US 11,316,501 B1 · Resampling technique for arbitrary sampling rate conversion

Abstract

A resampling method based on window function for flexible sampling rate conversion in broadband frequency measurement devices is described. The resampling algorithm can satisfy the requirements of different sampling rates. The frequency responses of the filter in the resampling model based on the Farrow structure are analyzed, and the design criterion of the filter in resampling model is considered. A fractional delay filter design model based on window function method is described. A fractional delay filter matrix, which is expressed by polynomial form, is constructed. Then the expression related to subfilter coefficients is obtained and subfilter coefficients are solved for by the least square method.

A resampling method for flexible sampling rate conversion in a broadband frequency measurement device, the method comprising:

revealing frequency responses of a filter in a resampling model;
specifying design conditions of the filter;
completing the resampling model, wherein:
a fractional delay filter design model hp(n) is an impulse response of a fractional delay filter with a delay of p, and a group delay τ of an obtained fractional delay filter is τ+p, where τ is a group delay of an ideal-low pass filter;
the fractional delay filter design model hp(n) is expressed as:
hp(n)=hd(n−p)·w(n−p), 0≤n≤N−1
wherein hd(n) is an impulse response of the ideal low-pass digital filter;
hd(n−p) is the impulse response of the ideal low-pass digital filter shifted by a delay p, w(n) is a sequence of a window function of a length N;
fractional delay filter coefficients with different group delay responses are designed by taking multiple values as p being limited as follows:
p=−0.5+bδ −0.5≤p≤0.5,
wherein δ is an interval and b is an integer;
a filter coefficients matrix is established by substituting p into the expressed fractional delay filter design model hp(n) to obtain multiple fractional delay filter coefficients;
a fractional delay filter coefficients matrix is constructed as follows:
[
h
p
⁢
⁢
1
h
p
⁢
⁢
2
⋮
h
pk
]
=
[
h
p
⁢
⁢
1
⁡
(
0
)
h
p
⁢
⁢
1
⁡
(
1
)
…
h
p
⁢
⁢
1
⁡
(
N
-
1
)
h
p
⁢
⁢
2
⁡
(
0
)
h
p
⁢
⁢
2
⁡
(
1
)
…
h
p
⁢
⁢
2
⁡
(
N
-
1
)
⋮
h
pk
⁡
(
0
)
h
p
⁢
⁢
k
⁡
(
1
)
…
h
p
⁢
⁢
k
⁡
(
N
-
1
)
]
,
wherein hpk is the filter coefficients whose delay is pk·hpk=[hpk(0), hpk(1), . . . hpk(N−1)];
a polynomial form of the filter coefficients matrix is established, wherein the fractional delay filter coefficients matrix is expressed in polynomial form:
[
h
p
⁢
⁢
1
h
p
⁢
⁢
2
⋮
h
pk
]
=
[
p
1
p
1
2
…
p
1
I
p
2
p
2
2
…
p
2
I
⋮
⋮
⋮
p
k
p
k
2
…
p
k
I
]
⁡
[
c
1
⁢
1
c
12
…
c
1
⁢
N
c
2
⁢
1
c
2
⁢
⁢
2
…
c
1
⁢
N
⋮
⋮
⋮
c
I
⁢
⁢
1
c
I
⁢
⁢
2
…
c
IN
]
subfilter coefficients are solved by least square method in which the following
H=P⋅C
is used to solve C by least square method as follows:
C=(PTP)−1PTH
wherein, a solution provides values for the subfilter coefficients;
the values for the subfilter coefficients are used to complete the resampling model by substituting in:
y
⁡
(
k
⁢
T
r
)
=
∑
m
=
-
∞
∞
⁢
∑
i
=
0
I
⁢
x
⁡
(
m
⁢
T
s
)
⁢
c
⁡
(
[
k
⁢
T
r
-
m
⁢
T
s
T
r
]
,
i
)
⁢
(
m
⁢
T
s
T
r
-
[
m
⁢
T
s
T
r
]
-
0
.
5
)
i
=
∑
m
=
-
∞
∞
⁢
∑
i
=
0
I
⁢
x
⁡
(
m
⁢
T
s
)
⁢
c
⁡
(
[
k
⁢
T
r
-
m
⁢
T
s
T
r
]
,
i
)
⁢
(
p
m
)
i
,
wherein x(mTs) is input samples at sampling cycles Ts, and Tr is a resampling cycle, c(n,i) is the subfilter coefficient cn,i, and [*] indicates the largest integer not exceeding (*);
wherein pm is associated with m, and
y
⁡
(
k
⁢
T
r
)
=
∑
m
=
-
∞
∞
⁢
∑
i
=
0
I
⁢
x
^
i
⁡
(
m
⁢
T
s
)
⁢
c
⁡
(
[
k
⁢
T
r
-
m
⁢
T
s
T
r
]
,
i
)
is implemented by the Transposed Farrow structure;
where {circumflex over (x)}i(mTs) is a representation of a sum of x(mTs) and pmi;
and
using the completed resampling model in the broadband frequency measurement device to achieve a predetermined sampling rate conversion and provide conditions for measuring different component signals.

397 more elements

Resampling technique for arbitrary sampling rate conversion

Life of this patent

Resampling technique for arbitrary sampling rate conversion

Life of this patent

Abstract

Claims1