南邮专业英语报告-信号处理导论完整版(包含翻译-原文和单词).doc

南京邮电大学专 业 英 语 译 文 报 告 学 号 学 生 姓 名 指 导 老 师 指 导 单 位 翻 译 日 期 翻 译 文 献 Introduction to Signal Processing译文部分S. J. Orfanidis, Introduction to Signal Processing, Prentice Hall International, Inc., 2003清华大学出版社有影印版，2003.7，中文书名：信号处理导论8.2数字音效象延时、回声、回响、梳理滤波、（flanging）凸缘（法兰）、合唱、pitch shifting(分声步)、立体声、变形、压缩、扩张、噪声消除、均衡等等这样一些音响效果在音乐制作和播放时是必不可少的。有些在家庭影院和汽车音响中已经使用。 大多数这样的音响效果是用数字滤波器来实现的。这种数字滤波器也许是单独的一个模块，也可能是内置在键盘或音调生成这样的器件内部。一般说来数字音效信号处理器如图8.2.1所示。 图 8.2.1 数字音效信号处理数字音效处理器的输入是由键盘或纪录在其他介质上的模拟信号，用一定的抽样率抽样。抽样好的信号用DSP算法处理好以后再模拟重建输出到下一级音频通道中，如喇叭、混响器等等。全数字式系统可以不需要抽样、重建部分，数字式输入音频信号可以一直在后续的DSP处理中保持数字化。本届中我们将讨论一些基本音响效果，如延时、回声、润色、合唱、回响、动态处理。具体的滤波器设计将在第十章和第十一章讨论。8.2.1 延时、回声、梳理滤波最基本的一种音效是延时，因为延时还常用作象回声这样的复杂音效模块当中。在房间、教堂或电影院中我们听到的声音包括直接声音和房间中由墙壁、其他物体反射回来的声波，这些声波延时和衰减各不相同。多次反射就会形成我们通常在房间、大厅或教堂中听到的回声效果。一次反射或回声可以用下面的滤波器来实现，也就是在我们听到的直接声音信号上加上一个衰减并且延时的信号自身。 (回声滤波器) (8.2.1)延时D代表的时从声源经反射物体反射厚往返传播的时间，系数a是反射和传播损耗的一种度量，因此一般有1a。上述滤波器的传递函数和冲激响应为： (8.2.2)滤波器的框图实现如图8.2.2。频率响应可以令(8.2.2)式中的得到： (8.2.3)回声、延时演示程序具体分析了书中所示的各种延时情况及其传递函数、冲激响应、零点极点分布。 8.2.2凸缘,合唱和调相抽样的延时数D(用秒表示TD=DT)对于我们听到的声音效果有戏剧性的影响。比如说，如果回声处理(8.2.1)式中延时大于10ms，延时信号听上去好像是原来信号的快速重复，Slap。 如果回声处理(8.2.1)式中延时小于10ms，延时信号与直接信号混合，因为只有部分频率被梳妆滤波器强化，合成的声音听上去由一种空虚(Hollow)感。也可以用延时来改变声源的stero imaging，在立体声混响中这是必不可少的工具。比方说对一个喇叭的输出延时几个毫秒可以形成立体声扩散效果。两个单声道喇叭采用这样一种效果听上去象是立体声。如果允许延时D随时间变化，可以产生更有趣的音响效果，如flanging、合唱。比如说(8.2.1)式中，延时D用d(n)代替得到： (8.2.17)让延时量d(n)用一个非常低的频率(1Hz)生成，在0到10ms之间周期性变化，就可以产生flanging效果。比如说，延时量在0,D之间周期性的作正弦变化： (8.2.18)其中Fd为一个非常低的频率，单位为周期/抽样(whoosh n嘶嘶声，飞快的移动 v. (使)飞快移动 int. (飞速行进等发出的声音)嗖, 呼, 咳) 随时间变化的梳状滤波器的频率响应峰点(频率为dfs的倍数)和陷点(频率为d2sf的奇数倍)在频率轴上往返移动，使得声音有一种whooshing特征，这样一种效果称为Flanging。a决定了陷点的深度。用radians/sample作单位，则凹陷的频率为/d的奇数倍。 过去，flanging effect是在两个磁带播放机上同时播放，然后人为地交替按住磁带的鼓轮实现flanging效果。 由于延时量d可以在0，D以内取非整数，因此要求计算延时线上这些非整数点的输出x(n-d)。可以采用截断、舍入或插值的办法来实现。 线形插值是比较精确的一种方法。程序tapi.c就是用来计算插值点上的值。线性插值对于最高频率远小于Nyquist频率的低频应该说足够了。对于快速变化的输入信号，插值可以采用第十二章介绍的方法。正弦信号的flanged效果。程序flanged.m演示的是正弦信号仅不同的延时后的效果。也可以采用递归形式的Flanger，这种Flanger是基于全极点的梳状滤波器之上的。图8.2.6中的反馈回路现在用可调节延时d替代。Flange效果更象是FIR情形，摆动使得梳的峰值更加尖锐。 合唱模仿了由一组演奏人员同时演奏某一个乐器这种效果。演奏人员中有些同步很好，有些同步差些，但是弹奏的强度或时间差别甚小。正是这样一些微小的差别才形成合唱效果。合唱效果的数字实施方法如图8.2.10，图中模仿了三个人的演奏。 时间和幅度上的微小差别可以通过对幅度和时间加上一个随机的变化量来模仿。用： (8.2.20)来产生一个位于0,D之间的低频随机延时量d(n)。当延时限定在D1，D2之间时，则：(8.2.21)信号v(n)为一平均值为0的随机变量，取值范围为-0.5，0.5。可以用随机变量生成函数rand.m产生。作为例子，我们还是考虑一正弦信号，但延时是由式(8.2.20)给定的。程序chorus.m演示的是正弦信号经合唱处理后的情形。调相(Phase Shifting)对吉他手、键盘演奏人员、歌唱家来说是经常采用的一种效果。调相是把声音信号用一个窄带陷状滤波器过滤，再把过滤信号的一部分与源信号相加而得到的。陷点的频率以可控的方式调节，比如说可以用一个低频振荡器，也可以用脚踏板控制。陷点附近的频率有较强的漂移，与原来的直接声音结合，使得相位在频率轴上发生抵消或加强，整个相位在频率轴上出现波动。一般说来，典型的单零点陷状滤波器的幅频响应和相频响应如图所示。notch.m。(see page 252 for the review of notch filter)。注意到相频响应在相点处等于0，而在相点附近变化极快。6.4.3中，我们讨论了一种构造陷状滤波器的简单方法，也就是相设计一个notch多项式N(z)，其零点就是我们要设计的陷点。然后再单位圆以内靠外一点的相同频率上设置滤波器的极点。这样的滤波器的传递函数具有以下形式：这样设计的滤波器可以构造多陷点的相位漂移。选择接近等于1可以实现非常窄，但是这样的滤波器不能够对各个频率陷点的相位单独控制。 用双线性变换法(第十一章讨论)设计的这种滤波器可以对陷点频率和3-dB宽度进行精确控制。这样设计的滤波器单陷点滤波器的传递函数具有以下形式： (8.2.22)其中参数b用3-dB宽度表示为： (8.2.23)衡量陷状滤波器的另一个参数为品质因数Q，用3-dB宽度表示为： (8.2.24)也就是说，品质因数越高，陷点宽度越窄。因为处了陷点以外幅频响应基本上不发生变化(Flat)，所以可以用多个这样的滤波器级联起来形成多陷点滤波器，各滤波器的陷点频率和相位可以单独调节。 举例来说，要设计一个陷点频率为0=0.35的陷频滤波器，品质因数分别为Q=3.5和Q=35两种情况下，3-dB宽度为： 和 有(8.2.3)式计算得到滤波器系数和传递函数为：幅频响应和相位响应如图所示 频率漂移演示程序若陷点频率随时间变化，则3-dB宽度也会随时间变化，滤波器的系数也是时间变化的。这样的滤波器的时域实现可以采用规范形式。比方说，如果陷频是在12之间以SWEEP正弦变化，即0(n)=1+2sin(SWEEPn)，可以采用下列样值处理算法来计算飘动的滤波器系数，再分别计算每次输入抽样的滤波。 Flanging、合唱、调相三种效果都是把一个简单滤波器的系数设计尾随输入抽样变化而使滤波器成为时变滤波器。自适应信号处理也是随时间改变滤波器的系数。系数与时间之间的关系是受某些设计条件的限制，即滤波器系数相对于输入抽样调节并且优化。自适应算法的实施也就是要求滤波器的样值处理算法当中考虑到随输入抽样的不同系数有不同的权。 自适应滤波应用范围非常广，象通道均衡、回声消除、消噪声、自适应天线系统、自适应喇叭均衡、自适应系统辨识和控制、神经网络等等8.2.3 回响回响回响的时间常数定义为房间的冲激响应衰减到60dB的时间。一般的影院时间常数为1.82秒。 电影院的声音质量取决于回声冲激响应，而冲激响应主要是由声源与观众的相对位置决定的。因此数字上模拟任何一个电影院回响特性几乎是不可能的事。作为一种简化，数字回响滤波器试图模拟放映大厅具有特征性的回响冲激响应，让用户有选择性的调节某些参数，如前期反射的延时时间、或者是总体的回响时间。另一种有趣的回响效果是模拟滤波器无法完成的，这就是截断IIR响应使其成为FIR而得到gated reverb(选通回响)并且可以让用户调节截断的时间。snare drum(小鼓)的声音就很适用于这样处理。逆时间截断的回响响应在模拟领域是无法做到的。图示的普通回响滤波器太简单，难以产生实际的回响效果。Schroeder以依此为基础来构造复杂的回响器，这种滤波器可以由early reflection 和 late diffuse效果。大部分数字信号处理中，我们感兴趣的是稳态响应，而回响是例外，我们感兴趣的是滤波器的暂态响应，因为正是电影院的暂态响应才形成了回响效果。稳态响应决定了总体声音质量。普通回响滤波器稳态频谱的峰值加强了输入信号峰值频率附近的那些频率。为了避免这种输入声音的加强程度不一致，Schroeder提出了一种全通滤波器，这种滤波器的幅频响应特性为一直线。滤波器的传递函数如下： (8.2.25)其I/O方程如下： (8.2.26)用z=ej代入传递函数得到频率响应： (8.2.27)因为分子多项式和分母多项式的幅值相同，所以对所有频率幅频响应为常数。 尽管稳态响应为常数，滤波器的暂态响应像普通的回响滤波器一样指数衰减。事实上，将H(z)永部分分式展开得到： (8.2.28)其中，把后面一项展开乘几何级数得到：其冲激响应为：(8.2.29)图8.2.17是其框图实现方法：普通回响器与全通回响器结合就可以形成实际的回响器。Schroeder的回响器就是用几个普通回响单元并联，后面在接上几个级联的全通滤波器组成的。(见本书封面上图形和page 372所示图)。六个单元中不同的延时是回声的强度增加，形成的冲激响应具有典型的前期回声和后期回声效果。图示为下列参数是回响器的冲激响应。英文原文8.2 Digital Audio EffectsAudio effects, such as delay, echo, reverberation, comb filtering, flanging, chorusing,pitch shifting, stereo imaging, distortion, compression, expansion, noise gating, andequalization, are indispensable in music production and performance 115151. Someare also available for home and car audio systems. Most of these effects are implemented using digital signal processors, which mayreside in separate modules or may be built into keyboard workstations and tone generators.A typical audio effects signal processor is shown in Fig. 8.2.1. The processor takes in the “dry” analog input, produced by an instrument such asa keyboard or previously recorded on some medium, and samples it at an appropriateFig. 8.2.1 Audio effects signal processor.audio rate, such as 44.1 kHz (or less, depending on the effect). The sampled audiosignal is then subjected to a DSP effects algorithm and the resulting processed signal isreconstructed into analog form and sent on to the next unit in the audio chain, such asa speaker system, a recording channel, a mixer, or another effects processor.In all-digital recording systems, the sampling/reconstruction parts can be eliminatedand the original audio input can remain in digitized form throughout the successiveprocessing stages that subject it to various DSP effects or mix it with similarly processedinputs from other recording tracks.In this section, we discuss some basic effects, such as delays, echoes, flanging, chorusing,reverberation, and dynamics processors. The design of equalization filters willbe discussed in Chapters 10 and 11.8.2.1 Delays, Echoes, and Comb FiltersPerhaps the most basic of all effects is that of time delay because it is used as the buildingblock of more complicated effects such as reverb.In a listening space such as a room or concert hall, the sound waves arriving at ourears consist of the direct sound from the sound source as well as the waves reflectedoff the walls and objects in the room, arriving with various amounts of time delay andattenuation.Repeated multiple reflections result in the reverberation characteristics of the listeningspace that we usually associate with a room, hall, cathedral, and so on.A single reflection or echo of a signal can be implemented by the following filter,which adds to the direct signal an attenuated and delayed copy of itself: y(n)= x(n)+ax(n D) (echo filter) (8.2.1)The delay D represents the round-trip travel time from the source to a reflectingwall and the coefficient a is a measure of the reflection and propagation losses, so that|a| 1. The transfer function and impulse response of this filter are: H(z)= 1 + azD, h(n)= (n)+a(n D) (8.2.2)Its block diagram realization is shown in Fig. 8.2.2. The frequency response is obtainedfrom Eq. (8.2.2) by setting z = ej:（8.2.3）8.2.2 Flanging, Chorusing, and PhasingThe value of the delay D in samples, or in seconds TD = DT, can have a drastic effect onthe perceived sound 119,120,128. For example, if the delay is greater than about 100milliseconds in the echo processor (8.2.1), the delayed signal can be heard as a quickrepetition, a “slap”. If the delay is less than about 10 msec, the echo blends with thedirect sound and because only certain frequencies are emphasized by the comb filter,the resulting sound may have a hollow quality in it.Delays can also be used to alter the stereo image of the sound source and are indispensabletools in stereo mixing. For example, a delay of a few milliseconds applied toone of the speakers can cause shifting and spreading of the stereo image. Similarly, amono signal applied to two speakers with such a small time delay will be perceived instereo.More interesting audio effects, such as flanging and chorusing, can be created byallowing the delay D to vary in time 119,120,128. For example, Eq. (8.2.1) may bereplaced by: (flanging processor) (8.2.17)A flanging effect can be created by periodically varying the delay d(n) between 0 and10 msec with a low frequency such as 1 Hz. For example, a delay varying sinusoidallybetween the limits 0 d(n) D will be: (8.2.18)where Fd is a low frequency, in units of cycles/sample.Its realization is shown in Fig. 8.2.8. The peaks of the frequency response of theresulting time-varying comb filter, occurring at multiples of fs/d, and its notches atodd multiples of fs/2d, will sweep up and down the frequency axis resulting in thecharacteristic whooshing type sound called flanging. The parameter a controls the depthof the notches. In units of radians/sample, the notches occur at odd multiples of /d.In the early days, the flanging effect was created by playing the music piece simultaneouslythrough two tape players and alternately slowing down each tape by manuallypressing the flange of the tape reel.Because the variable delay d can take non-integer values within its range 0 d D,the implementation of Eq. (8.2.17) requires the calculation of the output x(n d) ofa delay line at such non-integer values. As we discussed in Section 8.1.3, this can beaccomplished easily by truncation, rounding or linear interpolation. Linear interpolation is the more accurate method, and can be implemented with thehelp of the following routine tapi.c, which is a generalization of the routine tap tonon-integer values of d. The input d must always be restricted to the range 0 d D. Note that if d is oneof the integers d = 0, 1, . . . , D, the routines output is the same as the output of tap.The mod-(D+1) operation in the definition of j is required to keep j within the arraybounds 0 j D, and is effective only when d = D, in which case the output is thecontent of the last register of the tapped delay line. The following routine tapi2.c is a generalization of the routine tap2, which is implementedin terms of the offset index q instead of the circular pointer p, such thatp = w + q./* tapi2.c - interpolated tap output of a delay line */Linear interpolation should be adequate for low-frequency inputs, having maximumfrequency much less than the Nyquist frequency. For faster varying inputs, more accurateinterpolation methods can be used, designed by the methods of Chapter 12. As an example illustrating the usage of tapi, consider the flanging of a plain sinusoidalsignal of frequency F = 0.05 cycles/sample with length Ntot = 200 samples, sothat there are FNtot = 10 cycles in the 200 samples. The flanged signal is computed bywith d(n) given by Eq. (8.2.18), D = 20, and Fd = 0.01 cycles/sample, so that there areFdNtot = 2 cycles in the 200 samples.The following program segment implements the calculation of the term s(n)= xand y(n). A delay-line buffer of maximal dimension D + 1 = 21 was used:double *w, *p;w = (double *) calloc(D+1, sizeof(double);p = w;for (n=0; nNtot; n+) d = 0.5 * D * (1 - cos(2 * pi * Fd * n); time-varying delayx = cos(2 * pi * F * n); input x(n)s = tapi(D, w, p, d); delay-line output x(n d)y = 0.5 * (x + s); filter output*p = x; delay-line inputcdelay(D, w, &p); update delay line Figure 8.2.9 shows the signals x(n), s(n)= xn d(n), y(n), as well as the time-varying delay d(n) normalized by D.Recursive versions of flangers can also be used that are based on the all-pole combfilter (8.2.13). The feedback delay D in Fig. 8.2.6 is replaced now by a variable delay d. The resulting flanging effect tends to be somewhat more pronounced than in the FIRcase, because the sweeping comb peaks are sharper, as seen in Fig. 8.2.7.Chorusing imitates the effect of a group of musicians playing the same piece simultaneously. The musicians are more or less synchronized with each other, except for smallvariations in their strength and timing. These variations produce the chorus effect. Adigital implementation of chorusing is shown in Fig. 8.2.10, which imitates a chorus ofthree musicians. The small variations in the time delays and amplitudes can be simulated by varyingthem slowly and randomly 119,120. A low-frequency random time delay d(n) in theinterval 0 d(n) D may be generated by358 8. SIGNAL PROCESSING APPLICATIONS Fig. 8.2.10 Chorus effect, with randomly varying delays and amplitudes.d(n)= D0.5 + v(n) (8.2.20)or, if the delay is to be restricted in the interval D1 d(n) D2d(n)= D1 + (D2 D1)0.5 + v(n) (8.2.21) The signal v(n) is a zero-mean low-frequency random signal varying between 0.5, 0.5).It can be generated by the linearly interpolated generator routine ranl of Appendix B.2.Given a desired rate of variation Fran cycles/sample for v(n), we obtain the periodDran = 1/Fran of the generator ranl. As an example, consider again the signal y(n) defined by Eq. (8.2.19), but with d(n)varying according to Eq. (8.2.20). The input is the same sinusoid of frequency F = 0.05and length Ntot = 200. The frequency of the random signal v(n) was taken to beFran = 0.025 cycles/sample, corresponding to NtotFran = 5 random variations in the 200samples. The period of the periodic generator ranl was Dran = 1/Fran = 40 samples.The same program segment applies here, but with the change: d = D * (0.5 + ranl(Dran, u, &q, &iseed);where the routine parameters u, q, iseed are described in Appendix B.2. Figure 8.2.11 shows the signals x(n), s(n)= xn d(n), y(n), as well as thequantity d(n)/D. Phasing or phase shifting is a popular effect among guitarists, keyboardists, andvocalists. It is produced by passing the sound signal through a narrow notch filter andcombining a proportion of the filters output with the direct sound. The frequency of the notch is then varied in a controlled manner, for example, usinga low-frequency oscillator, or manually with a foot control. The strong phase shifts thatexist around the notch frequency combine with the phases of the direct signal and causephase cancellations or enhancements that sweep up and down the frequency axis. A typical overall realization of this effect is shown in Fig. 8.2.12. Multi-notch filterscan also be used. The effect is similar to flanging, except that in flanging the sweepingnotches are equally spaced along the frequency axis, whereas in phasing the notchescan be unequally spaced and independently controlled, in terms of their location andwidth. The magnitude and phase responses of a typical single-notch filter are shown inFig. 8.2.13. Note that the phase response argH() remains essentially zero, except inthe vicinity of the notch where it has rapid variations.In Section 6.4.3, we discussed simple methods of constructing notch filters. Thebasic idea was to start with the notch polynomial N(z), whose zeros are at the desirednotch frequencies, and place poles behind these zeros inside the unit circle, at someradial distance . The resulting pole/zero notch filter was then H(z)= N(z)/N(1z). Such designs are simple and effective, and can be used to construct the multi-notchfilter of a phase shifter. Choosing to be near unity gives very narrow notches. However,we cannot have complete and separate control of the widths of the different notches. A design method that gives precise control over the notch frequency and its 3-dBwidth is the bilinear transformation method, to be discussed in detail in Chapter 11.Using this method, a second-order single-notch filter can be designed as follows: (8.2.22) where the filter parameter b is expressible in terms of the 3-dB width (in units ofradians per sample) as follows: (8.2.23) The Q-factor of a notch filter is another way of expressing the narrowness of thefilter. It is related to the 3-dB width and notch frequency by: (8.2.24) Thus, the higher the Q, the narrower the notch. The transfer function (8.2.22) isnormalized to unity gain at DC. The basic shape of H(z) is that of Fig. 8.2.13. Because|H()| is essentially flat except in the vicinity of the notch, several such filters can becascaded together to create a multi-notch filter, with independently controlled notchesand widths.As an example, consider the design of a notch filter with notch frequency 0 =0.35, for the two cases of Q = 3.5 and Q = 35. The corresponding 3-dB widths are inthe two cases: 和 The filter coefficients are then computed from Eq. (8.2.23), giving the transfer functionsin the two cases: The subject of adaptive signal processing 27 is also based on filters with timevaryingcoefficients. The time dependence of the coefficients is determined by certaindesign criteria that for