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README.md

Chirp compression

Motivation, goal and review

I studied Signal Processing very hard in 2018, and I was especially interested in Chirp Compression technique used by radars. I thought it could have been used for transmitting some emergency event over ultrasonic. But it turned out that STM32L476RG and the MEMS mic used in this project cannot achive the goal because of their physical limitations.

Chirp compression technique

It is very simple:

c(n)=IFFT[FFT{a(n)} * FFT{b(n)}]

a(n): raw wave of received chirp signal with zero padding
    [ raw wave of N samples       | zero padding of N samples   ]

b(n): inverse reference chirp signal with zero padding
    [ matched filter of N samples | zero padding of N samples   ]

First half of c(n) is added to the second half of previous c(n):
    [ A                           | B                           ]
                                  [ A                           | B                           ]
                                                  |
                                                  V
                                                output

All the noise is not compressed, that is the point.

System components

Experiments (Dec 2, 2018)


Jupyter
Notebook                                                                          Chirp compression
 [PC]--[Mini speaker] ------ Chirp 15000Hz~18000Hz ------> [MEMS mic]--PDM-->[DFSDM][Arm Cortex-M4]
                                                                                          |
                                                                                         UART
                                                                                          V
                                                                                    [Oscilloscope GUI]

The screenshot above is captured by the oscilloscope GUI:

  • Chirp transmitted by a very very cheap mini speaker at $1.
  • Very small volume of the sound.
  • 2 meters distance between the transmitter and the receiver.
  • Background music (not background noise for me): Framenco guitar music by Paco de Lucia.

Parameters:

  • Clock: 80_000_000/25(Divider)/42(FOSR) = 76.2kHz
  • Frame length: 1024 samples, 13.4msec
  • Sweep range: 15000Hz ~ 18000Hz

Remaining issues (Nov 3, 2018)

  • It is still bad comression.
  • It requires to increase the sampling frequency.
  • FFT of 1024 samples per frame is too small, but I could not increase the size due to the limitaion of RFFT in CMSIS-DSP somehow...

So I give up this work for the time being...

Reference