优化FIR数字滤波器在降采样与插值中的实现
需积分: 15 151 浏览量
更新于2024-09-22
收藏 1.23MB PDF 举报
"该论文主要探讨了用于降采样和升采样的最优FIR数字滤波器实现方法，提出了多级降采样器和插值器的一般理论，并给出了一套优化设计多级降采样器的曲线和关系。论文指出，降采样和插值过程是互逆的，因此相同的优化设计曲线适用于这两个问题。此外，通过级联降采样和插值过程，可以得到高效实现的窄带FIR滤波器，其效率与递归椭圆滤波器设计相当。"
在信号处理领域，特别是在数字技术的应用日益增多的情况下，不同采样频率之间的转换需求变得越来越重要。例如，在通信、音频处理和图像处理中，降采样和升采样是常见的操作，用于调整信号的采样率以适应不同的系统需求或进行数据压缩。
FIR（有限脉冲响应）滤波器是一种线性相位的数字滤波器，由于其灵活性和可设计性，常用于信号滤波、降噪和信号整形等任务。在本论文中，作者关注的是如何优化设计FIR滤波器以实现高效的降采样和升采样。多级降采样器和插值器的设计理论为实现这一目标提供了基础，它们可以通过级联多个简单的滤波器来实现更复杂的滤波功能，从而提高计算效率。
论文中给出的优化设计曲线和关系为工程师提供了指导，帮助他们在设计过程中找到最佳的滤波器参数，以达到特定的采样率转换效果。同时，通过将降采样和插值结合，可以实现对窄带信号的高效处理。窄带FIR滤波器在保持较高效率的同时，能够精确地通过或阻塞特定频带内的信号，这对于频率选择性的滤波任务至关重要。
比较了这种通过级联降采样和插值获得的FIR滤波器实现与递归椭圆滤波器设计的效率，表明这两种方法在性能上是相当的。递归椭圆滤波器以其高选择性和优良的频率响应特性而闻名，但通常需要更多的计算资源。因此，本文提出的方法提供了一种替代方案，可以在保持高性能的同时，降低计算复杂度，对于资源受限的系统尤其具有价值。
这篇论文为信号处理领域的研究人员和工程师提供了一种新的工具，用于设计和实现高效且适应性强的FIR滤波器，以应对各种采样率转换的需求。通过优化的多级降采样和插值策略，不仅可以实现窄带滤波，而且在效率上与传统方法相比毫不逊色，对于实际应用具有重要的意义。
446
IEEE TRANSACTIONS ON ACOUSTICS, SPEECH, AND SIGNAL PROCESSING, OCTOBER
1975
put
w(n)
by the relation
u(n)=
h(m)w(n-
m)
N-
1
m=o
where
h(m),
(m
=
0,
1,
.,
N
-
1) are the filter coefficients
and
N
is the duration of the unit sample response of the filter.
From (1) it is seen that the computation of an output point
depends only upon past and present values of
w(n)
and not
upon past values of any internal filter variables. Thus the filter
computations need only be made once for every Mth output
point. Furthermore,
it
is known that
w(n)
is nonzero
only
for
every Lth input point. Thus only one multiplication and addi-
tion must be performed for every Lth input point. Therefore
the effective number of multiplications and additions is
N/(LM)
per output sample: instead of
N
as predicted by a simple ap-
plication of (1). For
this
and other reasons to be discussed
later, we will assume for the remainder of this paper that the
low-pass filter is
a
linear phase FIR design used in a direct
form implementation.
111.
OPTIMUM
DESIGN
OF
MULTISTAGE
DECIMATORS
FOR SAMPLING
RATE
REDUCTION
In the previous section a general one-stage technique for
changing the sampling rate of a signal by the factor LIM was
discussed. For large changes in sampling rate, however, it is
generally more efficient to reduce the sampling rate
with
a
series of decimation stages rather than making the entire rate
reduction with one stage. In
this
way the simpling rate
is
reduced gradually resulting
in
much less severe filtering require-
ments on the low-pass filters at each stage. Bellanger
et
al.
[SI
and Nelson
et
al.
[8]
also have implemented sampling rate re-
ductions using several decimation stages; however they re-
stricted their results by only using factors of
2
at each stage.
Shively
[9]
considered a more general approach with integer
decimation for a two-stage design similar to that of Fig. l(b).
He also suggested a procedure for optimizing the two-stage de-
sign by properly choosing the decimation ratios of each
of
the
stages. In
this
section we extend and generalize the work of
Shively using the more general decimation stage shown in
Fig. 3(b). Design curves and formulas are presented for imple-
menting optimum decimators for a wide range of parameters
and conditions.
The basic multistage process for sampling rate reduction
with
K
stages is illustrated in Fig. 4(a) and a frequency domain
interpretation of this process
is
given in Fig. 4(b). The initial
sampling rate is
fro
and the fmal sampling rate is
fui
with in-
termediate sampling frequencies designated as
frl
,
fr2,
.
.
*,
fr(K-1).
The sampling rate reduction achieved by each stage
of the decimation process is denoted as
Di,
i
=
1,2,
-
.,
K and
therefore the intermediate sampling frequencies are given by
2This
does not imply that greater efficiencies can be obtained by
si-
multaneously increasing
L
and
M
as
both
Nand the
sampling
rate in
(1)
are proportional
to
L.
LPF-
STAGE
K
FINPUT
SAMPLING
RATE
OUTPUT SAMPLING RATE
0
fn
fs
frK fr(K-1)
0
f,
f,,
f--
(b)
Fig.
4.
(a) Illustration of a K-stage decimator and (b) frequency re-
sponse interpretation of this process.
The overall sampling rate reduction achieved
by
this process is
denoted as
D
and is given as
D
=
fro
/frK
K
=
n
Di.
(3)
i=1
In Fig. 4(b)
I
X[exp
j(27rflfu,,)J
I
represents the magnitude
of
the spectrum of
x(n)
and
I
Y[exp
j(hflfrK)]
I
corresponds to
the magnitude
of
the spectrum
of
y(n).
From the sampling
theorem, we recognize that the highest frequency
in
y
(n)
is
f,
which
is
f,<-.
frK
2
Because of practical considerations in the design of the low-
pass filters used in the decimation process, this bandwidth can
never be fully realized and the usable portion of the base-
band will always be somewhat less than
f,.
We denote this
bandwidth as being froh zero to
fp
corresponding to the band
over which the magnitude response of the composite
of
the
low-pass filters remains flat within specified tolerance limits of
1
k
6,.
Also
because of practical considerations a inakimum
toierance must be allowed for the magnitude response of the
low-pass filters in the stopband and this will be denoted as
6,.
We can now focus on the design requirements for each stage.
We will permit the most general
form
for each stage as dis-
cussed in the previous section [see Fig. 3(b)]
.
This form for
stage
i
is illustrated in Fig. 5(a). Li corresponds to the sam-
pling rate increase and
Mi
corresponds to the sampling rate de-
crease for stage
i.
As
there
is
a net sampling rate reduction
this
implies,Mi
>
Li.
Then
剩余12页未读，继续阅读
2012-02-26 上传
2009-01-13 上传
2014-04-07 上传
2019-09-13 上传
2019-09-13 上传
2021-02-10 上传
2021-02-11 上传
2023-12-31 上传
2009-03-27 上传
usficiw
- 粉丝: 0
- 资源: 2
我的内容管理
展开
最新资源
- Aspose资源包：转PDF无水印学习工具
- Go语言控制台输入输出操作教程
- 红外遥控报警器原理及应用详解下载
- 控制卷筒纸侧面位置的先进装置技术解析
- 易语言加解密例程源码详解与实践
- SpringMVC客户管理系统：Hibernate与Bootstrap集成实践
- 深入理解JavaScript Set与WeakSet的使用
- 深入解析接收存储及发送装置的广播技术方法
- zyString模块1.0源码公开-易语言编程利器
- Android记分板UI设计：SimpleScoreboard的简洁与高效
- 量子网格列设置存储组件：开源解决方案
- 全面技术源码合集：CcVita Php Check v1.1
- 中军创易语言抢购软件：付款功能解析
- Python手动实现图像滤波教程
- MATLAB源代码实现基于DFT的量子传输分析
- 开源程序Hukoch.exe：简化食谱管理与导入功能
