Equalizer using infinitive impulse response filtering and associated method
View Patent ↗An equalizer for equalizing an input signal includes an infinitive impulse response (IIR) filtering portion for filtering the input signal to produce N filtered outputs; a gain-adjusting portion coupled to the IIR filtering portion with N gains for adjusting the N filtered outputs to produce N gained outputs, respectively; and an adder for summing the N gained outputs to generate an equalized output signal. N is an integer larger than 2.
1. An equalizer for equalizing an input signal, comprising:
an infinitive impulse response (IIR) filtering portion for filtering the input signal to produce N filtered outputs, wherein the IIR filtering portion includes N IIR filters for simultaneously filtering the input signal to produce the N filtered outputs, respectively, which have respective frequency response transfer functions SB 1 (f)˜SB N (f) fulfilling the following equation:
∑
n
=
1
N
SBn
(
f
)
=
∏
n
=
1
N
-
1
APn
(
f
)
where n is an integer no greater than N−1 and no less than 1 and AP n (f) are frequency response transfer functions of IIR all-pass filters fulfilling the following equation:
LP n ( f )+HP n ( f )=AP n ( f )
where LP n (f) are IIR low-pass filters, and HP n (f) are IIR high-pass filters;
a gain-adjusting portion coupled to the IIR filtering portion for adjusting the N filtered outputs with N gains to produce N gained outputs, respectively; and
an adder for summing the N gained outputs to generate an equalized output signal;
wherein N is an integer larger than 2, and when N gains are all set to a first level, an ideally flat frequency response is obtainable by the equalizer and the equalized output signal is an ideal equalized output signal.
2. The equalizer according to claim 1 wherein:
SB 1 (f) is generated using a series combination of at least one LP(f) and at least one AP(f);
SB N−1 (f) is generated using a series combination of at least one HP(f) and at least one AP(f); and
for each of 1<n<N−1, SB n (f) is generated using a series combination of at least one LP(f), at least one HP(f), and at least one AP(f).
3. The equalizer according to claim 2 , wherein:
the at least one LP(f) used to generate SB 1 (f) includes LP 1 (f) and LP 2 (f); and
the at least one HP(f) used to generate SB N−1 (f) includes HP N−1 (f) and HP N−2 (f).
4. The equalizer according to claim 1 wherein each of the IIR high-pass filter, IIR low-pass filter and IIR band-pass filter consists of (N−1) cascaded filtering units selected from a group consisting of LP n (f), HP n (f) and AP n (f).
5. The equalizer according to claim 1 wherein the IIR filtering portion includes a plurality of filtering units which are allocated to form a tree structure.
6. The equalizer according to claim 5 wherein the plurality of filtering units include at least one pair of complementary IIR high-pass and low-pass filters sharing the same input, wherein the pair of complementary IIR high-pass filter HPn(f) and IIR low-pass filter LPn(f) are implemented with lower-order IIR all-pass filter converters APna(f) and APnb(f) according to the following equations:
LP n ( f )=(AP na ( f )+AP nb ( f ))/2; and
HP n ( f )=(AP na ( f )−AP nb ( f ))/2.
7. The equalizer according to claim 5 wherein the tree structure includes N filtering paths for processing the input signal, and each of the N filtering paths include (N−1) cascaded filtering units selected from a group consisting of LP n (f), HP n (f) and AP n (f), where LP n (f) are IIR low-pass filters, HP n (f) are IIR high-pass filters, AP n (f) are IIR all-pass filters, and n is an integer no greater than N−1 and no less than 1.
8. The equalizer according to claim 1 wherein the IIR all-pass filters AP n (f) have a filter-order lower than that of the IIR low-pass filters LP n (f) and that of the IIR high-pass filters HP n (f) according to a MATLAB tool.
9. The equalizer according to claim 1 wherein the N IIR filters include a low-pass filter, which has the frequency response transfer functions SB 1 (f) equal to
∏
n
=
1
N
-
2
LPn
(
f
)
*
AP
N
-
1
(
f
)
.
10. The equalizer according to claim 1 wherein the N IIR filters include a high-pass filter, which has the frequency response transfer functions SB N (f) equal to
∏
n
=
2
N
-
1
HPn
(
f
)
*
AP
1
(
f
)
.
11. A method applied to an equalizer for equalizing an input signal applied to an N-band equalizer, comprising steps of:
receiving the input signal;
producing N filtered outputs by a plurality of infinitive-impulse-response (IIR) filters filtering the input signal in N bands, wherein the IIR filters includes N IIR filters for simultaneously filtering the input signal to produce the N filtered outputs, respectively, which have respective frequency response transfer functions SB 1 (f)˜SB N (f) fulfilling the following equation:
∑
n
=
2
N
SBn
(
f
)
=
∏
n
=
1
N
-
1
APn
(
f
)
where n is an integer no greater than N−1 and no less than 1 and AP n (f) are frequency response transfer functions of IIR all-pass filters fulfilling the following equation:
LP n ( f )+HP n ( f )=AP n ( f )
where LP n (f) are IIR low-pass filters, and HP n (f) are IIR high-pass filters;
providing N gains respectively to the N filtered outputs to generate N gained outputs; and
adding the N gained outputs into an equalized output signal;
wherein N is an integer larger than 2, and when N gains are all set to a first level, an ideally flat frequency response is obtainable by the equalizer and the equalized output signal is an ideal equalized output signal.
12. The method according to claim 11 wherein:
SB 1 (f) is generated using a series combination of at least one LP(f) and at least one AP(f);
SB N−1 (f) is generated using a series combination of at least one HP(f) and at least one AP(f); and
for each of 1<n<N−1, SB n (f) is generated using a series combination of at least one LP(f), at least one HP(f), and at least one AP(f).
13. The method according to claim 12 wherein:
the at least one LP(f) used to generate SB 1 (f) includes LP 1 (f) and LP 2 (f); and
the at least one HP(f) used to generate SB N−1 (f) includes HP N−1 (f) and HP N−2 (f).
14. The method according to claim 11 wherein the IIR all-pass filter transfer functions AP n (f) is of a first-order
3
and LP n (f) are second-order IIR low-pass filter transfer functions, and HP n (f) are second-order IIR high-pass filter transfer functions.
15. The method according to claim 14 wherein the filter transfer functions LP n (f), HP n (f) and AP n (f) are generated by way of a MATLAB tool.
16. The method according to claim 11 wherein the IIR filtering step is performed along N parallel filtering paths to produce the N filtered outputs, respectively, each of the N parallel filtering paths uses cascaded (N−1) filter transfer functions, and adjacent two of the N parallel filtering paths share a common filter transfer function.
17. The method according to claim 16 wherein the N parallel filtering paths form a tree structure of filter transfer functions.