- 数据案例实现
测试数据采用x=np.linspace(0,1,1400)，a=7*np.sin(2*np.pi*200*x) + 5*np.sin(2*np.pi*400*x)+3*np.sin(2*np.pi*600*x)生成的。
import numpy as np
# a = np.array([1,2,3])
x=np.linspace(0,1,1400)
a=7*np.sin(2*np.pi*200*x) + 5*np.sin(2*np.pi*400*x)+3*np.sin(2*np.pi*600*x)
N=a.shape[0]
temps=[]
for k in range(N):
temp=0
for n in range(N):
wn=complex(np.cos(2.0*k*np.pi*(n/N)),-(np.sin(2.0*k*np.pi*(n/N))))
temp+=a[n]*wn
temps.append(temp)
print(temps[0:5])
输出：
output: [(-4.217055953999462e-12+0j), (9.66210986046634e-05-0.043057556148230036j), (0.00038650807000099153-0.08611995903966796j), (0.0008697320363069723-0.12919205775395143j), (0.0015464115722406502-0.17227870600313114j)]
其实际过程就是根据下面的公式进行变换：
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X(k)=sum_{n=0}^{N-1}{x(n)cos(2pi kfrac{n}{N})-jx(n)sin(2pi kfrac{n}{N})}
X(k)=n=0∑N−1x(n)cos(2πkNn)−jx(n)sin(2πkNn)
