Stability and Phase Response Analysis of Optimum Reduced-Order IIR Filter Designs for ECG R-Peak Detection

Table 1

Comparison of transfer functions for various filters used in ECG peak detection using the filter design.

Filter technique	Considered transfer functions
FIR 60-order LPF (low-pass filter)	h60 = −4.168e − 19 s^60 + 0.0004528 s^59 0.0008864 s^58 + 0.001208 s^57 − 0.00127 s^56 + 0.0009014 s^55 − 5.451e − 18 s^54 − 0.001371 s^53 + 0.002909 s^52 − 0.004086 s^51 + 0.004272 s^50 − 0.002955 s^49 + 3.791e − 17 s^48 + 0.004159 s^47 − 0.008473 s^46 + 0.01146 s^45 − 0.01158 s^44 + 0.00778 s^43 − 2.215e − 17 s^42 − 0.01052 s^41 + 0.02122 s^40 − 0.02865 s^39 + 0.02921 s^38 − 0.02005 s^37 + 2.962e − 17 s^36 + 0.02986 s^35 − 0.06616 s^34 + 0.1037 s^33 − 0.1364 s^32 + 0.1587 s^31 + 0.8331 s^30 + 0.1587 s^29 − 0.1364 s^28 + 0.1037 s^27 − 0.06616 s^26 + 0.02986 s^25 + 2.962e − 17 s^24 − 0.02005 s^23 + 0.02921 s^22 − 0.02862 s^21 + 0.02122 s^20 − 0.01052 s^19 − 2.215e − 17 s^18 + 0.00758 s^17 − 0.01158 s^16 + 0.01146 s^15 − 0.008473 s^14 + 0.004159 s^13 + 3.791e − 17 s^12 − 0.002955 s^11 + 0.004272 s^10 − 0.004086 s^9 + 0.002909 s^8 − 0.001371 s^7 − 5.451e − 18 s^6 + 0.0009014 s^5 − 0.00127 s^4 + 0.001208 s^3 − 0.0008864 s^2 + 0.0004528 s − 4.168e − 19 [28]
Pan–Tompkins 32-order LPF
BPF (band-pass filter)
16-order IIR filter
Optimum reduced-order IIR filter