簡介
波相乘(調變)廣泛應用在聲波和通訊領域。本文中，我們定義了 2 個不同頻率的波，用 python 計算和劃出波相乘後的波形。
定義 2 個不同頻率的波
wave1(波1), f1 = 1,000Hz, 在 1ms 區間內畫出波1
wave2(波2), f2 = 5,000Hz, 在 1ms 區間內畫出波2
wave(調變) = 波1 x 波2, 在 1ms 區間內畫出相乘波
導入函示庫 numpy 和 matplotlib
## Import library import numpy as np import matplotlib.pyplot as plt # library for plotting
定義畫圖函式
def drawGraph(xp, yp, titleLabel = 'Draw Graph', xLabel = 'X Axis', yLabel = 'y Axis'):
'''
Draw graph
Parameters:
xp : x axis data
yp : y axis data
'''
# Draw graph data
fig, ax = plt.subplots(nrows=1, ncols=1) # create figure handle
ax.plot(xp, yp)
ax.set_title(titleLabel) # window title
ax.set_xlabel(xLabel) # x-axis label
ax.set_ylabel(yLabel) # y-axis label
#fig.show()
Wave1(波1), f1 = 1kHz, 在 1ms 區間內劃出波1
樣品數 = F2(waves) ∗ 10(samples/wave) ∗ 0.001(s)
x 軸是一個時間陣列, [t0,t1,...,tn]
y 軸是時間 t 的正弦波函式頻率為 f1, [sin(2πf1t0),sin(2πf1t1),...,sin(2πf1tn)]
y=f(t)=sin(2πf1t)
f1 = 1000 f2 = 5000 nBlock = 10 # 10 points/wave dt = 0.001 # 1ms samples = f2 * nBlock * dt # samples in 5ms # generate t array on x axis xTime = np.arange(0, dt+(1/(f2*nBlock)), 1/(f2*nBlock)) # time base # Draw point p(xt,yt) @ 1kHz yValue1 = np.sin(2*np.pi*xTime*f1) # sine wave of f1 drawGraph(xTime, yValue1, "Draw wave at frequency 1kHz", "Time(s)", "Value")
Wave2(波2), f2 = 5,000Hz, 在 1ms 區間內劃出波2
樣品數 = F2(waves) ∗ 10(samples/wave) ∗ 0.001(s)
x 軸是一個時間陣列, [t0,t1,...,tn]
y 軸是時間 t 的正弦波函式頻率為 f2, [sin(2πf2t0),sin(2πf2t1),...,sin(2πf2tn)]
y=f(t)=sin(2πf2t)
# Draw point p(xt,yt) @ 5kHz yValue2 = np.sin(2*np.pi*xTime*f2) # sine wave of f2 drawGraph(xTime, yValue2, "Draw wave at frequency 5kHz", "Time(s)", "Value")
wave(調變) = wave1(波1) x wave2(波2) in 1ms
wave = wave1 x wave2
y 軸是時間 t 的相乘波函式, [sin(2πf1t0)∗sin(2πf2t0),sin(2πf1t1)∗sin(2πf2t1),...,sin(2πf1tn)∗sin(2πf2tn)]
y=f(t)=sin(2πf1t)∗sin(2πf2t)
# Draw modulation point p(xt,yt) yValue = yValue1 * yValue2 # modulation wave = wave1 x wave2 drawGraph(xTime, yValue, "Draw modulation wave", "Time(s)", "Value")
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