# fft

**Repository Path**: kishomoe/fft

## Basic Information

- **Project Name**: fft
- **Description**: fft by python and matlab
- **Primary Language**: Python
- **License**: MIT
- **Default Branch**: main
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 1
- **Forks**: 1
- **Created**: 2022-04-24
- **Last Updated**: 2023-09-26

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# FFT

## 傅里叶分解

### 1. Modeling

The magnetization directions of the PMs based on the Halbach linear motor are shown in the figure below,

![image-20210908200741305](https://cdn.jsdelivr.net/gh/kishomoe/blogpic@master/picgo/image-20210908200741305.png)

### 2. FFT by Maxwell

The magnetic density waveform of the air-gap under a pair of poles is obtained by Maxwell as  shown in the figure below,

![image-20210908201602626](https://cdn.jsdelivr.net/gh/kishomoe/blogpic@master/picgo/image-20210908201602626.png)

The Fourier decomposition is obtained by maxwell's FFT as shown in the figure below,

![image-20210908201806589](https://cdn.jsdelivr.net/gh/kishomoe/blogpic@master/picgo/image-20210908201806589.png)

### 3. FFT by python & Matplotlib (Recommended)

Export the air-gap magnetic density ($B_x$) to csv format and the FFT code in python is as follows,

```python
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from matplotlib.pylab import mpl
 
mpl.rcParams['font.sans-serif'] = ['SimSun']
mpl.rcParams['axes.unicode_minus']=False
#plt.rcParams['figure.dpi'] = 300
plt.rcParams['figure.constrained_layout.use'] = True

fig = plt.figure()
fixed_width_mm = 340
fixed_height_mm = 170
fixed_width_inch = fixed_width_mm / 25.4
fixed_height_inch = fixed_height_mm / 25.4
fig.set_size_inches(fixed_width_inch, fixed_height_inch)

ax1 = fig.add_subplot(121)
ax2 = fig.add_subplot(122)

data = pd.read_csv('Bx.csv')
x = data['Distance [mm]']
y = data['bx []']
ax1.plot(x,y,color='r',label='orgin',ls='--')

fft_y=np.fft.fft(y)
N=fft_y.shape[0]

orders=11
order=orders+1

fundamental=np.abs(fft_y[1])/N*2
harmonics=np.abs(fft_y[2:order])/N*2
thd=np.sqrt(np.sum(harmonics**2))/fundamental
thd_per = round(thd*100, 2)

for i in range(order):
	new_fft_y=np.zeros_like(fft_y)
	new_fft_y[i]=fft_y[i]
	ifft_y=np.fft.ifft(new_fft_y).real*2
	ax1.plot(x,ifft_y,label='order='+str(i))
	normalization_y=np.abs([fft_y[i]])/N*2
	ax2.bar(i,normalization_y)

ax1.legend()
ax1.set_title('各次谐波分解示意图')
ax1.set_xlabel('长度(mm)')
ax1.set_ylabel('各次谐波幅值大小')
ax1.set_xlim(x[0],x[len(x)-1])

ax2.set_title('各次谐波FFT分解柱状图 (THD='+str(thd_per)+'%)')
ax2.set_xlabel('谐波次数')
ax2.set_ylabel('各次谐波幅值大小')
ax2.set_xlim(0,order)
ax2.set_xticks(np.arange(0,order,1))

plt.show()

```

The FFT is as follows,

![Figure_1.jpeg](https://s2.loli.net/2023/09/26/y6nZUO17WlaIRH4.jpg)

### 4. FFT by Matlab (Not recommended)

Export the air-gap magnetic density ($B_x$) to csv format and the FFT code in matlab is as follows,

```matlab
clc
clear all;
format long;
Ns=1001;		%采样点
order=11;		%谐波数
filename='Bx.csv';		%导出的气隙磁密数据集
data=csvread(filename,1,0);     %从行偏移量 R1 和列偏移量 C1 开始读取文件中的数据
x=data(:,1);        %取第一列
y=data(:,2);        %取第二列
figure;
plot(x,y,'r');      %plot origional waveform
hold on;
grid on;
fft1=fft(y,Ns);
j=0;
amp_har=zeros(1,(order));
%%
for m=1:1:order
j=j+1;
fft1=fft(y,Ns);
fund_ele_front=fft1(m+1);
fund_ele_back=fft1(Ns+1-m);
amp_har(j)=(abs(fund_ele_front))/Ns*2;
fft1=0*fft1;
fft1(m+1)=fund_ele_front;
fft1(Ns+1-m)=fund_ele_back;
fft1=ifft(fft1,Ns);
fft1=real(fft1);
plot(x,fft1);
title('各次谐波分解示意图')
xlabel('长度(mm)')
ylabel('各次谐波幅值大小')
hold on;
end
%%
k=(1:1:order);
figure;
bar(k,amp_har);
title('各次谐波FFT分解柱状图')
xlabel('谐波次数')
ylabel('各次谐波幅值大小')
grid on;
peak_b=max(fft1);
rms_b=0.707*peak_b;
s=amp_har.^2;
THD = sqrt(sum(s(2:(order+1)/2)))/(amp_har(1));
THD_pct = 100*THD;
```

The decomposition of each harmonic is as follows,

![image-20210908202606806](https://cdn.jsdelivr.net/gh/kishomoe/blogpic@master/picgo/image-20210908202606806.png)

The histogram of FFT decomposition of each harmonic is as follows,

![image-20210908202728889](https://cdn.jsdelivr.net/gh/kishomoe/blogpic@master/picgo/image-20210908202728889.png)

### About Project

- Version：ANASYS Electronics Suite 2021 R2