Wavelet transformation can be either continuous or discrete. However, the Discrete Wavelet Transformation (DWT) is more widely used, chiefly due to its computational efficiency and data compression capability. The following is a brief description of wavelet transformation theory.
The standard waveshape for the surge, according to references [27] and [28], can be written in terms of two exponentials,
(1) 
Where k, α, β are constants and t is time in microseconds. The typical surge waveform is show below:
Typical Surge Waveform
In power system studies, the surge waveform is usually defined in terms of wavefront time (Tf) and wavetail time (Tt). As seen in the figure above, wavetail time is the time when the current waveform reaches half of its maximum value (i.e. Tt = T2). Similarly the wavefront time (or rise time) is defined as 1.67(T0.9  T0.1) or 1.25(T0.9  T0.3). The factor k in (1) is selected such that the maximum voltage is unity.
The following values were generated using the MATLAB optimization algorithm (except for the 8/20 us waveform):
Waveform 
Reference 
Wavefront and Wavetail Basis 
Parameters of the Waveform 

a 
b 
k 

1.2/50 
IEC 6100045 IEC 600601 
T1 = 1.67T T2 = 50 
0.0145 
2.8353 
1.0328 
8/20 
IEC 6100045 IEC 600601 
T1 = 1.25T T2 = 50 
0.1732 
0.0866 
4 
1/50 
IEC 694691 
T1 = 1.25T T2 = 501 
0.014576 
2.5293 
1.0363 
250/2500 
T1 = 1.25T T2 = 2500 
0.00035239 
0.0080519 
1.2068 

250/1500 
T1 = 1.25T T2 = 1500 
0.00072065 
0.0065795 
1.4741 

10/700 
IEC 600601 
T1 = 1.67T T2 = 700 
0.0010222 
0.3063 
1.0227 
5/320 
IEC 600601 
T1 = 1.25T T2 = 320 
0.0022548 
0.51343 
1.0288 
Method 1: Using α and β values as in equation (1). The k factor is defined as:
(2) 
Where
(3) 
Method 2: Construction of the waveform based on wavefront and wavetail times. This is an approximate method. It is assumed that α << β and k ≈ 1. Then, it can be shown that, the fronttime (Tf, defined as 10% and 90% basis) is:
, 
(4) 
And:
(5) 
If defined as 30% and 90% basis:
(6) 
Similarly the wavetail time Tt is:
, 
(7) 
Once α and β are defined, the surge waveform is:
(8) 
EXAMPLE:
The following figure compares the approximate waveform using the above method and the accurate solution obtained using the MATLAB optimization algorithm for the 1.2/50 us surge waveform.
The CIGRÉ standard waveform is defined as follows.
For the current front:
(9) 
For the current tail:
(10) 
The constants are found in reference [29].