201040744 六、發明說明： 【發明所屬之技術領域】 本發明是有關於—種信號分析裝置及一電腦程式產品 ，特別是指-種用於快速分析具有多數個分量之信號，以 反應-系統之動態行為的信號分析裝置及電腦程式產品。 【先前技術】 目前信號分析的方法已廣泛地使用於電力設備、通訊 、能源管理、及穩定度分析等不同領域卜透過信號分析 〇 丨法可以有效建立—系統模型，進而分析該系統的穩態、 暫態及動態行為 '然而，對於一系統的動態行為通常以微 分方程式來表示’而微分方程式的解皆以複指數所構成。 目前對於-分4的參數分析技術可时為在頻域或時 • 財處理之。在時域分析上，常見的方法為自動迴歸分析 方法、以遺傳演算法為基礎的分析方法，或是以類神經網 路為基礎的分析方法，而在頻域分析上可分為多項式法或 是圓嵌合法。綜觀上述目前常見的方法來說，因為一分量 〇 通常疋以暫悲形式出現，而在例如控制、保護的領域中， 控制系統或是保護系統的設計常需要即時地獲得暫態信 號的分析結果，所以往往因為資料量不足的關係，以上的 方法在應用上會受到限制，此外，該等分析方法往往無法 同時兼顧快速的計算速度及準確的分析結果，因此，如何 找出一既可快速取得分析結果且有效提高該分析結果的準 確度’是相關領域的人士努力的方向之一。 【發明内容】 3 201040744 因此’本發明之目的，即在提供一種信號分析裝置， 適用於分析一系統之動態行為，其包含·· -信號轉換單元，將—與該系統之動態行為相關的取 樣信號進行時域至頻域轉換，以產生一頻譜信號； 一 k號處理單το，根據該頻譜信號的振幅設定—第— 變數及一第二變數； 一信號產生單元，根據該第一變數及該第二變數產生 一模擬信號，該模擬信號包括數量為該第一變數個第—類 型分置及數量為該第二變數個第二類型分量丨及 ' 一運算單兀，根據該模擬信號設定一價可比矩陣，並 根據該取樣信號、該模擬信號及該價可比矩陣利用牛頓 拉夫生法更新該模擬信號的每一類型分量的參數，以使該 模擬信職合該取樣信號，而反應該系統之動態行為。” 本發明另外提供-種電腦程式產品，適用於分析_系 統之動態行為，其包含： -信號轉換單元，將—與該系統之動態行為相關的取 樣信號進行時域至頻域轉換，以產生一頻譜信號； 一#號處理單元，根據該頻譜信號的振幅設定—第一 變數及一第二變數； 一 k號產生單TL，根據該第—變數及該第二變數產生 —模擬信號，該模擬信號包括數量為該第一變數個第一類 型为里及數Ϊ為該第二變數個第二類型分量，及 一運算單70，根據該模擬信號設定一價可比矩陣，並 根據該取樣信號、該模擬信號及該價可比矩陣，利用牛頓 201040744 . 拉夫生法更新該模擬信號的每一類型分量的來叙 个致，以使該 模擬信號嵌合該取樣信號，而反應該系統之動織行為 【實施方式】 有關本發明之前述及其他技術内容、特點與功效，在 以下配合參考圖式之一個較佳實施例的詳細說明中，將可 清楚的呈現。 參閱圖1，本發明之一較佳實施例適用於分析一系統的 動態行為，其包含一取樣器11、一信號轉換單元12、一产 ❹ 號處理單元13、一信號產生單元14、一運算單元Η、及一 載體16。 其中’該取樣器11根據一預設的取樣速率^及取樣點 - 數斤對一輸入信號外)進行取樣，並輸出一取樣信號咖）；然 後’ s亥彳§號轉換早元12將該取樣信號；y(n)經由快速傅利葉 轉換（Fast Fourier Transform, FFT)轉換為—頻譜信號^⑽ 並送出至該信號處理單元13中；該信號處理單元13根據 該頻譜信號r(m)進行頻率分析，以分別得到一第一變數^及 ◎ 一弟二變數A ’並根據該第一變數&及該第二變數&設定一 序列長度參數ϋ:;然後將第一變數A、第二變數A，及序列 長度參數尺輸出至信號產生單元14中。該信號產生單元14 > 亦根據第一變數尽、第二變數吳產生一模擬信號/(χ，„)，且 該模擬信號包括數量為該第一變數個第一類型分量及數量 為該第二變數個第二類型分量，然後將對應的模擬信號 /(Χ，η)輸入至該運算單元15中。 該運算早元15接收該信號產生單元14所產生之模擬 5 201040744 信號/(χ>)後，建立一價可比矩陣（Jacobian matrix)並根 據該取樣信號κ”）、該模擬信號及該價可比矩陣，利用 牛頓拉夫生法（Newton-Raphson Method)更新該模擬信號 的每一類型分量的參數，以使該模擬信號八尤⑻嵌合該 取樣信號y(«)，而反應該系統之動態行為，換句話說，模擬 信號/X&n)中的參數即可代表取樣信號^⑻中對應的參數。最 後，該載體16用以展示該運算單元15處理完之信號參數 分析結果或是儲存其信號參數分析結果，在本實施例中， 其是一顯示器（monitor)，以將分析之後的結果顯示出來， 當然，該載體16也可以是其他種顯示裝置、列印裝置或是 儲存裝置等。 首先需要先說明的是，一取樣信號〆„)包含足個獨立的 刀量，且每一分量中皆包括振幅A、相位0、阻尼“，及角 速度ω等四個參數，然後，根據每一分量的性質可以將其分 類成如下之三種分量形式： (一） 指數弦波分量：該分量的阻尼參數α及角速度參 數ω皆不為零時，即為指數弦波分量形式； (二） 弦波分量：該分量的阻尼參數“為零時，即為弦 波分量形式；及 (三） 指數分量：該分量的角速度參數你為零時，即為 指數分量形式。 在本實施例中，該信號處理單元13將該頻譜信號W 中的該等分量依照頻率上的位置而區分為二種分量：一種 為接近頻率刻度0的分量及另一種為遠離頻率刻度〇的分 201040744 量0 Ο ❹ —般而言，接近頻率刻度G的分量是由-常數分量或 一指數分量所構成’而每-遠離頻率刻度G的分量是由一 弦波分量或是-指數弦波分量所構成，因此，在本實施例 中’該信號處理單7G 13會先預設接近頻率刻度Q的分量是 由-指數分量所構成，每-遠離頻率刻度G的分量都是由 一指數弦波分量所構成。當該信號處理單元13判定有接近 頻率刻度0的分量存在時，則設定該第—變數U i，否則 該第-變數Μ皮設定為0,而該信號處理單元13根據遠離 頻率刻度0的分量之數量而設定該第二變數最後，由於 指數分量有二個不為零的參數、指數弦波分量有四個不為 零的參數，因此根據如下的關係式設定該序列長度參數尤^ ^ = 2^+4^2 舉例來說’參閱圖2, 一輸入信號魏轉換為頻譜信 號Om)之後，可以分成五個分量、~戽5，其中第―分量曰: 為-接近頻率刻度0的分量且第二〜第五分量為遠離^率^ 度〇的分量，因此，該信號處理器13設定該第—變數尽為 1、設定該第二變數欠2為4，且該序列長度參數尺為18。Μ 此外，該信號產生單元14產生一如下列方程式所表示 的模擬信號八1，《)並送出至該運算單元15: 尤2+1 / (Ζ,«) = Λ^ηΓ + Σ Ake-a^ sin(^«r + ^), „ = 〇X......㈣ 其中，X =[臬巧，夂％，〇^2]’且X為所有分量分別抖庙 之該等參數所形成的集合。 、… 201040744 因此’該運算單…據該序列長度參數續取一段 長度為㈣取樣信號終—+ι)並進行信號參數之運算 以下先要_的是，本實施例之運算單元u 參數運算的數學理論主要是根據牛頓拉夫生法計算如_； 假π又函數為y = /〇),且已知一應變數兔》 ★亥庳變數;針庳“， 地變數為 當欲求出 ”亥應變數讀應的自變數：時，首先假設該函數 處的泰勒展開式為：201040744 VI. Description of the Invention: [Technical Field of the Invention] The present invention relates to a signal analysis device and a computer program product, and more particularly to a signal for quickly analyzing a signal having a plurality of components for reaction-system Dynamic behavior signal analysis device and computer program product. [Prior Art] At present, the method of signal analysis has been widely used in different fields such as power equipment, communication, energy management, and stability analysis. Through the signal analysis method, the system model can be effectively established, and then the steady state of the system is analyzed. Transient and dynamic behavior 'However, the dynamic behavior of a system is usually expressed in differential equations' and the solutions of differential equations are composed of complex exponents. At present, the parameter analysis technique for -4 is time-frequency or time-consuming processing. In time domain analysis, common methods are automatic regression analysis methods, genetic algorithm-based analysis methods, or neural network-based analysis methods, and frequency domain analysis can be divided into polynomial methods or It is a circular fitting method. Looking at the above-mentioned common methods, because a component 〇 usually appears in a temporary form of sorrow, in the field of, for example, control and protection, the design of the control system or the protection system often needs to obtain the analysis result of the transient signal in real time. Therefore, because of the lack of data, the above methods are limited in application. In addition, these analysis methods often cannot simultaneously take into account the fast calculation speed and accurate analysis results. Therefore, how to find one can be quickly obtained. Assessing the results and effectively improving the accuracy of the results of the analysis is one of the efforts of people in related fields. SUMMARY OF THE INVENTION 3 201040744 Accordingly, it is an object of the present invention to provide a signal analysis apparatus suitable for analyzing the dynamic behavior of a system comprising a signal conversion unit that samples the dynamic behavior associated with the system. The signal is subjected to time domain to frequency domain conversion to generate a spectral signal; a k processing unit το, according to the amplitude of the spectrum signal, a first variable and a second variable; a signal generating unit according to the first variable The second variable generates an analog signal, the analog signal includes a quantity of the first variable number-type division and the quantity is the second variable second type component 丨 and an operation unit, and is set according to the analog signal a price-comparable matrix, and updating parameters of each type component of the analog signal by using a Newton-Raphson method according to the sampling signal, the analog signal, and the valence matrix, so that the analog signal matches the sampling signal, and reacts The dynamic behavior of the system. The invention further provides a computer program product suitable for analyzing the dynamic behavior of the system, comprising: - a signal conversion unit for performing time domain to frequency domain conversion on the sampled signal related to the dynamic behavior of the system to generate a spectrum signal; a ## processing unit, according to the amplitude of the spectrum signal set - a first variable and a second variable; a k number to generate a single TL, according to the first variable and the second variable - analog signal, the The analog signal includes a first variable, a first type, a first type, a second type component, and an operation unit 70, and a monovalent comparable matrix is set according to the analog signal, and according to the sampling signal The analog signal and the comparable matrix, using Newton 201040744. The Rafson method updates each type of component of the analog signal to make the analog signal fit the sampling signal, and reacts to the motion of the system. Behavior [Embodiment] The foregoing and other technical contents, features and effects of the present invention are described in detail below with reference to a preferred embodiment of the drawings. DETAILED DESCRIPTION OF THE INVENTION Referring to Figure 1, a preferred embodiment of the present invention is suitable for analyzing the dynamic behavior of a system comprising a sampler 11, a signal conversion unit 12, and a processing unit 13 a signal generating unit 14, an arithmetic unit Η, and a carrier 16. The 'sampler 11 samples a predetermined sampling rate ^ and a sampling point - a kilogram to an input signal), and outputs a sampling The signal coffee); then the s 彳 转换 转换 早 早 早 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 12 The signal processing unit 13 performs frequency analysis based on the spectrum signal r(m) to obtain a first variable ^ and ◎ a second two variable A ' and according to the first variable & and the second variable & Setting a sequence length parameter ϋ:; then outputting the first variable A, the second variable A, and the sequence length parameter ruler to the signal generating unit 14. The signal generating unit 14 > is also based on the first variable, the second variable Wu produces one Analog signal /(χ,„), and the analog signal includes the first variable of the first type component and the quantity of the second variable of the second type component, and then the corresponding analog signal /(Χ,η) It is input to the arithmetic unit 15. After the operation early element 15 receives the analog 5 201040744 signal /(χ>) generated by the signal generating unit 14, a Jacobian matrix is established and the analog signal and the price are comparable according to the sampling signal κ") a matrix, using a Newton-Raphson Method to update the parameters of each type of component of the analog signal such that the analog signal is interspersed with the sampled signal y(«) to reflect the dynamic behavior of the system In other words, the parameters in the analog signal /X&n) can represent the corresponding parameters in the sampled signal ^(8). Finally, the carrier 16 is used to display the signal parameter analysis result processed by the arithmetic unit 15 or to store it. The signal parameter analysis result is, in the embodiment, a monitor to display the result after the analysis. Of course, the carrier 16 may be other display devices, printing devices or storage devices. First, it needs to be explained first that a sampling signal 〆„) contains a sufficient amount of knives, and each component includes amplitude A, phase 0, damping “, and angular velocity ω, etc. The parameters, then, according to the nature of each component, can be classified into the following three component forms: (1) The exponential sine wave component: when the damping parameter α and the angular velocity parameter ω of the component are not zero, it is an exponential sine wave Component form; (2) Sine wave component: When the damping parameter of the component is “zero, it is the form of the sine wave component; and (3) exponential component: when the angular velocity parameter of the component is zero, it is the exponential component form. In this embodiment, the signal processing unit 13 divides the components in the spectral signal W into two components according to the position on the frequency: one is a component close to the frequency scale 0 and the other is a distance away from the frequency scale 〇.分201040744量0 Ο ❹ In general, the component close to the frequency scale G is composed of a constant component or an exponential component, and the component per G away from the frequency scale G is composed of a sine wave component or an -index sine wave. The component is composed. Therefore, in the present embodiment, the signal processing unit 7G 13 first presets the component close to the frequency scale Q to be composed of the -exponential component, and the component of each of the -off frequency scales G is composed of an exponential string. The wave component is composed. When the signal processing unit 13 determines that there is a component near the frequency scale 0, the first variable U i is set, otherwise the first variable is set to 0, and the signal processing unit 13 is based on the component away from the frequency scale 0. The second variable is set last. Since the exponential component has two non-zero parameters and the exponential sine wave component has four non-zero parameters, the sequence length parameter is set according to the following relationship. 2^+4^2 For example, 'refer to Figure 2, after an input signal is converted into a spectral signal Om, it can be divided into five components, ~戽5, where the ―component 曰: is - the component close to the frequency scale 0 And the second to fifth components are components that are far away from the ^ rate, so the signal processor 13 sets the first variable to be 1, and sets the second variable to 2 to 4, and the sequence length parameter is 18. Further, the signal generating unit 14 generates an analog signal 八1, ") represented by the following equation and sends it to the arithmetic unit 15: 尤 2+1 / (Ζ, «) = Λ^ηΓ + Σ Ake-a ^ sin(^«r + ^), „ = 〇X...(4) where X = [臬巧,夂%,〇^2]' and X is the parameter of all components shaking the temple separately The formed set. ..., 201040744 Therefore, the operation unit... According to the sequence length parameter, a length is (4) the sampling signal end - + ι) and the signal parameter is calculated. The following is the operation unit of the embodiment. u The mathematical theory of parameter operation is mainly calculated according to Newton's law, such as _; false π and function is y = /〇), and a strain number of rabbits is known. ★Hui 庳 variable; acupuncture", the ground variable is when the desire When the "self-variable of the strain of the sea strain is read: first, first assume that the Taylor expansion at the function is:
"〇、 〇*0 1 〇 * A (F.2) f(x) + f '(x)(jc- x) + — f \x)(x~ x)2 +. 其中，/W為函數/(,)的一階導數，/u)為 階導數，其餘依此類推。 八）的"〇, 〇*0 1 〇* A (F.2) f(x) + f '(x)(jc- x) + — f \x)(x~ x)2 +. where /W is The first derivative of the function /(,), /u) is the order derivative, and so on. Eight)
* Q 田I似於X時，方程式（凡幻的高次項可以忽略，進而簡 化成如下所示： y = f(x) + f'(x)(x-x) .•…(尸_3) 因為函數/W為-非線性函數，所以可以藉由更新自變 數的疊代法找出—適當的自變數使得方程式（F.3)兩邊相等， 假設執行該疊代法v次之後，該自變數為；，且根據方程式 ㈣預估Θ疊代法執行第叫次時可以滿足下列方程式㈣： 本 y = f(x)+f'(x)(x-x) .•…(厂4) 因此，由方程式（F.4)可以得到 V+1 v X =x-\- y-f(x) /'ώ XF.5) 經由方程式（F·5)不斷地疊代將自變數；趨近於；時，當 收斂到疋的範圍時，則可以視該疊代法已找出其解。 201040744 應用方程式（F·5)於尺個非線性函數時，則該函數可表示 為如下之方程式： 因此’方程式（F·5)可以轉換為如下所示之矩陣表示式 X = X+\ J(X) Y-F(X) •.…(R6) 其中 Ο V 4 …4]Γ ·.···(F.7) Υ >1 >2 …；Vat •(厂 8) F(X) 腦 MX) ··· MX) XF.9) (F· ^^:a/2la%;^L^砉奢·：鸯却丨i^arl…也k 1~~ = (x 00即為一價可比矩陣（Jacobian matrix )。 最後，以相似於方程式（广5)的求解方式，藉由疊代法運 箅解出每—自變數'，w 之^覆參閱圖1’本實施例中該運算單元15是應用上述 之=于理淪對一長度為尤的取樣後輸入信號進行運算，且該 以單％ 15包括—矩陣建立模组151、—矩陣運算模组 ⑸，-參數運算模組153,及—誤差判定模组心在詳 細介紹該運算單元15如何運算前，以下先說明運算單元15 如何對不_式之分4進行 9 201040744 指教弦波分量之分析 因為對於一指數弦波分量其阻尼參數“及角速度參數历 皆不為零，所以該指數弦波分量可表示為如下之方程式 (F.U)： Λ?⑻以 a"rsin(伽：Γ+約，„ = 〇，】，2,........CF.11) 而方程式（F.11)中具有四個未知數，因此，該信號產生 單元13會根據連續四筆資料以形成一組聯立方程式（厂12) fss (n) ~ ^ anT sin(6)nT+φ) /es (η -1) = Ae'a{nA)T sin(/w(n - 1)Γ + φ) fES (η-2) = Aea(n-2)T sin(<y(n - 2)7 + φ) fES(η -3) = Aea(n'3)T δΐη(ω(η - 3)Γ + φ) .....(F.12) 該方程式組（F.12)可以視為一組如同方程式（F.5)所示之非 線性的聯立方程式組，因此，可以如下之矩陣式表示如下 X = [ω a A .....(F.13) F = [：y(/0 y(n-l) y(n-2) y(n-3)f ·.·.·(F.14) F(x、= [fEs(n) fEs(n-'、fEs(n_2、fssbSi ·..··(F.\S)* Q Field I is like X, the equation (the high-order term of the illusion can be ignored, and then simplified as follows: y = f(x) + f'(x)(xx) .•...(尸_3) because The function /W is a non-linear function, so it can be found by updating the self-variable iterative method—the appropriate self-variable makes the equations (F.3) equal on both sides, assuming that the iterative method is performed v times, the independent variable According to equation (4), the following equation (4) can be satisfied when the implementation of the iteration method is performed: y = f(x) + f'(x)(xx) .•... (factory 4) Equation (F.4) can give V+1 v X =x-\- yf(x) /'ώ XF.5) continually iterative over the arguments via equation (F·5); approaching; When it converges to the range of 疋, the solution can be found by the iteration. 201040744 When applying the equation (F·5) to a nonlinear function, the function can be expressed as the following equation: Therefore, the equation (F·5) can be converted into the matrix representation X = X+\ J ( X) YF(X) •....(R6) where Ο V 4 ...4]Γ ·.···(F.7) Υ >1 >2 ...;Vat •(Factory 8) F(X) Brain MX) ··· MX) XF.9) (F· ^^:a/2la%;^L^砉 Luxury·:鸯鸯丨i^arl...also k 1~~ = (x 00 is a price comparable Matrix (Jacobian matrix). Finally, in a solution similar to the equation (5), the iterative method is used to solve each-self-variable', and the reference to Figure 1' is the arithmetic unit in this embodiment. 15 is to apply the above-mentioned = 沦理沦 to a length of the sampled input signal is calculated, and the single% 15 includes a matrix building module 151, a matrix computing module (5), a parameter computing module 153, And - the error determination module core before describing in detail how the operation unit 15 operates, the following describes how the operation unit 15 performs the analysis of the sine wave component of the sine wave component because the sine wave component is damped for an sine wave component. parameter And the angular velocity parameters are not zero, so the exponential sine wave component can be expressed as the following equation (FU): Λ? (8) with a"rsin(Gaga: Γ+约, „ = 〇,], 2,... .....CF.11) and the equation (F.11) has four unknowns. Therefore, the signal generating unit 13 forms a set of simultaneous equations based on four consecutive data (factory 12) fss (n) ~ ^ anT sin(6)nT+φ) /es (η -1) = Ae'a{nA)T sin(/w(n - 1)Γ + φ) fES (η-2) = Aea(n- 2) T sin(<y(n - 2)7 + φ) fES(η -3) = Aea(n'3)T δΐη(ω(η - 3)Γ + φ) .....(F .12) The equation group (F.12) can be regarded as a set of nonlinear simultaneous equations as shown in equation (F.5). Therefore, the following matrix can be expressed as follows: X = [ω a A . ....(F.13) F = [:y(/0 y(nl) y(n-2) y(n-3)f ·····(F.14) F(x, = [ fEs(n) fEs(n-', fEs(n_2, fssbSi ·..·.(F.\S)
3/» a/» I⑻ 3/£S(«) 3ω da dA d(p 〇1) 3/£i(n-l) da dA dtp 3/ES(n-2) 3/es (灯 _2) Kn-2) 3/£s(n-2) 9ω da dA Βφ L3) 3/£S(«-3) ^ES (n ' 3) 9ω da dA (尸.16) 其中，方程式（F.16)為一個四階價可比矩陣。 10 201040744 將方程式（F.13)〜(F.16)代入到方程式5)中，然後該運算 單兀15執行疊代運算以計算出該指數弦波分量之對應的參 數 <»、ar、A、穸。 弦波分董之分浙 因為對於一弦波分量其阻尼參數α為零，所以該弦波分 量可表示為如下之方程式（厂17): fs(n) = Asin(anT+φ), η = 0,1,2.........(厂 17) 而方程式（凡Π)中具有三個未知數，因此，該信號產生 Ο 單元13會根據連續三筆資料以形成一組聯立方程式（厂18) fs (n) = A sin(ffi»nr + φ) (^ 1)= Asin(iy(w -1)77+^) fs(n-2) = A sin(a(n - 2)T+φ)•…·(F.18) 該方程式組（F_l8)可以視為一組如同方程式习所示之非 線性的聯立方程式組，因此，可以如下之矩陣式表示如下 Χ=[ω Λ ^]Γ ..…(F.19)3/» a/» I(8) 3/£S(«) 3ω da dA d(p 〇1) 3/£i(nl) da dA dtp 3/ES(n-2) 3/es (light_2) Kn -2) 3/£s(n-2) 9ω da dA Βφ L3) 3/£S(«-3) ^ES (n ' 3) 9ω da dA (corporate.16) where equation (F.16) Is a fourth-order comparable matrix. 10 201040744 Substituting equations (F.13)~(F.16) into equation 5), then the operation unit 15 performs an iterative operation to calculate the corresponding parameter of the exponential sine wave component <», ar, A, hehe. The sine wave is divided into two parts. Because the damping parameter α is zero for a sine wave component, the sine wave component can be expressed as the following equation (factor 17): fs(n) = Asin(anT+φ), η = 0,1,2.........(factor 17) and the equation (where) has three unknowns, so the signal is generated. Unit 13 will form a group of simultaneous data based on three consecutive data. Equation (factor 18) fs (n) = A sin(ffi»nr + φ) (^ 1)= Asin(iy(w -1)77+^) fs(n-2) = A sin(a(n - 2) T+φ)•...·(F.18) This equation group (F_l8) can be regarded as a set of nonlinear simultaneous equations as shown in the equations. Therefore, the following matrix can be expressed as follows: [ω Λ ^]Γ .....(F.19)
F = [j(n) Xn-1) y{n-2)f .•…(F.20) F(X) = [/5W Λ(«-1) /s(»-2)f (F.21) 3/s(n) dfs(n) dfs(n) dw dA Βφ a/s(n-l) a/s(n-l) 3Λ(η-1) da dA 3/s(n-2) 9/i(w-2) d〇) dA d(/> (F.22) J(X) = 其中 方程式（F.22)為一個三階價可比矩陣。 將方程式（F_19)~(F·22)代入到方程式（F_5)中，然後該運算 11 量之對應的參數<3 201040744 單元15執行疊代運算以計算出該弦波分F = [j(n) Xn-1) y{n-2)f .•...(F.20) F(X) = [/5W Λ(«-1) /s(»-2)f (F .21) 3/s(n) dfs(n) dfs(n) dw dA Βφ a/s(nl) a/s(nl) 3Λ(η-1) da dA 3/s(n-2) 9/ i(w-2) d〇) dA d(/> (F.22) J(X) = where equation (F.22) is a third-order comparable matrix. Equation (F_19)~(F·22 Substituting into the equation (F_5), and then the corresponding parameter of the operation 11 <3 201040744 unit 15 performs an iterative operation to calculate the string division
A 指數分量之分析 因為對於—指數分量其角速度參數4零，所以該指數 分量可表示為如下之方程式（F23): fE(n) = A'e~anT, « = 0,1,2,... . (F 23) 比車义方程式（F.11)，當角速度历為零時，相位《只會成為 W或1/2，使得方程式㈣）中_成為丄或心。該值與方程 式（F.11)中的A相乘可得一乘積A，。 方程式（F.23)中具有二個未知數，因此，該信號產生單 元13會根據連續二筆資料以形成一組聯立方程式（厂以）：The analysis of the A exponential component is because the angular velocity parameter of the exponential component is zero, so the exponential component can be expressed as the following equation (F23): fE(n) = A'e~anT, « = 0,1,2,. . . . (F 23) Compared with the car meaning equation (F.11), when the angular velocity is zero, the phase "will only become W or 1/2, so that the equation (4)) becomes 丄 or heart. This value is multiplied by A in equation (F.11) to obtain a product A. There are two unknowns in equation (F.23). Therefore, the signal generating unit 13 will form a set of simultaneous equations based on two consecutive data:
fE(n) = A'e~anT fE{n~l) = A'e~ain~l)T 該方程式組（F·24)可以視為一組如同方程式（F S)所示之非 線性的聯立方程式組，因此，可以如下之矩陣式表示如下 X=[a A'f ..…(厂25) F = [;y(n) y(n-l)f •…·(R26) J(X) = da da dA' dA'~ (F.28) 其中，方程式（F·28)為一個二階價可比矩陣。 將方程式（F.25)~(F.28)代入到方程式（F·5)中，然後該運算 單元15執行疊代運算以計算出該指數分量之對應的參數^ 12 201040744 、4。 由上可知，該運算單元15之矩陣建立模組151會根據 不同分量型式所對應的價可比矩陣方程式（綱、㈣或 (8)刀別針對-指數分量建立一個二階價可比矩陣，針 對^，波分量建立一個三階價可比矩陣，及針對一指數弦 、曰建立個四階價可比矩陣。然後，該矩陣建立模組 ^將組口其所有分量的價可比矩陣以建立-大小為ΛΓχ/ξ：的 賈了比矩陣，即根據&個二階價可比矩陣和[2個四階價 0 可比矩陣就可以組合出一足階價可比矩陣。 然後，該矩陣運算模組152對該z階價可比矩陣進行行 列式運算，若是該尤階價可比矩陣的行列式值不為0時，表 不一開始假設接近頻率刻度〇的分量是由一指數分量所構 成及所有遠離頻率刻度0的分量都是一指數弦波分量所構 成疋成立的。但若是該[階價可比矩陣的行列式值為0時， 表不該/i:階價可比矩陣中有參數是相依的，因此，將所有分 量中最接近0的一阻尼參數α設定為〇之後，將該尺階價可 Ο 比矩陣降一階為一足-1階價可比矩陣，換句話說，將原本尺 階價可比矩陣的變數數量及矩陣大小減一之後，形成一尤·i 階價可比矩陣。 然後，該參數運算模組153根據該阻尼值被設定為〇 的分量所對應的聯立方程式（凡切、（F⑻或（F抑，重新計算 並更新該等參數，再根據方程式（F·6)計算出一誤差值，即第 V次疊代所計算出的：Ϊ值與前一次疊代所計算出的X值之差 ’並將該誤差值送出至該誤差判定模組154,當該誤差已小 13 201040744 於一預設於該誤差判定模組154内之誤差門檻值時，該誤 差判疋模組154將停止該參數運算模組〗53，並重設該運算 單元15以重新擷取下一長度為尤的取樣信號；或是當該參 數運算模組153執行疊代運算的次數已達到一預設於該誤 差判定模組154内之上限值時，該誤差判定模組154亦將 停止該參數運算模組153,並重設該運算單元15以重新擷 取下一長度為尤的取樣信號，若是上述條件不成立，則該運 算單元15以計算出該等參數值作為下一次疊代運算時的初 始值，然後再重新計算該尤4階價可比矩陣的行列式值。 最後，該運算處理器15將該取樣信號^⑻中所有資料 運算完成之後，最終運算結果之該等信號參數被輸出至該 載體16以顯示或是儲存之。值得一提的是，當一指數弦波 分量的阻尼參數α因為最接近0而被設定為〇之後，該指數 弦波分量就變成一弦波分量，同理，若是一指數分量的阻 尼參數α因為最接近〇而被設定為〇之後，該指數分量就變 成一常數分量。 延續圖2之範例來加以說明，因為該信號處理器13設 定該序列長度參數ϋ：為18，因此，該運算單元15每次都從 該模擬信號/(Χ，η)中擷取18筆資料進行運算，首先，該矩陣 建立模組151依據該模擬信號中的五個分量，分別設定對 應的五個價可比矩陣，依照前述的說明，該第一 为量為—指數分量’所以該第一價可比矩陣/JX)為一個二階 價可比矩陣’而其他四個分量皆被預設為一指數弦波分量 ’因此，該第二~第五價可比矩陣乃^)〜以幻皆為一個四階 14 201040744 價可比矩陣，隨後，該矩陣運算模組152將五個價可比矩 陣~ J5(X)依序組合成一大小為18幻8的18階價可比矩陣 ’並計算該18階價可比矩陣的行列式值，當該18階價可 比矩陣的行列式值不為〇時’表示該第一分量的確是指數 分量且其餘分量皆為指數弦波分量’反之，當該18階價可 比矩陣的行列式值為〇時，此時，將五個分量中最小的阻 尼參數設定為0，並移除掉在該18階價可比矩陣中與該阻 尼參數相關的矩陣元素’因此，該18階價可比矩陣會降階 0 為一 17階價可比矩陣’然後再重新計算該17階價可比矩 陣的行列式值，依此類推，持續降階至該行列式值不為〇 時，因此，以本範例來說，最大的可能就是五個分量的阻 尼參數皆一—被移除之後，職—13階價可比矩陣，換句 話說，該模擬信冑肌„)的五個分量的形式變為一常數分量 及四個弦波分量。 此外，本發明之信號分析裝置亦可以軟體方式來實現 相關的電腦程式產品，例如將該信號轉換單元12、信號處 〇 自單7" 13、信號產生單元…及該運算單it 15的功能設 十成相關的程式之後，輪入至一具備電腦處理能力的硬體 裝置^如：一電力分析儀等，並藉由其硬體裝置上的電腦 進行程式處理之後，可以β ^ 以進仃前述信號參數的分析及運算 動作，並且最終可以將分姓 _ , x 析〜果輸出至一載體16(如：一 電力分析儀中的顯示器）上。 知上所述，本發明之 之佗諕分析裝置，可以處理一 中不同分量的參數分析，…… 说 無淪疋具有單一種分量或是具有 15 201040744 複數種分量的信號，皆可得到較習知計算方式更快速的計 算速度以獲得對應的分析結果，此外，因為本實施例之信 號分析裝置可以針對每個分量進行獨立的分析因此可以 大幅提升該分量分析結果的準確度，同時，藉由模組化設 s十降低设計成本’故確實能達成本發明之目的。 惟以上所述者，僅為本發明之較佳實施例而已，當不 能以此限定本發明實施之範圍，即大凡依本發明申請專利 範圍及發明說明内容所作之簡單的等效變化與修飾，皆仍 屬本發明專利涵蓋之範圍内。 【圖式簡單說明】 圖1是本發明之一較佳實施例之系統方塊圖；及 圖2是本發明之一信號的頻譜分析示意圖。 16 201040744 【主要元件符號說明】 11" ......取樣器 15 1 * …“ * *矩陣建立模組 12 …. ......信號轉換單元 152…… 。矩陣運算模組 13"*' ……信號處理單元 153""" •參數運算模組 14… ……信號產生單元 154"**" ，誤差判定模組 15 * * *1 ……運算單元 1 -載體fE(n) = A'e~anT fE{n~l) = A'e~ain~l)T This equation group (F·24) can be regarded as a set of nonlinearities as shown by equation (FS) The simultaneous equations, therefore, can be expressed as follows: X = [a A'f ..... (Factory 25) F = [; y (n) y (nl) f • ... (R26) J (X = da da dA' dA'~ (F.28) where equation (F·28) is a second-order valence comparable matrix. The equations (F.25) to (F.28) are substituted into the equation (F·5), and then the arithmetic unit 15 performs an iterative operation to calculate the corresponding parameter ^ 12 201040744 , 4 of the exponential component. As can be seen from the above, the matrix building module 151 of the computing unit 15 establishes a second-order valence matrix for the valence matrix equation (class, (4), or (8) knives for the different component types, for ^, The wave component establishes a third-order valence comparable matrix, and establishes a fourth-order valence comparable matrix for an exponential chord and 曰. Then, the matrix establishment module ^ sets the valence comparable matrix of all components of the group to establish-size ΛΓχ/ ξ:Jia has a ratio matrix, that is, according to & a second-order comparable matrix and [2 fourth-order valence 0 comparable matrices, a one-step valence comparable matrix can be combined. Then, the matrix operation module 152 selects the z-order valence The determinant operation is performed on the comparable matrix. If the determinant value of the comparable order matrix is not 0, the table assumes that the component close to the frequency scale 〇 is composed of an exponential component and all components far from the frequency scale 0 are It is formed by an exponential sine wave component. However, if the determinant value of the valence matrix is 0, the table should not be /i: the order price is dependent on the parameters in the matrix, therefore, After a damping parameter α closest to 0 in the component is set to 〇, the first-order valence ratio can be reduced by one order to a one-and-one-order comparable matrix, in other words, the variable of the original scalar comparable matrix After the quantity and the matrix size are decremented by one, a special matrix of the i-i order is formed. Then, the parameter operation module 153 is set to the simultaneous equation corresponding to the component of the 根据 according to the damping value (F(8) or (F(8) or ( F, recalculate and update the parameters, and then calculate an error value according to the equation (F·6), which is calculated by the Vth iteration: the Ϊ value and the X value calculated by the previous iteration. And the error value is sent to the error determination module 154. When the error is small 13 201040744 in an error threshold preset in the error determination module 154, the error determination module 154 will stop. The parameter operation module 〖53, and resets the operation unit 15 to recapture the sampling signal of the next length; or when the parameter operation module 153 performs the iteration operation has reached a preset error When the upper limit value in the module 154 is determined, the The difference determination module 154 will also stop the parameter operation module 153, and reset the operation unit 15 to recapture the sampling signal of the next length. If the above condition is not satisfied, the operation unit 15 calculates the parameters. The value is used as the initial value of the next iterative operation, and then the determinant value of the comparable 4th order comparable matrix is recalculated. Finally, the arithmetic processor 15 completes all the data in the sampled signal ^(8), and finally performs the operation. The resulting signal parameters are output to the carrier 16 for display or storage. It is worth mentioning that after the damping parameter α of an exponential sine wave component is set to 〇 because it is closest to 0, the exponential sine wave The component becomes a sine wave component. Similarly, if the damping parameter α of an exponential component is set to 〇 because it is closest to 〇, the exponential component becomes a constant component. Continuing with the example of FIG. 2, since the signal processor 13 sets the sequence length parameter ϋ: 18, the arithmetic unit 15 extracts 18 data from the analog signal /(Χ,η) each time. Performing an operation, first, the matrix establishing module 151 respectively sets corresponding five valence comparable matrices according to five components in the analog signal. According to the foregoing description, the first amount is an exponential component, so the first The price comparable matrix /JX) is a second-order comparable matrix' and the other four components are all preset to an exponential sine wave component. Therefore, the second to fifth price comparable matrices are ^)~ The order 14 201040744 is a comparable matrix. Subsequently, the matrix operation module 152 sequentially combines the five valence comparable matrices ~ J5(X) into an 18-order comparable matrix of size 18 and selects the 18-order comparable matrix. The determinant value, when the determinant value of the 18-order comparable matrix is not ', 'represents that the first component is indeed an exponential component and the remaining components are all exponential sine wave components', whereas when the 18-order valence matrix is comparable When the determinant value is 〇, The minimum damping parameter of the five components is set to 0, and the matrix element associated with the damping parameter in the 18-order comparable matrix is removed. Therefore, the 18-order comparable matrix is reduced by 0. The 17th order comparable matrix 'then recalculates the determinant value of the 17th order comparable matrix, and so on, and continues to downgrade until the determinant value is not ,, so, in this example, the biggest possibility is The damping parameters of the five components are all one—after being removed, the position of the job- 13-order comparable matrix, in other words, the five components of the analog letter-folding muscle „) becomes a constant component and four sine wave components. In addition, the signal analysis device of the present invention can also implement related computer program products in a software manner, for example, the signal conversion unit 12, the signal from the single 7" 13, the signal generating unit, and the function of the operation unit it 15 After setting up a 10% related program, it is rotated into a hardware device with computer processing capability, such as a power analyzer, and processed by a computer on its hardware device. The analysis and operation of the foregoing signal parameters are performed, and finally, the surname _, x is extracted to a carrier 16 (such as a display in a power analyzer). As described above, the present invention佗諕Analytical device can process the parameter analysis of different components in a different area.... It can be obtained with a single component or a signal with 15 201040744 complex components, which can get faster calculation speed than the conventional calculation method. The corresponding analysis result is obtained. In addition, since the signal analysis device of the embodiment can perform independent analysis for each component, the accuracy of the component analysis result can be greatly improved, and at the same time, the design is reduced by modularizing The cost 'is indeed the object of the invention. The above is only the preferred embodiment of the present invention, and the scope of the invention is not limited thereto, that is, the simple equivalent changes and modifications made by the scope of the invention and the description of the invention are All remain within the scope of the invention patent. BRIEF DESCRIPTION OF THE DRAWINGS FIG. 1 is a block diagram of a system according to a preferred embodiment of the present invention; and FIG. 2 is a schematic diagram of spectrum analysis of a signal of the present invention. 16 201040744 [Explanation of main component symbols] 11" ...... Sampler 15 1 * ... " * * Matrix building module 12 .... ... signal conversion unit 152 .... Matrix operation module 13 "*' ......Signal Processing Unit 153""" Parameter Operation Module 14... Signal Generation Unit 154"**", Error Determination Module 15 * * *1 ... Operation Unit 1 - Carrier
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