Channel equalization with transmitter redundancy - Signal Processing and Optimization for Transceiver Systems - page 271

H 0

corresponds
to 13 dB

(a)

ω

2 / M 4 / M 2 π

0

π π

H

1

(b)

ω

2 π

2 π / M 4 π / M

0

0123 456 70

(c)

ω

2 π / M 4 π / M

0 2 π

1

h ( n )
k

(d)

n

− L

− L − M + 1

Figure 7.20 . Responses of the receiving filters in the DMT system. (a) Prototype
magnitude |H 0 ( e jω ) | , (b) magnitude of H 1 ( e jω ), (c) magnitudes of all filters with side-
lobes suppressed for clarity, and (d) impulse response magnitudes.

Because of the uniformly shifted nature of the filters, this system is called
the uniformDFT filter bank . All the receiving filters H k ( z ) are FIR with length
M , and their impulse responses h k ( n ) are nonzero only in

− L − M +1 ≤ n ≤− L.

All the impulse responses have unit magnitude in this region as shown in Fig.
7.20(d). With proper delays inserted, the filters can be adjusted to the causal
form