【導(dǎo)讀】又廣泛應(yīng)用于眾多領(lǐng)域的新興學(xué)科。早在20世紀(jì)60年代，數(shù)字信號(hào)處理(即信。法基礎(chǔ)才被人提出。不久之后，1982年世界上第一枚DSP芯片誕生了。這枚DSP芯片在當(dāng)時(shí)運(yùn)。算速度很快，尤其是在編碼解碼和語(yǔ)音合成方面得到廣泛應(yīng)用。展，也使得它得到了很多的實(shí)際應(yīng)用，由此奠定了DSP這一詞的地位。本文主要講述了IIR濾波器的設(shè)計(jì)原理和在DSP上實(shí)現(xiàn)IIR濾波器的過(guò)程。的性能進(jìn)行了測(cè)試分析，結(jié)果表明：所設(shè)計(jì)的濾波器能有效實(shí)現(xiàn)濾波。

　　

【正文】 最好的同時(shí)也是極其困難 2 的，而且不可能的是，先用模擬濾波器實(shí)現(xiàn)。另外，數(shù)字濾波器的特性，可以很容易地在軟件控制下發(fā)生變化。數(shù)字濾波器被分類為有限持續(xù)時(shí)間脈沖響應(yīng) (FIR)濾波器或無(wú)限持續(xù)時(shí)間脈沖響應(yīng) (IIR)濾波器，這取決于該系統(tǒng)的脈沖響應(yīng)的形式 。在 FIR 系統(tǒng)中，脈沖響應(yīng)序列是有限的持續(xù)時(shí)間，即，它具有非零項(xiàng)的數(shù)量有限。數(shù)字無(wú)限脈沖響應(yīng) (IIR)濾波器通?？梢蕴峁┍绕涞刃в邢廾}沖響應(yīng) (FIR)濾波器更好的性能和更少的計(jì)算成本，并已成為越來(lái)越感興趣的目標(biāo)。 但是，由于 IIR 濾波器的誤差表面通常是非線性的，多式聯(lián)運(yùn)，傳統(tǒng)的基于梯度的設(shè)計(jì)方法可以很容易地陷入錯(cuò)誤的表面。因此當(dāng)?shù)貥O小，一些研究者已經(jīng)試圖開發(fā)基于設(shè)計(jì)方法現(xiàn)代啟發(fā)式優(yōu)化算法，如遺傳算法 (GA)，模擬退火 (SA)，禁忌搜索 (TS).簡(jiǎn)單的迭代方法通常導(dǎo)致次優(yōu)的設(shè)計(jì)。因此，有必要的優(yōu)化方法 (啟發(fā)式 型 )，可以是用來(lái)設(shè)計(jì)數(shù)字濾波器，將滿足規(guī)定的規(guī)格。古德伯格呈現(xiàn)遺傳算法的詳細(xì)的數(shù)學(xué)模型。本韋努托切在書中描述在設(shè)計(jì)數(shù)字濾波器具有線性相位數(shù)字濾波器的上下文中使用模擬退火 (SA)算法的顯著特征。該算法然后被應(yīng)用到 FIR 濾波器的設(shè)計(jì)。其結(jié)果是并不令人印象深刻。此外，它在計(jì)算上的花費(fèi)是非常昂貴的。 艾哈邁德用遺傳算法設(shè)計(jì)與 CSD 系數(shù)限制的低通濾波器的一階IIR 濾波器。艾哈邁德和安東尼屋探討了 FIR 濾波器和均衡器，通過(guò)遺傳算法的使用，因而氣需要大量的計(jì)算。 2020 年 奧利維拉等人提出了利用非線性隨機(jī)全局優(yōu)化的模擬退火 技術(shù)，設(shè)計(jì)基于線性 FIR 濾波器的一種新方法。 2020 年 維斯和唐評(píng)價(jià)了遺傳編程 (GP)的適用性的 3 分布式算法的進(jìn)化。上述各種方法的基本限制是它們主要是用來(lái)設(shè)計(jì)FIR 數(shù)字濾波器。前面的設(shè)計(jì)方法的缺點(diǎn)是計(jì)算時(shí)間是相當(dāng)長(zhǎng)的測(cè)試優(yōu)化方法，所提出的算法在 MATLAB 和實(shí)現(xiàn)的結(jié)果是非常令人鼓舞的。本文的組織如下：在第 2 節(jié)中， IIR 數(shù)字濾波器的設(shè)計(jì)問(wèn)題進(jìn)行了討論。在 3 節(jié)中，遺傳算法 (GA)的方法作了簡(jiǎn)要的闡述。遺傳算法(GA)對(duì)濾波器的設(shè)計(jì)是在 4 節(jié)中提出了相關(guān)的。設(shè)計(jì)實(shí)例的仿真結(jié)果進(jìn)行簡(jiǎn)要描述在 5 節(jié)。結(jié)論和未來(lái)的范圍是在 6 節(jié) 中描述的。響應(yīng) IIR濾波器的遞推或是依賴于一個(gè)或更多的過(guò)去的輸出。如果這樣的過(guò)濾器進(jìn)行一個(gè)脈沖的輸出不一定為零。這表明，系統(tǒng)很容易反饋和不穩(wěn)定。每個(gè)解決方案與健身價(jià)值，反映了它是多么的好，在人群中有 [ 16 ]其他方案進(jìn)行了比較。通過(guò)交叉機(jī)制，交流部分之間的數(shù)據(jù)字符串模擬染色體重組過(guò)程。新的遺傳物質(zhì)也通過(guò)突變導(dǎo)致的隨機(jī)變化的字符串了。對(duì)這些遺傳操作的發(fā)生頻率是由一定的概率控制。的選擇，交叉，變異過(guò)程如圖 2 所示 [ 17 ]構(gòu)成的基本遺傳算法的循環(huán)或生成，這是重復(fù)直到預(yù)定的標(biāo)準(zhǔn)是滿意的。通過(guò)這一過(guò)程，先后更好個(gè) 體的物種生成。隨著計(jì)算能力的集成電路技術(shù)的進(jìn)步提供了進(jìn)化系統(tǒng)，仿真越來(lái)越聽(tīng)話的氣被應(yīng)用到許多現(xiàn)實(shí)世界的問(wèn)題，包括數(shù)字濾波器的設(shè)計(jì)。 1 外文文獻(xiàn)原文 Geic Algorithm for the Design of Optimal IIR Digital Filters Ranjit Singh, Sandeep K. Arya ABSTRACT This paper presents the design of Optimal InfiniteImpulse Response (IIR) digital filters using Geic Algorithm (GA). IIR filter is essentially a digital filter with Recursive responses. Since the error surface of digital IIR filters is generally nonlinear and multimodal, global optimization techniques are required in order to avoid local minima. This paper presents heuristic way for the designing IIR filters. GA is a powerful global optimization algorithm introduced in binatorial optimization problems. The paper finds the optimum Coefficients of IIR digital filter through GA. Design of Low pass and High pass IIR digital filter is proposed to provide estimate of transition band. It is found that the calculated values are more optimal than fda tool available for the design of filter in MATLAB. The simulation result of the employed examples shows an improvement on transition band and meansquareerror (MSE). The position of polezero is also presented to describe stability and results are pared with Simulated Annealing (SA) method. Keywords: Digital Filter。 InfiniteImpulse Response (IIR)。 Geic Algorithm (GA)。 Optimization 1. Introduction 1. Over the last few decades the field of Digital Signal Processing (DSP) has grown to important both theoretically and technologically. In DSP, there are two important types of Systems. The first of systems performs signal filtering in time domain and hence it is known as Digital filters. The second type of systems provide signal representation frequency domain and are known as Spectrum Analyzer. Digital filtering is one of the most powerful tools of DSP. Digital filters are capable of performance specifications that would, at best, be extremely difficult, if not impossible, to achieve with an analog implementation. In addition, the characteristics of a digital filter can be easily changed under software control. Digital filters are classified either as Finite duration impulse response (FIR) filters or Infinite duration impulse response (IIR) filters, depending on the form of impulse response of the system. In the FIR system, the impulse response sequence is of finite duration, ., it has a finite number of non zero terms. Digital infiniteimpulseresponse (IIR) filters can often provide a much better performance and less putational cost than their equivalent finiteimpulseresponse (FIR) filters and have bee the target of growing interest . However, because the error surface of IIR filters is usually nonlinear and multimodal, conventional gradientbased design methods may easily get stuck in the local minima of error , some researchers have attempted to develop design methods based on modern heuristic optimization algorithms such as geic algorithm (GA) , simulated annealing (SA), tabu search (TS) .Analytical or simple iterative methods usually lead to suboptimal designs. Consequently, there is a need of optimization methods (heuristic type) that can be use to design digital filters that would satisfy prescribed specifications. Goldberg presented a detailed mathematical model of Geic Algorithm . Benvenuto et al. (1992) described the salient features of using a simulated annealing (SA) algorithm in the context of designing digital filters with linear phase digital filter. The algorithm is then applied to the design of FIR filter. The result was not impressive. Moreover, it is putationally very expensive. Ahmadi et al.(2020) used geic algorithm to design 1D IIR filter with canonicalsigneddigit coefficients restricted to lowpass filter. Ahmad and Antoniou (2020) explored FIR filters and 2 equalizers through the use of GA. Consequently GAs requires a large amount of putation. Oliveira et al. (2020) presented a new approach for designing linear FIR filters by using nonlinear stochastic global optimization based on simulated annealing techniques. Jung et al. (2020) found the design method of a linear phase finite word length finiteduration impulse response (FIR) filter using simulated annealing. Weise and Tang (2020) evaluated the applicability of geic programming (GP) for the evolution of distributed algorithms. The basic limitation of all the above methods is that they can mainly be used to design FIR digital filters. The drawback of preceding design methods is that the putation time is quite long To test the optimization procedure, the proposed algorithm is