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### 1.1.1. 比特位反序输入、自然顺序输出
![4-point radix-2 DIT-FFT 比特位反序输入、自然顺序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-010-4PointRadix2DITFFTIRON.png!sign){width=400px}
![4-point radix-2 DIT-FFT 比特位反序输入、自然顺序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-010-4PointRadix2DITFFTIRON.png){width=400px}
<!-- more -->
### 1.1.2. 自然顺序输入、比特位反序输出
![4-point radix-2 DIT-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-020-4PointRadix2DITFFTINOR.png!sign){width=400px}
![4-point radix-2 DIT-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-020-4PointRadix2DITFFTINOR.png){width=400px}
## 1.2. 基-2 按频率抽取 FFT（4-point radix-2 DIF-FFT）
### 1.2.1. 比特位反序输入、自然顺序输出
![4-point radix-2 DIF-FFT 比特位反序输入、自然顺序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-030-4PointRadix2DIFFFTIRON.png!sign){width=400px}
![4-point radix-2 DIF-FFT 比特位反序输入、自然顺序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-030-4PointRadix2DIFFFTIRON.png){width=400px}
### 1.2.2. 自然顺序输入、比特位反序输出
![4-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-040-4PointRadix2DIFFFTINOR.png!sign){width=400px}
![4-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-040-4PointRadix2DIFFFTINOR.png){width=400px}
## 1.3. 分裂基按频率抽取 FFT（4-point split radix-2/4 DIF-FFT）
![4-point split radix-2/4 DIF-FFT](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-050-4PointSplitRadix24DIFFFT.png!sign){width=400px}
![4-point split radix-2/4 DIF-FFT](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-050-4PointSplitRadix24DIFFFT.png){width=400px}
## 1.4. 基-4 按频率抽取 FFT（4-point radix-4 DIF-FFT）
![4-point radix-4 DIF-FFT](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-060-4PointRadix4DIFFFT.png!sign){width=400px}
![4-point radix-4 DIF-FFT](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-060-4PointRadix4DIFFFT.png){width=400px}
# 2. 8 点 FFT
@@ -62,25 +62,25 @@ categories:
### 2.1.1. 比特位反序输入、自然顺序输出
![8-point radix-2 DIT-FFT 比特位反序输入、自然顺序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-070-8PointRadix2DITFFTIRON.png!sign){width=600px}
![8-point radix-2 DIT-FFT 比特位反序输入、自然顺序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-070-8PointRadix2DITFFTIRON.png){width=600px}
### 2.1.2. 自然顺序输入、比特位反序输出
![8-point radix-2 DIT-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-080-8PointRadix2DITFFTINOR.png!sign){width=600px}
![8-point radix-2 DIT-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-080-8PointRadix2DITFFTINOR.png){width=600px}
## 2.2. 基-2 按频率抽取 FFT（8-point radix-2 DIF-FFT）
### 2.2.1. 比特位反序输入、自然顺序输出
![8-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-090-8PointRadix2DIFFFTIRON.png!sign){width=600px}
![8-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-090-8PointRadix2DIFFFTIRON.png){width=600px}
### 2.2.2. 2自然顺序输入、比特位反序输出
![8-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-100-8PointRadix2DIFFFTINOR.png!sign){width=600px}
![8-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-100-8PointRadix2DIFFFTINOR.png){width=600px}
## 2.3. 分裂基按频率抽取 FFT（8-point split radix-2/4 DIF-FFT）
![8-point split radix-2/4 DIF-FFT](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-110-8PointSplitRadix24DIFFFT.png!sign){width=600px}
![8-point split radix-2/4 DIF-FFT](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-110-8PointSplitRadix24DIFFFT.png){width=600px}
# 3. 16 点 FFT
@@ -88,37 +88,37 @@ categories:
### 3.1.1. 比特位反序输入、自然顺序输出
![16-point radix-2 DIT-FFT 比特位反序输入、自然顺序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-120-16PointRadix2DITFFTIRON.png!sign){width=1000px}
![16-point radix-2 DIT-FFT 比特位反序输入、自然顺序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-120-16PointRadix2DITFFTIRON.png){width=1000px}
### 3.1.2. 自然顺序输入、比特位反序输出
![16-point radix-2 DIT-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-130-16PointRadix2DITFFTINOR.png!sign){width=1000px}
![16-point radix-2 DIT-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-130-16PointRadix2DITFFTINOR.png){width=1000px}
## 3.2. 基-2 按频率抽取 FFT（16-point radix-2 DIF-FFT）
### 3.2.1. 比特位反序输入、自然顺序输出
![16-point radix-2 DIF-FFT 比特位反序输入、自然顺序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-140-16PointRadix2DIFFFTIRON.png!sign){width=1000px}
![16-point radix-2 DIF-FFT 比特位反序输入、自然顺序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-140-16PointRadix2DIFFFTIRON.png){width=1000px}
### 3.2.2. 自然顺序输入、比特位反序输出
![16-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-150-16PointRadix2DIFFFTINOR.png!sign){width=1000px}
![16-point radix-2 DIF-FFT 自然顺序输入、比特位反序输出](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-150-16PointRadix2DIFFFTINOR.png){width=1000px}
## 3.3. 分裂基按时间抽取 FFT（16-point split radix-2/4 DIT-FFT）
![16-point split radix-2 DIT-FFT](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-160-16PointSplitRadix24DITFFT.png!sign){width=1000px}
![16-point split radix-2 DIT-FFT](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-160-16PointSplitRadix24DITFFT.png){width=1000px}
## 3.4. 分裂基按频率抽取 FFT（16-point split radix-2/4 DIF-FFT）
![16-point split radix-2 DIF-FFT](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-170-16PointSplitRadix24DIFFFT.png!sign){width=1000px}
![16-point split radix-2 DIF-FFT](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-170-16PointSplitRadix24DIFFFT.png){width=1000px}
## 3.5. 基-4 按频率抽取 FFT（16-point radix-4 DIF-FFT）
![16-point radix-4 DIF-FFT](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-180-16PointRadix4DITFFT.png!sign){width=1000px}
![16-point radix-4 DIF-FFT](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-180-16PointRadix4DITFFT.png){width=1000px}
可以定义如下基-4 DIF-FFT 简化蝶形来简化流图表示的复杂程度
![基-4 DIF-FFT 简化蝶形](https://josh-blog-1257563604.cos.ap-beijing.myqcloud.com/img/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-190-SimplifiedRadix4Butterfly.png!sign){width=800px}
![基-4 DIF-FFT 简化蝶形](../images/post/2023-04-15-josh-dsp-part-5/2023-04-15-josh-dsp-part-5-190-SimplifiedRadix4Butterfly.png){width=800px}
# 参考文献