DSP Challenge: Loudspeaker Compensation Filter Design

This repository contains the implementation of a digital compensation filter designed to enhance loudspeaker audio quality. The project focuses on improving low-frequency extension and achieving a broadband linear phase response.

🎯 Objective

The goal is to design a Compensator that corrects the original system (Loudspeaker + Air + Microphone) so that the overall system response matches a specific Desired Model. Key requirements include:

• Correcting Non-linear Phase to Linear Phase.
• Enhancing magnitude response.
• Ensuring the filter remains Stable and Causal.

🛠️ Methodology

The project was implemented using Python with the following steps:

1. System Identification:
   • Used cross-correlation between input_white_noise.wav and output_white_noise.wav to identify a 128-sample bulk delay.
   • Aligned signals to estimate the transfer function ($H_{est}$) without the bulk delay to avoid non-causality in the inverse filter.
2. Compensator Design:
   • Applied Inverse Compensation: $H_{comp}(f) = \frac{H_{des}(f)}{H_{est}(f)}$.
   • Evaluated the system for Stability (Minimum Phase check) and High-frequency noise amplification.
3. Verification:
   • Performed Residual Spectrum Analysis to ensure low error in the audible range (1kHz+).
   • Conducted a Pre-Ringing Check to confirm the IRF peak aligns perfectly at 128 samples without non-causal oscillations.

📂 File Structure

• data/: Contains the given input/output wav files and the desired FRF (.npy).
• code.py: Main script for system identification and filter generation.

📊 Results

Design Method	Mean Squared Error (MSE)	Perceptual Evaluation of Audio Quality (PEAQ)
Inverse Compensation	1.66E-06	-2.2778

💻 Requirements

• Python 3.10
• NumPy
• SciPy
• Matplotlib
• Soundfile