I'm implementing a digital low-pass filter for real-time sensor data processing, but the output signal has significant delay and phase distortion. How can I minimize this while maintaining good frequency response?

To minimize delay and phase distortion in real-time signal processing, consider switching from an IIR filter like Butterworth to a linear-phase FIR filter, which has a constant group delay and no phase distortion. Here's a practical approach using Python with scipy:

• Design a linear-phase FIR filter: Use the scipy.signal.firwin function to design a low-pass filter. For example:

  import numpy as np
  
  from scipy.signal import firwin, lfilter
  
  N = 64  # Filter order, adjust based on your constraints
  
  cutoff = 5  # Cut-off frequency in Hz
  
  fs = 100  # Sampling frequency in Hz (adjust as per your system)
  
  taps = firwin(N, cutoff, fs=fs)

  This ensures linear phase, but note that FIR filters typically have higher latency than IIR filters for the same attenuation.
• Optimize for real-time processing: If latency is critical, use a lower-order filter or implement a moving average filter as a simple FIR option. Alternatively, consider using a Bessel filter (IIR) which has better phase linearity than Butterworth, though it may still have some delay.
• Check resource constraints: On a microcontroller, you might pre-compute filter coefficients and use efficient convolution algorithms. Refer to the scipy signal documentation for more details and examples.

For your accelerometer data, ensure the sampling frequency is sufficiently high to avoid aliasing, and test with simulated data to balance performance and latency.