数字滤波器简介外文翻译

毕业设计(论文)外文资料翻译

系：电子信息系

专业：电子信息科学与技术

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外文出处：DSP Design Line,Techonline

Community, By Dr Iain A. Robin 附件：1.外文资料翻译译文；2.外文原文

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附件1：外文资料翻译译文

数字滤波器简介

模拟和数字滤波器

在信号处理过程中，滤波器的功能是去除信号中不需要的部分，如随机噪声，或者是提取信号中有用的部分，如包含在一定频率范围内的有用信号。

下面的框图表明了这一基本观点：

滤波器有两种主要的类型：模拟滤波器和数字滤波器。他们的物质组成和工作原理都是完全不同的。

模拟滤波器是由模拟电子电路组成的，如电阻、电感和运算放大器来产生所需的过滤效果。这样的滤波器电路被广泛应用在噪声的降低、视频信号的增强、音响系统中的图像均衡以及其他的多个领域中。目前已经有很完善的技术标准来满足一个已经提出要求的模拟滤波器电路的设计。在各个阶段，过滤信号就是一个有物理量参与并且直接被模拟的电压或电流量。

一个数字滤波器使用数字处理器来执行信号的采样值的数值计算。该处理器可以是通用计算机，如PC机（个人电脑）或者是一个专用的数字信号处理芯片。

模拟输入信号必须先使用一个ADC（模拟到数字转换器）采样和数字化。由此产生代表连续采样输入信号值的二进制数字，是转移到能够对它们进行数值处理器上。这些计算通常都涉及乘以由常量与输入信号相加的最终输入值。如果需要，这些现在代表采样的信号值滤波结果的计算，是由一个DAC（数字到模拟转换器）输出的信号转换回模拟形式。

请注意，在数字滤波中，信号是由一组数字序列，而不是电压或电流。

下图显示了一个这样系统的基本设置：

使用数字滤波器的优点

下面的列表给出了数字比模拟滤波器的一些主要优点：

1. 数字滤波器是可编程的，即它的操作决定与其存储在处理器内存中的程序。这就意味着数字滤波器在不影响电路（硬件）的前提下可以很容易的被改变。模拟滤波器只能通过重新设计滤波器硬件电路来改变；

2. 数字滤波器很容易设计，测试以及实行于通用计算机或工作站中；

3. 模拟滤波电路的特点（特别是那些含有不稳定性元件）受温度漂移的影响并且依赖于温度。而数字滤波器不受制于这些问题，因此对于温度和时间，它极其的稳定；

4. 跟模拟滤波器不同，数字过滤器可以准确地处理低频信号；随着技术的DSP的速度继续增加，数字过滤器被应用到高频信号的RF（射频）领域，这个在过去曾经是模拟技术专有的；

5. 数字滤波器是非常灵活，他们具有以不同的方式来处理信号能力，这其中包括一些典型数字滤波器能够适应信号按其特点变化而变化的能力；

6. DSP处理器可以快速处理一系列由并联或串联级的等复杂组合的过滤器，与等效的模拟电路相比较，这使得硬件要求相对简单、紧凑。

数字滤波器的操作

在本节中，我们将介绍数字滤波器运行的基本理论。这对于理解如何设计和使用数字滤波器是一个必不可少的。

假设被数字化的“原始”信号以电压波形的时间函数来描述：

V x(t)

其中t代表时间。

这个信号是以时间间隔h（采样间隔）进行采样的。其第i个信号的采样值是时间t = i*h的函数：

x i x( ih )

因此由ADC至处理器转换来的数字值就由下列的数字序列表示：

x0 , x1 , x2 , x3 , ...

信号的波形值与时间相对应：

t = 0, h, 2h, 3h, ...

并且当t = 0时，开始采样。

在时间t = nh（其中n是正整数），将值

x0 , x1 , x2 , x3 , ... x n

提供给处理器，并存储在内存中。

注意，采样值x n+1, x n+2等是不可用的，因为他们还不存在。

y0 , y1 , y2 , y3 , ... y n

通常来说，数值y n是由x序列计算得到的。由y序列得到x序列的算法决定于具体的数字滤波器。

在下一节，我们将看看一些简单数字滤波器的例子。

简单数字滤波器

下面例子说明了数字滤波器的基本特征：

1.单位增益滤波器：

每一个输出值y n与输入值x n 相等：

y0 x0

y1 x1

y2x2

...etc

这是一个经常用到的滤波器，滤波器对输入信号没有影响。

2. 简单的增益滤波器：

y n =Kx n

其中K是常数，

该滤波器只使输入信号有一个K倍的增益。

当K > 1时，滤波器是一个放大器，当0 < K < 1时，它是一个衰减器，当K < 0时，对应的是一个反相器。上例1只是其的一种特殊的情况。

3. 纯延迟滤波器：

y n =x n-1

在t = nh时的输出值只是简单的等于t = (n-1)h时的输入值，即信号延迟时间h：

y0 = x-1

y1 = x0

y2 = x1

y3 = x2

... etc

注意，由于抽样是在t = 0开始，输入值x- 1 在t = -h是不确定的。因此一般假设在t =

0时（以及t = 0之前），输出值都设为0。

4. 差分滤波器：

y n = x n - x n-1

在t = nh时的输出值等于当前输入值x n与前一个输入值x n-1的差值：

即输出值是最近一次采样值间隔h输入的变化。该滤波器对信号的影响就是类似于模拟电路中的微分电路。

5.均值滤波器：

该输出值是当前输入值和前一个输入值的平均值（算术平均）。

这是一个简单的低通滤波器，其通常将高频中的信号过滤掉。（之后，我们将着眼于更有效的低通滤波器。）

6.三均值滤波器：

该滤波器是当前的输入值和先前两个输入值的均值，类似于先前的那个均值滤波器。

类似于之前，x-1和x-2取0。

7.中心差分滤波器：

该滤波器的滤波效果类似于例（4），输出值等于当前输入值与前两个时间间隔h差值的二分之一。

附件2：外文原文

INTRODUCTION TO DIGITAL FILTERS

Analog and digital filters

In signal processing, the function of a filter is to remove unwanted parts of the signal, such as random noise, or to extract useful parts of the signal, such as the components lying within a certain frequency range.

The following block diagram illustrates the basic idea.

There are two main kinds of filter, analog and digital. They are quite different in their physical makeup and in how they work.

An analog filter uses analog electronic circuits made up from components such as resistors, capacitors and opamps to produce the required filtering effect. Such filter circuits are widely used in such applications as noisereduction, video signal enhancement, graphic equalisers in hi-fi systems, and many other areas.

There are well-established standard techniques for designing an analog filter circuit for a given requirement.

At all stages, the signal being filtered is an electrical voltage or current which is the direct analogue of the physical quantity (e.g. a sound or video signal or transducer output) involved.

A digital filter uses a digital processor to perform numerical calculations on sampled values of the signal. The processor may be a general-purpose computer such as a PC, or a specialised DSP (Digital Signal Processor) chip.

The analog input signal must first be sampled and digitised using an ADC (analog to digital converter). The resulting binary numbers, representing successive sampled values of the input signal, are transferred to the processor, which carries out numerical calculations on them. These calculations typically involve multiplying the input values by constants and adding the products together. If necessary, the results of these calculations,which now represent sampled values of the filtered signal, are output through a DAC (digital to analog converter) to convert the signal back to analog form.

Note that in a digital filter, the signal is represented by a sequence of numbers, rather than a voltage or current.

The following diagram shows the basic setup of such a system.

Advantages of using digital filters

The following list gives some of the main advantages of digital over analog filters. 1. A digital filter is programmable, i.e. its operation is determined by a program stored in the processor's

memory. This means the digital filter can easily be changed without affecting the circuitry (hardware).

An analog filter can only be changed by redesigning the filter circuit.

2. Digital filters are easily designed, tested and implemented on a general-purpose computer or

workstation.

3. The characteristics of analog filter circuits (particularly those containing active components) are

subject to drift and are dependent on temperature. Digital filters do not suffer from these problems,

and so are extremely stable with respect both to time and temperature.

4. Unlike their analog counterparts, digital filters can handle low frequency signals accurately. As the

speed of DSP technology continues to increase, digital filters are being applied to high frequency

signals in the RF (radio frequency) domain, which in the past was the exclusive preserve of analog

technology.

5. Digital filters are very much more versatile in their ability to process signals in

a variety of ways; this

includes the ability of some types of digital filter to adapt to changes in the characteristics of the

signal.

6. Fast DSP processors can handle complex combinations of filters in parallel or cascade (series),

making the hardware requirements relatively simple and compact in comparison with the equivalent

analog circuitry.

Operation of digital filters

In this section, we will develop the basic theory of the operation of digital filters. This

is essential to an

understanding of how digital filters are designed and used.

Suppose the "raw" signal which is to be digitally filtered is in the form of a voltage waveform described by the function

V x(t)

where t is time.

This signal is sampled at time intervals h (the sampling interval). The sampled value at time t = ih is

x i x( ih )

Thus the digital values transferred from the ADC to the processor can be represented by the sequence

x0 , x1 , x2 , x3 , ...

corresponding to the values of the signal waveform at

t = 0, h, 2h, 3h, ...

and t = 0 is the instant at which sampling begins.

At time t = nh(where n is some positive integer), the values available to the processor, stored in memory, are

x0 , x1 , x2 , x3 , ... x n

Note that the sampled values x n+1, x n+2 etc. are not available, as they haven't happened yet! y0 , y1 , y2 , y3 , ... y n

In general, the value of y n is calculated from the values x0, x1, x2, x3, ... , x n. The way in which the y's are

calculated from the x's determines the filtering action of the digital filter.

In the next section, we will look at some examples of simple digital filters. Examples of simple digital filters

The following examples illustrate the essential features of digital filters.

1. Unity gain filter:

Each output value y n is exactly the same as the corresponding input value x n:

y0 x0

y1 x1

y2x2

...etc

This is a trivial case in which the filter has no effect on the signal.

2. Simple gain filter:

y n =Kx n

where K = constant.

This simply applies a gain factor K to each input value.

K > 1 makes the filter an amplifier, while 0 < K < 1makes it an attenuator. K < 0 corresponds to an

inverting amplifier. Example (1) above is simply the special case where K= 1.

3. Pure delay filter:

y n =x n-1

The output value at time t = nh is simply the input at time t = (n-1)h, i.e. the signal is delayed by time h:

y0 = x-1

y1 = x0

y2 = x1

y3 = x2

... etc

Note that as sampling is assumed to commence at t= 0, the input value x-1 at t=-h is undefined. It is

usual to take this (and any other values of x prior to t= 0) as zero.

4.Two-term difference filter:

y n = x n - x n-1

The output value at t = nh is equal to the difference between the current input x n and the previous

input x n-1:

i.e. the output is the change in the input over the most recent sampling interval h. The effect of this

filter is similar to that of an analog differentiator circuit.

5. Two-term average filter:

The output is the average (arithmetic mean) of the current and previous input: