First Order High-pass and Low-pass filters for Sensors

[latonita]

What does this implement/fix?

This implements simple but very useful first-order High-pass and Low-pass filters.

High-pass - removing static offset and reduce low-freq noise. y[i] := α × (y[i−1] + x[i] − x[i−1])
Low-pass - reducing high-freq noise on signals. y[i] := y[i-1] + α * (x[i] - y[i-1])

Types of changes

• Bugfix (non-breaking change which fixes an issue)
• New feature (non-breaking change which adds functionality)
• Breaking change (fix or feature that would cause existing functionality to not work as expected)
• Other

Related issue or feature (if applicable): fixes esphome/feature-requests#2705

Pull request in esphome-docs with documentation (if applicable): esphome/esphome-docs#3875

Test Environment

• ESP32
• ESP32 IDF
• ESP8266
• RP2040
• BK72xx
• RTL87xx

Example entry for config.yaml:

# Example config.yaml

sensor:
  - platform: template
    id: sensor1
    name: Sensor1
    update_interval: 2s
    unit_of_measurement: s
    lambda: |- 
      const float abc[] =  {70, 65.9375, 66.1875, 67, 66, 66.25, 66.25, 66.3125, 66.1875, 66.1875, 66.6875, 66.375, 1, 66.3125, 66.375, 67.125, 78.8125, 66.875, 73.75, 68.625, 70, 73.5, 66.9375, 66.1875, 65.9375, 66, 66.125, 67.4375, 66, 66.375, 66.3125, 66.125, 66.1875, 67, 66.125, 66.375, 89, 66.5625, 66.25, 67.625, 66.125, 66.25, 1, 66.1875, 66.375, 66.375, 1, 66.1875, 67.125, 78.8125, 66.875, 73.75, 68.625, 70, 73.5, 66.9375, 66.1875, 65.9375, 66.375, 66.125, 67.4375, 66.25, 66.375, 66.3125, 66.125, 66.1875, 123, 123, 66.375, 89, 66.5625, 66.25, 67.625, 66.125, 66.25, 66.3125, 66.1875, 20, 66.375, 66.1875, 66.1875};
      static int num = 0;
      float ret = abc[num++];
      if (num >= sizeof(abc)/sizeof(float)) num = 0;
      return ret;
  - platform: template
    id: sensor1_high_pass
    name: Sensor High Pass
    update_interval: 2s
    lambda: return id(sensor1).state;
    unit_of_measurement: s
    filters:
      - high_pass: 0.75
  - platform: template
    id: sensor1_low_pass
    name: Sensor Low Pass
    update_interval: 2s
    lambda: return id(sensor1).state;
    unit_of_measurement: s
    filters:
      - low_pass: 0.25  
    

Checklist:

• The code change is tested and works locally.
• Tests have been added to verify that the new code works (under tests/ folder).

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated in esphome-docs.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 53.90%. Comparing base (4d8b5ed) to head (92c2373).
Report is 702 commits behind head on dev.

Additional details and impacted files

@@            Coverage Diff             @@
##              dev    #6695      +/-   ##
==========================================
+ Coverage   53.70%   53.90%   +0.19%     
==========================================
  Files          50       50              
  Lines        9408     9623     +215     
  Branches     1654     1698      +44     
==========================================
+ Hits         5053     5187     +134     
- Misses       4056     4112      +56     
- Partials      299      324      +25     

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[probot-esphome]

Hey there @esphome/core, mind taking a look at this pull request as it has been labeled with an integration (sensor) you are listed as a code owner for? Thanks!
_{^{(message by CodeOwnersMention)}}

[clydebarrow]

Had you considered generalising this to allow higher-order filters?

[latonita]

Had you considered generalising this to allow higher-order filters?

@clydebarrow When I made these simple 1st order HPF/LPF I actually thought it might be generalized and made configurable.
For example, there is a good library which I used many times (original is https://github.com/dimtass/DSP-Cpp-filters, a little bit more interesting fork is here https://github.com/crylent/DSP-Cpp-filters).
So potentially we can have a generic DSP Filter component, which can be configured - whether its a high pass or low pass , 1st/2nd order, and provide configuration params like cut-off frequencies, width and so on.
However, it might be hard for regular users to understand how to work with it and select proper parameters, especialy having in mind the fact that in esphome we work with quite low-frequency signals and might be tough to operate with 'frequency' concepts.

I might actually to come up with the updated generic dsp filter component so we can review. Its not the rocket science, question is usability. maybe several separate specific components might be easier to use... maybe not.

like 1st_hpf, 1st_lpf, 2nd_hpf, 1st_butterworth, etc.

Ideas, thoughts?