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n > 0 <br />
<br />
M<br />
<br />
h (n) = − (akh (n − k))<br />
k=1<br />
h (n) M <br />
h (n)<br />
hd (n) ak <br />
<br />
⎛<br />
∞<br />
<br />
2 M<br />
⎝ |hd (n) + (akhd (n − k)) |<br />
⎞<br />
⎠<br />
ɛp 2 =<br />
n=1<br />
∞ N<br />
<br />
<br />
⎛<br />
⎜<br />
⎝<br />
<br />
k=1<br />
hd (0) 0 ... 0<br />
hd (1) hd (0) ... 0<br />
<br />
<br />
<br />
hd (N − 1) hd (N − 2) ... hd (N − M)<br />
Hda ≈ −hd<br />
⎞ ⎛<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎠ ⎝<br />
a1<br />
a2<br />
<br />
aM<br />
Hd alp = −<br />
H −1<br />
Hd Hd H <br />
hd<br />
H (z) M th <br />
<br />
H (z) =<br />
M <br />
k=0 bkz−k 1 + M k=1 (akz−k )<br />
⎞<br />
⎛<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ≈ − ⎜<br />
⎟ ⎜<br />
⎠ ⎝<br />
M h (n) = − k=1 (akh<br />
<br />
(n − k)) + M k=0 (bkδ (n − k))<br />
⎧ M ⎨ − k=1<br />
=<br />
⎩<br />
(akh<br />
<br />
(n − k)) + bn 0 ≤ n ≤ M<br />
M − k=1 (akh<br />
<br />
(n − k)) n > M<br />
hd (1)<br />
hd (2)<br />
<br />
hd (N)<br />
n > M <br />
<br />
<br />
⎛<br />
hd (M)<br />
⎜ hd ⎜ (M + 1)<br />
⎜ ⎝<br />
hd (M − 1)<br />
hd (M)<br />
<br />
...<br />
...<br />
hd (1)<br />
hd (2)<br />
<br />
hd (N − 1) hd (N − 2) ... hd (N − M)<br />
aopt =<br />
ˆHda ≈ ˆ hd<br />
⎞ ⎛<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎟ ⎜<br />
⎠ ⎝<br />
a1<br />
a2<br />
<br />
aM<br />
<br />
H<br />
−1<br />
ˆHd Hd Hd Hˆ hd<br />
hd (N)<br />
⎞<br />
⎟<br />
⎠<br />
⎞ ⎛<br />
⎞<br />
hd (M + 1)<br />
⎟ ⎜<br />
⎟<br />
⎟ ⎜ hd ⎟ ⎜ (M + 2) ⎟<br />
⎟ ≈ ⎜<br />
⎟ ⎜ <br />
⎟<br />
⎠ ⎝<br />
⎠