Designing optimal prototype filters for maximally decimated Cosine Modulated filter banks with rapid convergence

An analytic design of a prototype filter for M-channel maximally decimated cosine-modulated Near Perfect Reconstruction (NPR) filter banks is proposed in this work. The prototype filter is created using the least-square (CLS) method with weighted constraints, which is one-dimensional and requires single-parameter optimization. Compared to existing approaches, this suggested method achieves rapid convergence by analytically determining the optimal step size, ensuring the 3 dB cutoff frequency at π/2 M. The simulation results for design examples outperform the techniques in the available literature in terms of amplitude and aliasing distortion, reaching distortion around 2.4489 × 10^-4 and 3.4907 × 10^-9, respectively. This optimization algorithm's usefulness is further demonstrated with the sub-band coding of ECG signals. Implementing optimal prototype filters has tangible real-world effects, especially in critical sectors like healthcare and communications, improving diagnostics accuracy, data transmission efficiency, and overall performance.