Fast time-varying linear filters for suppression of baseline drift in electrocardiographic signals

Figures

• 

  Fig. 1. Main peaks (Q, R, S), waves (T, P), time intervals (PR, ST, RR) and segments (PQ, ST) in an ECG signal

• 

  Fig. 2. Example of a cascade of two identical Lynn’s LP filters. The amplitude frequency response G LP (H LP) for fs = 500 Hz, N = 500, and f c = fs/N = 1 Hz

• 

  Fig. 3. Graphical representation of the ratio of a couple of frequencies with transfers 1 and 0.9441 (−0.5 dB). The amplitude frequency response G HP (H HP) of the derived HP filter G HP(z) = z −τ − G LP(z) for fs = 500 Hz and f c ≈ 1 Hz

• 

  Fig. 4. Schematic representation of direct realization of the LP filter with minimum delay. Buffer A buffer of RR intervals (N max length), buffer B buffer of the input signal samples (2N max − 1 length), filter a filter with impulse response h(n) = {1, 2, 3,…, N,…, 3, 2, 1}, N RR number of sampling intervals, N RRmax number of samples of the longest expected RR interval, x(n) current input sample

• 

  Fig. 5. Schematic representation of realization of the LP filter by a cascade of two Lynn’s filters with knots inside QRS complexes. Buffer A a buffer of RR intervals (1.5N max length), buffer B a buffer of the input signal samples (1.5N max length), buffer C a buffer of the output signal from filter A (N max length), filter A a filter with impulse response 1 h(n) = {1, 1, 1,…, 1}, filter B a filter with impulse response 2 h(n) = {1, 1, 1,…, 1}, N 1 and N 2 odd numbers

• 

  Fig. 6. Schematic representation of RR interval interpolation for the LP filter realized by a cascade of two Lynn’s filters with knots between QRS complexes. Buffer A a buffer of RR intervals (2N max length)

• 

  Fig. 7. Histogram of errors after filtering with HP filter with attenuation −0.5 dB at cut-off frequency equal to heart frequency

• 

  Fig. 8. Input signal No. MA1_065_12 (lead V2) x(n) and output signal y(n) are visually identical in standard scale (upper panel) for the time-varying HP filter with −0.5 dB at f c = f ECG. Vertical detail of x(n) (light grey line) and y(n) (black line) (middle panel). Error signal e(n) = x(n) − y(n) (lower panel)

• 

  Fig. 9. Input signal No. MO1_023_12 (lead V3) (upper panel). Vertical detail of HP output for f c = 0.67 Hz (−0.5 dB) (light grey line) and time-varying HP output (−0.5 dB at f c = f ECG) with knots between QRS complexes (black line) (middle panel). Constant (0.67 Hz) and time-varied HP cut-off frequency (lower panel)