FIR Filters for Clap Detection

Core Concepts

Time vs Frequency
- Audio samples from your microphone are in the time domain.
- FIR coefficients are designed in the frequency domain.
- Key idea: convolution in time equals multiplication in frequency.
Impulse Response
- A FIR filter is a weighted sum of past samples.
- Changing the weights (coefficients) shapes which frequencies pass or get blocked.
Our Project
- Keep 2000–5000 Hz (claps), remove the rest.
- This is a band-pass filter specification.
- The coefficients you generate will enforce that specification.

Basically even though our source signal is in the time domain, and we designed our filter in the frequency domain since we end up doing a pointwise multiplication in the time domain it is equal to convolution in the frequency domain.

Apply to Your Codebase

Integrate FIR into your MCU clap-detection loop.

Set Up CMSIS FIR

Initialize FIR with your 50 coefficients and state buffer.
Match the block size to your DMA buffer.

  
  #define NUM_TAPS   50
  #define BLOCK_SIZE 4410

  static const float32_t firCoeffs[NUM_TAPS] = {
      // Paste your 50 coefficients here
  };

  static float32_t firState[NUM_TAPS + BLOCK_SIZE - 1];
  arm_fir_instance_f32 FIR;

  void FIR_Init(void) {
      arm_fir_init_f32(&FIR, NUM_TAPS, (float32_t *)firCoeffs, firState, BLOCK_SIZE);
  }

**Process a Block **

On DMA callback:
- Convert raw PCM samples to normalized floats.
- Pass them through the FIR filter.

    void FIR_Process(const float32_t *input, float32_t *output) {
      arm_fir_f32(&FIR, input, output, BLOCK_SIZE);
    }

**Detect Claps **
- Compute the energy of the filtered block.
- Compare to a threshold to trigger clap detection.
- Add a short refractory period (about 200 ms) to avoid multiple detections per clap.
```
    float32_t energy;
    arm_power_f32(outputBlock, BLOCK_SIZE, &energy);
```

Final Outcome

Clear understanding of FIR filters: time-domain implementation, frequency-domain design.
Ability to design and visualize your own filter coefficients.
Working CMSIS FIR integrated into your project for clap detection.

Sliding Window FIR filter for Audio - Designing the Filter

FPGAs Hmmm, Let’s learn by doing.