of an object is done through the majority vote by its neighbors. That is, the object is
added to the class which is most common among its k closest neighbors (k could
generally be a small positive whole number). The object is assigned solely to the
nearest neighbor’s single classification if the k equals one [11].
2.8 Evaluation Measures
Compression Ratio compares the designed system performance in terms of reduction
in the amount of information to be classified compared to the conventional approach
where acquired ECG data points are transmitted towards classifier without performing
any features selection. If N r and P are respectively the count of data points to be
classified, for a given time length of L T -Sec., in the conventional and the devised
approach then the compression ration, R COMP , can be calculated as:
R COMP ¼
N r
P
:
Computational Complexity compares the designed system performance with the
fixed-rate counter equals in terms of the count of required standard operations like
additions, multiplications and divisions [12]. In conventional case, the denoised signal
is segmented by employing a rectangular window. It splits the incoming samples
sequence in L T -Sec. segments. Each segment is composed of N r samples. The processing cost of this process is negligible compared to operations like additions and
multiplications [12]. Each segment is further split into subbands by using the 3
rd level
Daubechies wavelet decomposition. It consists of half-band FIR high-pass and lowpass filters with a subsampling factor of two. Let Kg be the order of half-band filters
and same filters are employed at all levels of decomposition. It is well known that a Kg
order filter performs Kg additions and Kg multiplications [5]. Therefore, the computational complexity of this fixed rate wavelet decomposition process C FRÀWD can be
mathematically expressed by Eq. (4). This mathematical derivation is also clear from
Fig. 2.
C FRÀWD ¼ 3:5 Â Kg: N r
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
Additions
þ 3:5 Â Kg: N r
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
Multiplications
:
ð4Þ
For the case of designed solution xf n is firstly subsampled and then xd n is segmented by employing a rectangular window. Each segment is composed of N ¼
0:25 Â N r samples. If Kg is the order of half-band filters and same filters are employed
at all levels of decomposition then the computational complexity of this process C PÀWD
can be mathematically expressed by Eq. (5). If M ¼ 0:5 Â M r is the count of samples
processed by the denoising module then the total computational complexity for the
designed front-end processing chain can be expressed by using Eq. (10).
C PÀWD ¼ 0:875 Â Kg: N r
|fflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflffl ffl}
Additions
þ 0:875 Â Kg: N r
|fflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflffl ffl}
Multiplications
ð5Þ
Multirate ECG Processing and k-Nearest Neighbor Classifier
333
added to the class which is most common among its k closest neighbors (k could
generally be a small positive whole number). The object is assigned solely to the
nearest neighbor’s single classification if the k equals one [11].
2.8 Evaluation Measures
Compression Ratio compares the designed system performance in terms of reduction
in the amount of information to be classified compared to the conventional approach
where acquired ECG data points are transmitted towards classifier without performing
any features selection. If N r and P are respectively the count of data points to be
classified, for a given time length of L T -Sec., in the conventional and the devised
approach then the compression ration, R COMP , can be calculated as:
R COMP ¼
N r
P
:
Computational Complexity compares the designed system performance with the
fixed-rate counter equals in terms of the count of required standard operations like
additions, multiplications and divisions [12]. In conventional case, the denoised signal
is segmented by employing a rectangular window. It splits the incoming samples
sequence in L T -Sec. segments. Each segment is composed of N r samples. The processing cost of this process is negligible compared to operations like additions and
multiplications [12]. Each segment is further split into subbands by using the 3
rd level
Daubechies wavelet decomposition. It consists of half-band FIR high-pass and lowpass filters with a subsampling factor of two. Let Kg be the order of half-band filters
and same filters are employed at all levels of decomposition. It is well known that a Kg
order filter performs Kg additions and Kg multiplications [5]. Therefore, the computational complexity of this fixed rate wavelet decomposition process C FRÀWD can be
mathematically expressed by Eq. (4). This mathematical derivation is also clear from
Fig. 2.
C FRÀWD ¼ 3:5 Â Kg: N r
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
Additions
þ 3:5 Â Kg: N r
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
Multiplications
:
ð4Þ
For the case of designed solution xf n is firstly subsampled and then xd n is segmented by employing a rectangular window. Each segment is composed of N ¼
0:25 Â N r samples. If Kg is the order of half-band filters and same filters are employed
at all levels of decomposition then the computational complexity of this process C PÀWD
can be mathematically expressed by Eq. (5). If M ¼ 0:5 Â M r is the count of samples
processed by the denoising module then the total computational complexity for the
designed front-end processing chain can be expressed by using Eq. (10).
C PÀWD ¼ 0:875 Â Kg: N r
|fflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflffl ffl}
Additions
þ 0:875 Â Kg: N r
|fflfflfflfflfflfflfflfflfflffl ffl{zfflfflfflfflfflfflfflfflfflffl ffl}
Multiplications
ð5Þ
Multirate ECG Processing and k-Nearest Neighbor Classifier
333