10.1. FFT 性能测试
10.1.1. 概述
fft性能测试主要测试了DSP、ffa以及软件进行fft和ifft变换的性能，包含如下计算单元
DSP FFT-RADIX-2
DSP FFT-RADIX-4
DSP IFFT-RADIX-4
DSP IFFT-RADIX-2
DSP FFT-RADIX-2 Q31
CPU Cooley-Tukey算法
Q格式和float32互转
10.1.2. 程序设计
软件生成生成几个幅值和相位不同的正弦波并叠加生成一个波形，然后使用fft变换求出幅频特性数据，最后做ifft回复原始数据， 并比对ifft的数据和fft变换的数据是否相一致。几个正弦波如下所示:
幅值11，频率8
幅值19，频率17
幅值13，频率24
10.1.3. 硬件设置
无特殊设置
10.1.4. 性能优化
segger已经默认开启O3优化
hpm_math默认开启了对CPU Cooley-Tukey算法的计算优化，会增加空间占用
10.1.5. 运行现象
当工程正确运行后，串口终端会输出计算的名称，采样点数，以及幅频特性的数据，以及每一个单元的运行时间，并在最后输出PASS或者ERROR NUM.
串口输出如下所示：
dsp fft radix-4 Total samples: 64.
total times:5813 tick.
------------------------------------
DC component amplitude:10.000006.
Frequency:8.000000, Amplitude:11.000008.
Frequency:17.000000, Amplitude:18.999988.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
dsp ifft radix-4 Total samples: 64.
total times:5961 tick.
------------------------------------
dsp fft radix-4 Total samples: 256.
total times:29671 tick.
------------------------------------
DC component amplitude:9.999996.
Frequency:8.000000, Amplitude:11.000002.
Frequency:17.000000, Amplitude:18.999998.
Frequency:24.000000, Amplitude:23.000003.
------------------------------------
dsp ifft radix-4 Total samples: 256.
total times:30220 tick.
------------------------------------
dsp fft radix-4 Total samples: 1024.
total times:144992 tick.
------------------------------------
DC component amplitude:9.999997.
Frequency:8.000000, Amplitude:11.000000.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
dsp ifft radix-4 Total samples: 1024.
total times:147161 tick.
------------------------------------
**************************************
dsp fft radix-2 Total samples: 64.
total times:9280 tick.
------------------------------------
DC component amplitude:10.000006.
Frequency:8.000000, Amplitude:11.000008.
Frequency:17.000000, Amplitude:18.999988.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
dsp ifft radix-2 Total samples: 64.
total times:9544 tick.
------------------------------------
dsp fft radix-2 Total samples: 128.
total times:21119 tick.
------------------------------------
DC component amplitude:9.999998.
Frequency:8.000000, Amplitude:11.000001.
Frequency:17.000000, Amplitude:18.999996.
Frequency:24.000000, Amplitude:23.000003.
------------------------------------
dsp ifft radix-2 Total samples: 128.
total times:21575 tick.
------------------------------------
dsp fft radix-2 Total samples: 256.
total times:47643 tick.
------------------------------------
DC component amplitude:9.999996.
Frequency:8.000000, Amplitude:11.000002.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:23.000003.
------------------------------------
dsp ifft radix-2 Total samples: 256.
total times:48582 tick.
------------------------------------
dsp fft radix-2 Total samples: 512.
total times:106047 tick.
------------------------------------
DC component amplitude:9.999997.
Frequency:8.000000, Amplitude:11.000000.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:22.999998.
------------------------------------
dsp ifft radix-2 Total samples: 512.
total times:108005 tick.
------------------------------------
dsp fft radix-2 Total samples: 1024.
total times:234172 tick.
------------------------------------
DC component amplitude:9.999997.
Frequency:8.000000, Amplitude:11.000000.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
dsp ifft radix-2 Total samples: 1024.
total times:237975 tick.
------------------------------------
**************************************
dsp fft q31 radix-2 Total samples: 64.
total times:3782 tick.
------------------------------------
DC component amplitude:10.000006.
Frequency:8.000000, Amplitude:11.000009.
Frequency:17.000000, Amplitude:18.999988.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
dsp ifft q31 radix-2 Total samples: 64.
total times:4220 tick.
------------------------------------
dsp fft q31 radix-2 Total samples: 128.
total times:8252 tick.
------------------------------------
DC component amplitude:9.999998.
Frequency:8.000000, Amplitude:11.000002.
Frequency:17.000000, Amplitude:18.999996.
Frequency:24.000000, Amplitude:23.000003.
------------------------------------
dsp ifft q31 radix-2 Total samples: 128.
total times:9274 tick.
------------------------------------
dsp fft q31 radix-2 Total samples: 256.
total times:17995 tick.
------------------------------------
DC component amplitude:9.999995.
Frequency:8.000000, Amplitude:11.000002.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:23.000005.
------------------------------------
dsp ifft q31 radix-2 Total samples: 256.
total times:20619 tick.
------------------------------------
dsp fft q31 radix-2 Total samples: 512.
total times:39039 tick.
------------------------------------
DC component amplitude:9.999995.
Frequency:8.000000, Amplitude:11.000001.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
dsp ifft q31 radix-2 Total samples: 512.
total times:45407 tick.
------------------------------------
dsp fft q31 radix-2 Total samples: 1024.
total times:85195 tick.
------------------------------------
DC component amplitude:9.999995.
Frequency:8.000000, Amplitude:11.000002.
Frequency:17.000000, Amplitude:19.000003.
Frequency:24.000000, Amplitude:23.000001.
------------------------------------
dsp ifft q31 radix-2 Total samples: 1024.
total times:99603 tick.
------------------------------------
**************************************
Software fft cooley tukey Total samples: 64.
total times:14493 tick.
------------------------------------
DC component amplitude:10.000006.
Frequency:8.000000, Amplitude:11.000014.
Frequency:17.000000, Amplitude:18.999998.
Frequency:24.000000, Amplitude:23.000019.
------------------------------------
Software fft cooley tukey Total samples: 128.
total times:29009 tick.
------------------------------------
DC component amplitude:9.999998.
Frequency:8.000000, Amplitude:11.000004.
Frequency:17.000000, Amplitude:19.000003.
Frequency:24.000000, Amplitude:23.000015.
------------------------------------
Software fft cooley tukey Total samples: 256.
total times:61116 tick.
------------------------------------
DC component amplitude:9.999996.
Frequency:8.000000, Amplitude:11.000000.
Frequency:17.000000, Amplitude:18.999998.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
Software fft cooley tukey Total samples: 512.
total times:131520 tick.
------------------------------------
DC component amplitude:9.999997.
Frequency:8.000000, Amplitude:10.999999.
Frequency:17.000000, Amplitude:19.000001.
Frequency:24.000000, Amplitude:23.000000.
------------------------------------
Software fft cooley tukey Total samples: 1024.
total times:285106 tick.
------------------------------------
DC component amplitude:9.999997.
Frequency:8.000000, Amplitude:10.999997.
Frequency:17.000000, Amplitude:19.000000.
Frequency:24.000000, Amplitude:22.999996.
------------------------------------
**************************************
------------------------------------
convert data from float to q31, nums:128.
total times:3163 tick.
convert data from q31 to float, nums:128.
total times:1177 tick.
------------------------------------
------------------------------------
convert data from float to q31, nums:256.
total times:6225 tick.
convert data from q31 to float, nums:256.
total times:2325 tick.
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------------------------------------
convert data from float to q31, nums:512.
total times:12269 tick.
convert data from q31 to float, nums:512.
total times:4629 tick.
------------------------------------
------------------------------------
convert data from float to q31, nums:1024.
total times:24395 tick.
convert data from q31 to float, nums:1024.
total times:9237 tick.
------------------------------------
------------------------------------
convert data from float to q31, nums:2048.
total times:47949 tick.
convert data from q31 to float, nums:2048.
total times:18453 tick.
------------------------------------
PASS.
性能如下表所示：
采样点 |
64 |
128 |
256 |
512 |
1024 |
|---|---|---|---|---|---|
DSP radix-4（fpu） |
5900 |
N |
29869 |
N |
145366 |
DSP radix-2（fpu） |
9345 |
21220 |
47762 |
106211 |
234534 |
DSP radix-2（Q31） |
4378 |
9581 |
21177 |
46126 |
101331 |
FFAQ31 |
2729 |
4923 |
7769 |
18999 |
N |
CPU（Cooley-Tukey） |
14495 |
29171 |
61176 |
131084 |
283441 |
DSP radix-4（fpu） |
6016 |
N |
30384 |
N |
147651 |
DSP radix-2（fpu） |
9558 |
21632 |
48733 |
108296 |
238775 |
DSP radix-2（Q31） |
4641 |
10301 |
22980 |
50645 |
111359 |
FFAQ31 |
2687 |
4898 |
9152 |
18956 |
N |
Q31 to Float |
1208 |
2392 |
4757 |
9493 |
18965 |
Float to Q31 |
5517 |
10958 |
21970 |
44022 |
88055 |