wavelet hammerstein wiener model

Question

Francis 2011-7-26

F(x)=(x-r)PL + a s_1f(bs_1((x-r)Q-cs_1))+... as_nsf(bs_ns((x-r)Q-cs_ns))+...aw_1g(bw_1((x-r)Q-cw_1))+...+aw_nwg(bw_nw((x-r)Q-cw_nw))+d

f is a scaling function.

g is the wavelet function.

where by

f(x)=exp(-0.5xx’)
g(x)=(Nr-xx’)exp(-0.5xx’)

where Nr is the length of x (number of regressors).

I need some help from all to understand the definition of Nr. Can anyone define the Nr to help me understand better?

And

Let say x=[ 6 7 8 9 10 11];

If g(6), what is the value of Nr?

If g(7), what is the value of Nr?

If g(8), what is the value of Nr?

Thanks.

Answer 1

Emanuel 2012-8-10

编辑：Emanuel 2012-8-10

Nr is the number of regressors, ex: if you have x={u(k-1),u(k-2),y(k-1),y(k-2)}, then Nr=4.