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数字滤波器是对数字信号进行滤波处理以得到期望的响应特性的离散时间系统。作为一种电子滤波器,数位滤波器与完全工作在模拟信号域的模拟滤波器不同。数位滤波器工作在数字信号域,它处理的对象是经由采样器件将模拟信号转换而得到的数字信号。
Digital filter is filtered to digital signal processing to achieve the desired response characteristics of discrete-time system. As a kind of electronic filters, digital filter and all work in analog signals domain simulation filter is different. Digital filter work in digital signal domain, it handles objects through sampling device is analog signal conversion for digital signals.
数位滤波器的工作方式与模拟滤波器也完全不同:后者完全依靠电阻、电容、晶体管等电子元件组成的物理网络实现滤波功能;而前者是通过数字运算器件对输入的数字信号进行运算和处理,从而实现设计要求的特性。
Digital filter way of working and simulation filter also completely different: the latter depend entirely on the resistor, capacitor, transistor, and other electronic components of physical network realization filter function; While the former is through digital computing devices for the entry of digital signal calculations and processing, thus realize the requirement of design characteristics.
数位滤波器理论上可以实现任何可以用数学算法表示的滤波效果。数位滤波器的两个主要限制条件是它们的速度和成本。数位滤波器不可能比滤波器内部的计算机的运算速度更快。但是随着集成电路成本的不断降低,数位滤波器变得越来越常见并且已经成为了如收音机、蜂窝电话、立体声接收机这样的日常用品的重要组成部分。
Digital filter theory can achieve any can use mathematical algorithm the filtering effect said. Digital filter's two main constraints is their speed and cost. Digital filter impossible internal computer than filter the faster. But as the integrated circuit costs continue to reduce, digital filter is becoming more and more common and has become such as radio, cell phones, stereo receivers such an important part of daily articles.
数位滤波器一般由寄存器、延时器、加法器和乘法器等基本数字电路实现。随着集成电路技术的发展,其性能不断提高而成本却不断降低,数位滤波器的应用领域也因此越来越广。按照数位滤波器的特性,它可以被分为线性与非线性、因果与非因果、无限脉冲响应(IIR)与有限脉冲响应(FIR)等等。其中,线性时不变的数字滤波器是最基本的类型;而由于数字系统可以对延时器加以利用,因此可以引入一定程度的非因果性,获得比传统的因果滤波器更灵活强大的特性;相对于IIR滤波器,FIR滤波器有着易于实现和系统绝对稳定的优势,因此得到广泛的应用;对于时变系统滤波器的研究则导致了以卡尔曼滤波为代表的自适应滤波理论
Digital filter generally by registers, delay device, on time-multiplier adder and basic digital circuit implementation. Along with the development of the integrated circuit technology, its with improving performance and cost is lower, digital filter application fields and therefore more and more widely. According to the characteristics of digital filter, it can be divided into linear and nonlinear, causal and the causal, infinite impulse response (IIR) and finite impulse response (FIR), etc. Among them, when the constant linear digital filter is the most basic type; And as a result of digital system can use them to delay device, so can introduce some degree of the causality, get more than traditional causal filter the characteristics of flexible strong; Relative to IIR filter, FIR filters have easy to realize and system is stable advantage, so widely applied; For time-varying system filter research is caused by kalman filter, as a representative of the adaptive filter theory
特性
characteristics
数字滤波器具有比模拟滤波器更高的精度,甚至能够实现后者在理论上也无法达到的性能。例如,对于数字滤波器来说很容易就能够做到一个 1000Hz 的低通滤波器允许 999Hz 信号通过并且完全阻止 1001Hz 的信号,模拟滤波器无法区分如此接近的信号。
Digital filters with higher precision than analog filter, even can realize the latter in theory cannot achieve performance. For example, it is very easy for digital filter is able to do a 1000Hz allowed the low-pass filter and completely prevent 999Hz signal through 1001Hz signal, the simulation filter can't distinguish so close to signal.
数字滤波器相比模拟滤波器有更高的信噪比。这主要是因为数字滤波器是以数字器件执行运算,从而避免了模拟电路中噪声(如电阻热噪声)的影响。数字滤波器中主要的噪声源是在数字系统之前的模拟电路引入的电路噪声以及在数字系统输入端的模数转换过程中产生的量化噪声。这些噪声在数字系统的运算中可能会被放大,因此在设计数字滤波器时需要采用合适的结构,以降低输入噪声对系统性能的影响。
Digital filters with a higher than analog filter SNR. This is mainly because digital filter based on digital devices perform operation so as to avoid the analog circuits noise (such as resistors thermal noise) influence. Digital filters the main noise source is in digital system introduced before the analog circuit noise and in digital system input to produce analog-to-digital conversion of quantization noise. These noise in digital system in the operations of may be amplified, so in design digital filter can be used to reduce the appropriate structure of input noise effect the performance of the system.
数字滤波器还具有模拟滤波器不能比拟的可靠性。组成模拟滤波器的电子元件的电路特性会随着时间、温度、电压的变化而漂移,而数字电路就没有这种问题。只要在数字电路的工作环境下,数字滤波器就能够稳定可靠的工作。
Digital filter also has not reliability simulation filter. Of analog filter circuits characteristic of electronic components with time, temperature, voltage change and drift, and digital circuit is no such problem. As long as the work environment in a digital circuit, digital filters can stable and reliable work.
由于奈奎斯特采样定理(en:Nyquist sampling theorem),数字滤波器的处理能力受到系统采样频率的限制。如果输入信号的频率分量包含超过滤波器1/2采样频率的分量时,数字滤波器因为数字系统的“混叠”而不能正常工作。如果超出1/2采样频率的频率分量不占主要地位,通常的解决办法是在模数转换电路之前放置一个低通滤波器(即抗混叠滤波器)将超过的高频成分滤除。否则就必须用模拟滤波器实现要求的功能。
Because Nyquist sampling theorem Nyquist sampling theorem (en: the processing, digital filters) sampling frequency by system of ability to limit. If the input signal frequency component contains more than filter 1/2 sampling frequency component, digital filters for digital systems "aliasing" and can't work normally. If exceed 1/2 sampling frequency frequency weight not predominant, usually solution is placed in frequency-field circuit before one low-pass filter (namely fight aliasing filter) will exceed filter the high frequency components. Otherwise we must realize with the simulated filter required functions.
类型
type
IIR滤波器与FIR滤波器参见:IIR滤波器、FIR滤波器、滤波器设计
IIR filter and FIR filters filter, IIR h.a.crosby FIR filters, filter design
线性移不变的数字滤波器包括无限长脉冲响应滤波器(IIR滤波器)和有限长脉冲响应滤波器(FIR滤波器)两种。这两种滤波器的系统函数可以统一以Z变换表示为:
Linear moving constant digital filter, including an infinite long impulse response filter (IIR filter) and limited long impulse response filter (FIR filter) two kinds. These two kinds of filter system function can be unified with Z transformation expressed as:
当时,M就是IIR滤波器的阶数,表示系统中反馈环的个数。由于反馈的存在,IIR滤波器的脉冲响应为无限长,因此得名。若A(z) = 1,则系统的脉冲响应的长度为N+1,故而被称作FIR滤波器。
At the time, M is the order number IIR filter, said the number of feedback loops in the system. Due to the existence of IIR filter, feedback the impulse response to an infinite long, therefore the name. If A (z) = 1, it is the length of the impulse response system for N + 1, so called FIR filter.
IIR滤波器的优点在于,其设计可以直接利用模拟滤波器设计的成果,因为模拟滤波器本身就是无限长冲激响应的。通常IIR滤波器设计的过程如下:首先根据滤波器参数要求设计对应的模拟滤波器(如巴特沃斯滤波器、切比雪夫滤波器等等),然后通过映射(如脉冲响应不变法、双线性映射等等)将模拟滤波器变换为数字滤波器,从而决定IIR滤波器的参数。IIR滤波器的重大缺点在于,由于存在反馈其稳定性不能得到保证。另外,反馈还使IIR滤波器的数字运算可能溢出。
The advantages of IIR filter is that its design can directly using simulation filter design results, because analog filter itself is an infinite long impulse response. Usually IIR filter design process are as follows: first of all, according to the requirements of the design parameters of the corresponding filters simulated filter (such as bart hepworth filter, chebyshev filters, etc), and then by mapping (such as pulse response don't strain and bilinear map, etc.) will transform into digital filter simulated filter, to decide IIR filter parameters. The major disadvantage is IIR filter, because it has feedback its stability cannot be guaranteed. In addition, feedback still make IIR filter number operations may overflow.
FIR滤波器最重要的优点就是由于不存在系统极点,FIR滤波器是绝对稳定的系统。FIR滤波器还确保了线性相位,这在信号处理中也非常重要。此外,由于不需要反馈,FIR滤波器的实现也比IIR滤波器简单。FIR滤波器的缺点在于它的性能不如同样阶数的IIR滤波器,不过由于数字计算硬件的飞速发展,这一点已经不成为问题。再加上引入计算机辅助设计,FIR滤波器的设计也得到极大的简化。基于上述原因,FIR滤波器比IIR滤波器的应用更广。
FIR filter is the most important advantages, because they do not exist system poles, FIR filters is absolutely stable system. FIR filter also ensures that the linear phase in signal processing, this also is very important. In addition, because do not need feedback, the realization of FIR filters than IIR filter simple. FIR filter's weakness is its performance as the same order number IIR filter, but due to the rapid development of digital computing hardware, this is not a problem. Plus introducing computer aided design, the design of FIR filters have also been great simplified. Based on the above reasons, FIR filters the application of IIR filter than more widely.
Digital filter is filtered to digital signal processing to achieve the desired response characteristics of discrete-time system. As a kind of electronic filters, digital filter and all work in analog signals domain simulation filter is different. Digital filter work in digital signal domain, it handles objects through sampling device is analog signal conversion for digital signals.
数位滤波器的工作方式与模拟滤波器也完全不同:后者完全依靠电阻、电容、晶体管等电子元件组成的物理网络实现滤波功能;而前者是通过数字运算器件对输入的数字信号进行运算和处理,从而实现设计要求的特性。
Digital filter way of working and simulation filter also completely different: the latter depend entirely on the resistor, capacitor, transistor, and other electronic components of physical network realization filter function; While the former is through digital computing devices for the entry of digital signal calculations and processing, thus realize the requirement of design characteristics.
数位滤波器理论上可以实现任何可以用数学算法表示的滤波效果。数位滤波器的两个主要限制条件是它们的速度和成本。数位滤波器不可能比滤波器内部的计算机的运算速度更快。但是随着集成电路成本的不断降低,数位滤波器变得越来越常见并且已经成为了如收音机、蜂窝电话、立体声接收机这样的日常用品的重要组成部分。
Digital filter theory can achieve any can use mathematical algorithm the filtering effect said. Digital filter's two main constraints is their speed and cost. Digital filter impossible internal computer than filter the faster. But as the integrated circuit costs continue to reduce, digital filter is becoming more and more common and has become such as radio, cell phones, stereo receivers such an important part of daily articles.
数位滤波器一般由寄存器、延时器、加法器和乘法器等基本数字电路实现。随着集成电路技术的发展,其性能不断提高而成本却不断降低,数位滤波器的应用领域也因此越来越广。按照数位滤波器的特性,它可以被分为线性与非线性、因果与非因果、无限脉冲响应(IIR)与有限脉冲响应(FIR)等等。其中,线性时不变的数字滤波器是最基本的类型;而由于数字系统可以对延时器加以利用,因此可以引入一定程度的非因果性,获得比传统的因果滤波器更灵活强大的特性;相对于IIR滤波器,FIR滤波器有着易于实现和系统绝对稳定的优势,因此得到广泛的应用;对于时变系统滤波器的研究则导致了以卡尔曼滤波为代表的自适应滤波理论
Digital filter generally by registers, delay device, on time-multiplier adder and basic digital circuit implementation. Along with the development of the integrated circuit technology, its with improving performance and cost is lower, digital filter application fields and therefore more and more widely. According to the characteristics of digital filter, it can be divided into linear and nonlinear, causal and the causal, infinite impulse response (IIR) and finite impulse response (FIR), etc. Among them, when the constant linear digital filter is the most basic type; And as a result of digital system can use them to delay device, so can introduce some degree of the causality, get more than traditional causal filter the characteristics of flexible strong; Relative to IIR filter, FIR filters have easy to realize and system is stable advantage, so widely applied; For time-varying system filter research is caused by kalman filter, as a representative of the adaptive filter theory
特性
characteristics
数字滤波器具有比模拟滤波器更高的精度,甚至能够实现后者在理论上也无法达到的性能。例如,对于数字滤波器来说很容易就能够做到一个 1000Hz 的低通滤波器允许 999Hz 信号通过并且完全阻止 1001Hz 的信号,模拟滤波器无法区分如此接近的信号。
Digital filters with higher precision than analog filter, even can realize the latter in theory cannot achieve performance. For example, it is very easy for digital filter is able to do a 1000Hz allowed the low-pass filter and completely prevent 999Hz signal through 1001Hz signal, the simulation filter can't distinguish so close to signal.
数字滤波器相比模拟滤波器有更高的信噪比。这主要是因为数字滤波器是以数字器件执行运算,从而避免了模拟电路中噪声(如电阻热噪声)的影响。数字滤波器中主要的噪声源是在数字系统之前的模拟电路引入的电路噪声以及在数字系统输入端的模数转换过程中产生的量化噪声。这些噪声在数字系统的运算中可能会被放大,因此在设计数字滤波器时需要采用合适的结构,以降低输入噪声对系统性能的影响。
Digital filters with a higher than analog filter SNR. This is mainly because digital filter based on digital devices perform operation so as to avoid the analog circuits noise (such as resistors thermal noise) influence. Digital filters the main noise source is in digital system introduced before the analog circuit noise and in digital system input to produce analog-to-digital conversion of quantization noise. These noise in digital system in the operations of may be amplified, so in design digital filter can be used to reduce the appropriate structure of input noise effect the performance of the system.
数字滤波器还具有模拟滤波器不能比拟的可靠性。组成模拟滤波器的电子元件的电路特性会随着时间、温度、电压的变化而漂移,而数字电路就没有这种问题。只要在数字电路的工作环境下,数字滤波器就能够稳定可靠的工作。
Digital filter also has not reliability simulation filter. Of analog filter circuits characteristic of electronic components with time, temperature, voltage change and drift, and digital circuit is no such problem. As long as the work environment in a digital circuit, digital filters can stable and reliable work.
由于奈奎斯特采样定理(en:Nyquist sampling theorem),数字滤波器的处理能力受到系统采样频率的限制。如果输入信号的频率分量包含超过滤波器1/2采样频率的分量时,数字滤波器因为数字系统的“混叠”而不能正常工作。如果超出1/2采样频率的频率分量不占主要地位,通常的解决办法是在模数转换电路之前放置一个低通滤波器(即抗混叠滤波器)将超过的高频成分滤除。否则就必须用模拟滤波器实现要求的功能。
Because Nyquist sampling theorem Nyquist sampling theorem (en: the processing, digital filters) sampling frequency by system of ability to limit. If the input signal frequency component contains more than filter 1/2 sampling frequency component, digital filters for digital systems "aliasing" and can't work normally. If exceed 1/2 sampling frequency frequency weight not predominant, usually solution is placed in frequency-field circuit before one low-pass filter (namely fight aliasing filter) will exceed filter the high frequency components. Otherwise we must realize with the simulated filter required functions.
类型
type
IIR滤波器与FIR滤波器参见:IIR滤波器、FIR滤波器、滤波器设计
IIR filter and FIR filters filter, IIR h.a.crosby FIR filters, filter design
线性移不变的数字滤波器包括无限长脉冲响应滤波器(IIR滤波器)和有限长脉冲响应滤波器(FIR滤波器)两种。这两种滤波器的系统函数可以统一以Z变换表示为:
Linear moving constant digital filter, including an infinite long impulse response filter (IIR filter) and limited long impulse response filter (FIR filter) two kinds. These two kinds of filter system function can be unified with Z transformation expressed as:
当时,M就是IIR滤波器的阶数,表示系统中反馈环的个数。由于反馈的存在,IIR滤波器的脉冲响应为无限长,因此得名。若A(z) = 1,则系统的脉冲响应的长度为N+1,故而被称作FIR滤波器。
At the time, M is the order number IIR filter, said the number of feedback loops in the system. Due to the existence of IIR filter, feedback the impulse response to an infinite long, therefore the name. If A (z) = 1, it is the length of the impulse response system for N + 1, so called FIR filter.
IIR滤波器的优点在于,其设计可以直接利用模拟滤波器设计的成果,因为模拟滤波器本身就是无限长冲激响应的。通常IIR滤波器设计的过程如下:首先根据滤波器参数要求设计对应的模拟滤波器(如巴特沃斯滤波器、切比雪夫滤波器等等),然后通过映射(如脉冲响应不变法、双线性映射等等)将模拟滤波器变换为数字滤波器,从而决定IIR滤波器的参数。IIR滤波器的重大缺点在于,由于存在反馈其稳定性不能得到保证。另外,反馈还使IIR滤波器的数字运算可能溢出。
The advantages of IIR filter is that its design can directly using simulation filter design results, because analog filter itself is an infinite long impulse response. Usually IIR filter design process are as follows: first of all, according to the requirements of the design parameters of the corresponding filters simulated filter (such as bart hepworth filter, chebyshev filters, etc), and then by mapping (such as pulse response don't strain and bilinear map, etc.) will transform into digital filter simulated filter, to decide IIR filter parameters. The major disadvantage is IIR filter, because it has feedback its stability cannot be guaranteed. In addition, feedback still make IIR filter number operations may overflow.
FIR滤波器最重要的优点就是由于不存在系统极点,FIR滤波器是绝对稳定的系统。FIR滤波器还确保了线性相位,这在信号处理中也非常重要。此外,由于不需要反馈,FIR滤波器的实现也比IIR滤波器简单。FIR滤波器的缺点在于它的性能不如同样阶数的IIR滤波器,不过由于数字计算硬件的飞速发展,这一点已经不成为问题。再加上引入计算机辅助设计,FIR滤波器的设计也得到极大的简化。基于上述原因,FIR滤波器比IIR滤波器的应用更广。
FIR filter is the most important advantages, because they do not exist system poles, FIR filters is absolutely stable system. FIR filter also ensures that the linear phase in signal processing, this also is very important. In addition, because do not need feedback, the realization of FIR filters than IIR filter simple. FIR filter's weakness is its performance as the same order number IIR filter, but due to the rapid development of digital computing hardware, this is not a problem. Plus introducing computer aided design, the design of FIR filters have also been great simplified. Based on the above reasons, FIR filters the application of IIR filter than more widely.
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