有关过滤器的一般文档
最近我参与处理来自不同设备的传感器的数据。这些传感器由加速度计、陀螺仪、磁力计等组成。这一切都始于我想要隔离重力并偶然发现了这个链接（代码来自 android android_frameworks_base / services /sensorservice / SecondOrderLowPassFilter.cpp ）：
/*
* Copyright (C) 2010 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <stdint.h>
#include <sys/types.h>
#include <math.h>
#include <cutils/log.h>
#include "SecondOrderLowPassFilter.h"
// ---------------------------------------------------------------------------
namespace android {
// ---------------------------------------------------------------------------
SecondOrderLowPassFilter::SecondOrderLowPassFilter(float Q, float fc)
: iQ(1.0f / Q), fc(fc)
{
}
void SecondOrderLowPassFilter::setSamplingPeriod(float dT)
{
K = tanf(float(M_PI) * fc * dT);
iD = 1.0f / (K*K + K*iQ + 1);
a0 = K*K*iD;
a1 = 2.0f * a0;
b1 = 2.0f*(K*K - 1)*iD;
b2 = (K*K - K*iQ + 1)*iD;
}
// ---------------------------------------------------------------------------
BiquadFilter::BiquadFilter(const SecondOrderLowPassFilter& s)
: s(s)
{
}
float BiquadFilter::init(float x)
{
x1 = x2 = x;
y1 = y2 = x;
return x;
}
float BiquadFilter::operator()(float x)
{
float y = (x + x2)*s.a0 + x1*s.a1 - y1*s.b1 - y2*s.b2;
x2 = x1;
y2 = y1;
x1 = x;
y1 = y;
return y;
}
// ---------------------------------------------------------------------------
CascadedBiquadFilter::CascadedBiquadFilter(const SecondOrderLowPassFilter& s)
: mA(s), mB(s)
{
}
float CascadedBiquadFilter::init(float x)
{
mA.init(x);
mB.init(x);
return x;
}
float CascadedBiquadFilter::operator()(float x)
{
return mB(mA(x));
}
// ---------------------------------------------------------------------------
}; // namespace android
虽然该代码确实工作得很好，但我感觉我需要了解一些有关过滤器原理的基础知识。例如，也许我需要更改该过滤器中的某些内容。
我开始阅读维基百科（卡尔曼，低通，...），但我仍然觉得在开始修改别人的代码之前我需要更好地感受/接触这个理论。
所以我问你们，SO 用户，我可以阅读什么才能对过滤器有一个更全面的了解？任何链接、资源、文档都很好。
另外：我有工程师学位，但在研究信号处理时除了一些傅里叶变换（DFT）之外并没有完全研究滤波器。数学应该不是一个大问题。
我问这个问题是因为我看到有很多与过滤器相关的问题。
非常感谢，
尤利安
Lately I am involved in processing data from sensors from different devices. These sensors consist of accelerometers, gyroscopes, magnetometers etc. It all started when I wanted to isolate the gravitational force and stumbled upon this link (code from android android_frameworks_base / services / sensorservice / SecondOrderLowPassFilter.cpp ):
/*
* Copyright (C) 2010 The Android Open Source Project
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
#include <stdint.h>
#include <sys/types.h>
#include <math.h>
#include <cutils/log.h>
#include "SecondOrderLowPassFilter.h"
// ---------------------------------------------------------------------------
namespace android {
// ---------------------------------------------------------------------------
SecondOrderLowPassFilter::SecondOrderLowPassFilter(float Q, float fc)
: iQ(1.0f / Q), fc(fc)
{
}
void SecondOrderLowPassFilter::setSamplingPeriod(float dT)
{
K = tanf(float(M_PI) * fc * dT);
iD = 1.0f / (K*K + K*iQ + 1);
a0 = K*K*iD;
a1 = 2.0f * a0;
b1 = 2.0f*(K*K - 1)*iD;
b2 = (K*K - K*iQ + 1)*iD;
}
// ---------------------------------------------------------------------------
BiquadFilter::BiquadFilter(const SecondOrderLowPassFilter& s)
: s(s)
{
}
float BiquadFilter::init(float x)
{
x1 = x2 = x;
y1 = y2 = x;
return x;
}
float BiquadFilter::operator()(float x)
{
float y = (x + x2)*s.a0 + x1*s.a1 - y1*s.b1 - y2*s.b2;
x2 = x1;
y2 = y1;
x1 = x;
y1 = y;
return y;
}
// ---------------------------------------------------------------------------
CascadedBiquadFilter::CascadedBiquadFilter(const SecondOrderLowPassFilter& s)
: mA(s), mB(s)
{
}
float CascadedBiquadFilter::init(float x)
{
mA.init(x);
mB.init(x);
return x;
}
float CascadedBiquadFilter::operator()(float x)
{
return mB(mA(x));
}
// ---------------------------------------------------------------------------
}; // namespace android
While that code does work quite well I feel like I need to understand some basics about the filter philosophy in general. For example maybe I need to change something in that filter.
I started reading on Wikipedia (Kalman, Low-Pass, ...) but I still feel like I need to feel/touch this theory better before starting to modify someone else's code.
So I'm asking you, SO users, what can I read in order to have a more than general idea about filters? Any link, resource, documentation will be good.
Also: I have an engineer degree but didn't quite study filters except for some Fourier transformations (DFT) when studying signal processing. Math should not be a big issue.
I'm asking this question because I saw there are MANY questions related to filters.
Thanks a lot,
Iulian
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我在以下章节中的 dspguide 中找到了一个不太复杂的介绍
更多有趣的答案此处位于 dsp stackexchange。
PS：我将其设为 wiki，以便人们可以添加他们的资源（欢迎贡献）。
I found a less complicated introduction at dspguide in the following chapters:
More interesting answers here on dsp stackexchange.
PS: I made this a wiki so people can add their resources (contributions are welcome).