Image Processing Reference
In-Depth Information
Fig. 13. Amplitude Response of Low-Pass Lynn's Filter for α=5
4.1.2 High pass filters
Like a low-pass Lynn's filters, there are high-pass Lynn's filters which are described in (Ahlstrom
& Tompkins, 1985) and applied to ECG signal processing on (Pan & Tompkins, 1985; Hamilton &
Tompkins, 1986). These filters are designed using an all-pass filter and resting over it a low-pass
filter, and the result is a high-pass filter (Vidal & Pavesi, 2004). However for an effective design,
low-pass filter and all-pass filter must be in phase (Smith, 1999).
The High-Pass Lynn's filter starts using the following low-pass filter transfer equation:
1
z
(4)
Hz
()
1
1
z
Amplitude and phase responses are got by:
j

1
e
1cos

jsen

H
()
j
1cos

jsen
1



2
2
sen
j sen
2
cos
2
2
2
2
2
sen
j sen
2
cos
2
2
2



sen
sen
j
cos
2
2
2
 
sen
sen
j
cos
2
2
2
(5)




sen
sen
j
cos
sen
j
cos

2
2
2
2
2

   
 
sen
sen
j
cos
sen
j
cos
 
2
2
2
2
2
 

 



sen
sen
sen
cos
cos
j
sen
cos
sen
cos
2
2
2
2
2
2
2
2
2
sen
2

sen
cos
(

1)
jsen
(
1)
2
2
2
sen
2
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