conv(x, y)
+z3 = linear_conv2(x, y)
+
+fig = plt.figure()
+fig.add_subplot(1,3,1)
+plt.stem(z1)
+plt.title('q01')
+fig.add_subplot(1,3,2)
+plt.stem(z2)
+plt.title('q02')
+fig.add_subplot(1,3,3)
+plt.stem(z3)
+plt.title('q03')
+
+fig.savefig('q04_graph')

yyamamoto/chapter03/q04_graph.png

@@ -0,0 +1,12 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+x = np.zeros(14)
+x[8] = 1
+y = np.zeros(10)
+n = np.arange(4, 14)  # ファンシーインデックス
+y = 0.2 * (x[n] + x[n-1] + x[n-2] + x[n-3] + x[n-4])
+
+fig = plt.figure()
+plt.stem(y)
+fig.savefig('q05_graph')

yyamamoto/chapter03/q05.py

@@ -0,0 +1,19 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+def difference_equation(x, y, n):
+    if n == 0:
+        return 0.4 * x[n]
+    else:
+        return 0.3 * y[n-1] + 0.4 * x[n]
+
+x = np.zeros(10)
+x[5] = 1
+y = np.zeros(10)
+
+for n in range(10):
+    y[n] = difference_equation(x, y, n)
+
+fig = plt.figure()
+plt.stem(y)
+fig.savefig('q06_graph')

yyamamoto/chapter03/q05_graph.png

@@ -0,0 +1,25 @@
+import numpy as np
+
+def difference_equation(a, b, x):
+    def calc_y(n):
+        N = a.size
+        M = b.size
+        sum_a, sum_b = 0
+        if n == 0:
+            return np.sum(b[k_b] * x[n-k_b])
+        else:
+            for k_a in range(N):
+                sum_a += a[k_a] * calc_y(n-k_a)
+        for k_b in range(M):
+            if n-k_b < 0:
+                continue
+            else:
+                sum_b += b[k_b] * x[n-k_b]
+
+        return (-sum_a + sum_b) / a[0]
+    
+    y = np.zeros(x.size)
+    for n in range(x.size):
+        y[n] = calc_y(n)
+
+    return y

yyamamoto/chapter03/q06.py

@@ -0,0 +1,11 @@
+import numpy as np
+
+def calc_H(a, b, omega):
+    N = a.size
+    M = b.size
+    k_a = np.arange(1, N)
+    k_b = np.arange(M)
+    sum_a = np.sum(a[k_a] * np.exp(-1j*omega*k_a))
+    sum_b = np.sum(b[k_b] * np.exp(-1j*omega*k_b))
+    
+    return sum_b / (1 + sum_a)

yyamamoto/chapter03/q06_graph.png

@@ -0,0 +1,36 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from q08 import calc_H
+
+fs = 16000
+a = np.array([0, 0])
+b = np.full(3, 0.33)
+N = 10000
+
+# グラフ用の配列
+omegas = np.zeros(N)
+Hs = np.zeros(N, dtype=complex)
+for i in range(N):
+    f = i / N * fs
+    omega = 2 * np.pi * f / fs
+    omegas[i] = omega
+    Hs[i] = calc_H(a, b, omega)
+
+
+A = np.abs(Hs)
+P = np.rad2deg(np.angle(Hs))
+# グラフの中心を調整
+omegas = omegas - 3
+A = np.roll(A, 2000)
+P = np.roll(P, 2000)
+
+fig = plt.figure()
+fig.add_subplot(1, 2, 1)
+plt.stem(omegas, A)
+plt.title('Amplitude Characteristics')
+plt.xlabel('omega')
+fig.add_subplot(1, 2, 2)
+plt.stem(omegas, P)
+plt.title('Phase Characteristics')
+plt.xlabel('omega')
+fig.savefig('q09_graph')

yyamamoto/chapter03/q07.py

@@ -0,0 +1,37 @@
+import numpy as np
+import matplotlib.pyplot as plt
+from q08 import calc_H
+
+fs = 16000
+a = np.array([0, 0.3])
+b = np.array([0.4, 0])
+N = 4000
+
+# グラフ用の配列
+omegas = np.zeros(N)
+Hs = np.zeros(N, dtype=complex)
+for i in range(N):
+    f = i / N * fs
+    omega = 2 * np.pi * f / fs
+    omegas[i] = omega
+    Hs[i] = calc_H(a, b, omega)
+
+
+A = np.abs(Hs)
+P = np.rad2deg(np.angle(Hs))
+# グラフの中心を調整
+omegas = omegas - 3
+A = np.roll(A, 2000)
+P = np.roll(P, 2000)
+
+fig = plt.figure()
+fig.add_subplot(1, 2, 1)
+plt.stem(omegas, A)
+plt.title('Amplitude Characteristics')
+plt.xlabel('omega')
+fig.add_subplot(1, 2, 2)
+plt.stem(omegas, P)
+plt.title('Phase Characteristics')
+plt.xlabel('omega')
+fig.savefig('q10_graph')
+