A Method to Design Efficient Noise Shaping IIR Filters for Delta-Sigma Modulators using Modified Jacobian Chain Functions

An optimized Infinite Impulse Response (IIR) Noise Transfer Function (NTF) with reduced in-band quantization noise particularly for audio applications complying with the realizability and stability criteria required by DSM is realized. A modified Jacobian Chain function (mJCF) polynomial is proposed to shape the passband of a continuous time high pass filter, as it yields Almost Maximally Flat (AMF) passband characteristics but not maximally flat characteristics. The reduced flatness enhances the stopband attenuation of the analog high pass filter and once it is bilinear transformed it is reflected as reduced in-band quantization noise in the NTF. For a fourth-order IIR NTF with a signal bandwidth of 22.05[Formula: see text]KHz and OSR of 32, the proposed polynomial outperforms the existing methods with an SQNR of 62.9302[Formula: see text]dB and achieves a better SNR for a wide range of input amplitude. The SQNR for the psycho-acoustically optimal A-weighted NTF for the proposed polynomial is found to be 68.22[Formula: see text]dB.