Time-Varying Pole-Radius IIR Multi-Notch Filters with Improved Performance

In signal processing applications, it is often required to have multi-notch filters (MNFs) which simultaneously possess an excellent quality factor, ‘Q’, and a brief transient response. Though, the duration of transient response can be improved by decreasing ‘Q’ which, however, also degrades the quality of the filter. Due to their contradictory nature, dealing with ‘Q’ and transient response becomes a difficult task. This paper is a sincere attempt to address this problem for MNFs by exploring time-varying pole-radius infinite impulse response MNF designs employing a hyperbolic tangent sigmoid (HTS) function-based pole-radius variation. Two-notch and three-notch filters, based on HTS function, are designed, analyzed for stability and tested for transient suppression, selectivity and noise removal. Experimental validations supported by simulations on sinusoids and ECG signals are performed in the LabVIEW\(^{\mathrm{TM}}\) environment and have been presented as complete performance assessment. In contrast to the recently reported and traditional MNF designs, significant performance enhancements were recorded for the proposed designs. Therefore, based on the presented investigations, it is concluded that the proposed MNFs are efficient designs for removing harmonics from sinusoids and ECG signals.