ECG Signal Analysis - ECG Acquisition and Automated Remote Processing - page 21

The common performance parameters used for noise removal from the ECG are
given as

Mean Square Error ð MSE Þ¼ N P

N

½ x ð i Þ x ð i Þ 2
Signal to Noise Ratio ð SNR Þ¼ 10 log P x 2 ð i Þ

i ¼ 1

P n 2 ð i Þ
Percentage Root Mean Square Difference ð PRD Þ¼

ð 2 : 1 Þ

r

P ½ x ð i Þ x ð i Þ 2
P x 2 ð i Þ

where N is the total number of samples, x is the clean sample, n is the known noise,
and x is the denoised sample. Some authors have also estimated a few indirect
measures, viz., percentage noise retention ratio (PNR) [ 36 ], noise reduction factors
(NRF) [ 37 ], and SNR improvement, defined as

Percentage Noise Retention ð PNR Þ¼ P ds P cs
P cs

100

s

P ½ _ ð i Þ x ð i Þ 2
P ½ x ð i Þ x ð i Þ 2

Noise Reduction Factor ð NRF Þ¼

P i

x 2 ð i Þ
n 2 ð i Þ

SNR Improvement ð SNR imp Þ½ dB ¼ SNR i SNR O ¼ 10 log

P

x 2 ð i Þ
½ x ð i Þ x ð i Þ 2
ð 2 : 2 Þ
where P ¼ 10 log P j x ð i Þj 2 ; P cs denotes the power of the clean signal, and P DS
the same of the denoised signal, _ is the composite (noisy) signal with the clean
ECG, x(i) - x(i) is the residual noise. SNR i and SNR o denote the SNR at input and
output, respectively.

i

2.3.2 R-peak Detection Methods

The rhythm statements of ECG can be obtained from the R-peak locations. Due to
its characteristic shape, QRS complex is the most prominent part of an ECG wave.
For this reason, R-peak detection is taken up as the starting point of many ECG
analysis algorithms. Typically, the QRS wave frequency is in the range 10-25 Hz.
Ideally, a band-pass filter with upper and lower cutoff frequencies at these levels
applied to ECG signal would reveal the QRS. However, the wide variation of QRS
morphologies and the presence of noise makes it difficult to identify the QRS is
abnormal heart signals. Till date, numerous QRS detection algorithms have been
reported and successfully tested. However, no reported work has achieved absolute
accuracy for all diseases. Normally, QRS detection is indicated by R-peak loca-
tions (QS peak for positive R-wave absent). The measures of QRS detection by
software are described by the following parameters [ 38 ]: