wordpress文章html頁面,廣州品牌seo推廣,網(wǎng)站建設(shè)費(fèi)用價(jià)格,網(wǎng)站設(shè)計(jì)常用軟件都有哪些MATLAB環(huán)境下一維時(shí)間序列信號(hào)的同步壓縮小波包變換 算法運(yùn)行環(huán)境為MATLAB R2018A#xff0c;執(zhí)行一維時(shí)間序列信號(hào)的同步壓縮小波包變換#xff0c;并給出了模擬信號(hào)和實(shí)際信號(hào)的例子。 算法可遷移至金融時(shí)間序列#xff0c;地震信號(hào)#xff0c;語音信號(hào)#xff0c;聲信號(hào)…MATLAB環(huán)境下一維時(shí)間序列信號(hào)的同步壓縮小波包變換 算法運(yùn)行環(huán)境為MATLAB R2018A執(zhí)行一維時(shí)間序列信號(hào)的同步壓縮小波包變換并給出了模擬信號(hào)和實(shí)際信號(hào)的例子。 算法可遷移至金融時(shí)間序列地震信號(hào)語音信號(hào)聲信號(hào)生理信號(hào)等一維時(shí)間序列信號(hào)。 % Inputs % x input signal, a vector of length N % % Optional Inputs % is_real Type of the transform % 0: complex-valued wave packets % 1: real-valued wave packets % [default set to 0] % is_unif whether x is sampled on a uniform grid % 0: No; 1: Yes % typeNUFFT 1: NUFFT by Air Force Lab % 2: USFFT by E. Candes % 3: NUFFT by L. Greengard and J.-Y. Lee % 4: Direct non-uniform Fourier Transform % xo non-uniform locations at which x is measured % NG number of subsampled points in time % [R_low R_high] The range of interested spectrum % rad a parameter to adjust the size of supports of the mother wave packet in % the frequency domain, rad 2. % is_cos Type of the window function % 0: C^infinity window function % 1: cosine window function % [default set to 0] % t_sc scaling parameter for radius % [default set to 1-1/4] % red redundancy parameter, red is a positive integer % [default set to 1] % epsl threshold for instantaneous frequency estimates % [default set to 1e-2] % h frequency band width per pixel in the synchrosqueezed % time-frequency representation % [default set to 1] % is_fac 0: do not increase the magnitude of high frequency wave % packet coefficients; 1: increase; % [default set to 1, better to visualize high frequency % instantaneous frequencies] % wedge_length_coarse % length of coarsest wedge % [default set to 4] % % Outputs % T_f 1D synchrosqueezed wave packet transform, a matrix with NG col在 MATLAB R2018A 這個(gè)強(qiáng)大的環(huán)境下我們可以實(shí)現(xiàn)一維時(shí)間序列信號(hào)的同步壓縮小波包變換。這種變換有著廣泛的應(yīng)用場景像金融時(shí)間序列、地震信號(hào)、語音信號(hào)、聲信號(hào)以及生理信號(hào)等一維時(shí)間序列信號(hào)都能通過該算法進(jìn)行處理分析。算法輸入?yún)?shù)詳解先來看下算法的輸入?yún)?shù)這是理解和運(yùn)用該算法的關(guān)鍵。% Inputs % x input signal, a vector of length N這里的x就是我們要處理的輸入信號(hào)它是一個(gè)長度為N的向量。比如我們生成一個(gè)簡單的模擬信號(hào)N 1000; t linspace(0, 1, N); x sin(2*pi*50*t) sin(2*pi*120*t);上述代碼生成了一個(gè)包含兩個(gè)不同頻率正弦波疊加的信號(hào)x時(shí)長為 1 秒采樣點(diǎn)數(shù)為 1000。再看看可選輸入?yún)?shù)% Optional Inputs % is_real Type of the transform % 0: complex-valued wave packets % 1: real-valued wave packets % [default set to 0]is_real用于設(shè)置變換類型0 代表復(fù)數(shù)形式的小波包1 則是實(shí)數(shù)形式的小波包默認(rèn)是 0。如果我們處理的信號(hào)特性更適合實(shí)數(shù)形式的小波包分析就可以將其設(shè)為 1。% is_unif whether x is sampled on a uniform grid % 0: No; 1: Yesis_unif表示信號(hào)x是否在均勻網(wǎng)格上采樣1 為是0 為否。像我們剛剛生成的x信號(hào)使用linspace函數(shù)生成的時(shí)間向量t對(duì)應(yīng)的采樣就是均勻的所以這個(gè)參數(shù)可設(shè)為 1。% typeNUFFT 1: NUFFT by Air Force Lab % 2: USFFT by E. Candes % 3: NUFFT by L. Greengard and J.-Y. Lee % 4: Direct non-uniform Fourier TransformtypeNUFFT用于選擇非均勻快速傅里葉變換NUFFT的類型有來自空軍實(shí)驗(yàn)室的、E. Candes 的 USFFT 等多種選擇。不同類型在計(jì)算效率和精度上可能有所差異要根據(jù)具體需求選擇。% xo non-uniform locations at which x is measured % NG number of subsampled points in time % [R_low R_high] The range of interested spectrum % rad a parameter to adjust the size of supports of the mother wave packet in % the frequency domain, rad 2. % is_cos Type of the window function % 0: C^infinity window function % 1: cosine window function % [default set to 0] % t_sc scaling parameter for radius % [default set to 1-1/4] % red redundancy parameter, red is a positive integer % [default set to 1] % epsl threshold for instantaneous frequency estimates % [default set to 1e-2] % h frequency band width per pixel in the synchrosqueezed % time-frequency representation % [default set to 1] % is_fac 0: do not increase the magnitude of high frequency wave % packet coefficients; 1: increase; % [default set to 1, better to visualize high frequency % instantaneous frequencies] % wedge_length_coarse % length of coarsest wedge % [default set to 4]這些參數(shù)分別從非均勻采樣位置、子采樣點(diǎn)數(shù)、感興趣頻譜范圍、小波包頻域支撐大小調(diào)整、窗函數(shù)類型、半徑縮放參數(shù)、冗余參數(shù)、瞬時(shí)頻率估計(jì)閾值、同步壓縮時(shí)頻表示中每個(gè)像素的頻帶寬度、高頻小波包系數(shù)幅度處理方式以及最粗楔形長度等方面對(duì)算法進(jìn)行精細(xì)化控制。輸出結(jié)果% Outputs % T_f 1D synchrosqueezed wave packet transform, a matrix with NG col算法的輸出T_f是一維同步壓縮小波包變換的結(jié)果是一個(gè)具有NG列的矩陣。這個(gè)矩陣包含了經(jīng)過變換后信號(hào)在不同頻率和時(shí)間尺度上的信息通過對(duì)它的進(jìn)一步分析我們就能挖掘出信號(hào)中的關(guān)鍵特征。實(shí)際應(yīng)用示例以語音信號(hào)處理為例假設(shè)我們有一個(gè)語音信號(hào)文件speech.wav可以這樣讀取并處理[x, fs] audioread(speech.wav); % 假設(shè)這里語音信號(hào)是單聲道若為立體聲需進(jìn)一步處理 is_unif 1; typeNUFFT 1; % 設(shè)置其他參數(shù)... T_f synchrosqueezed_wavelet_packet_transform(x, is_unif, typeNUFFT,...);通過這樣的處理我們就可以利用同步壓縮小波包變換對(duì)語音信號(hào)進(jìn)行時(shí)頻分析比如提取語音中的不同頻率成分隨時(shí)間的變化這對(duì)于語音識(shí)別、降噪等應(yīng)用有著重要意義。在金融時(shí)間序列分析中同樣可以運(yùn)用該算法。比如分析股票價(jià)格的波動(dòng)將股票價(jià)格隨時(shí)間的序列作為輸入信號(hào)x通過調(diào)整合適的參數(shù)就能從變換結(jié)果T_f中發(fā)現(xiàn)價(jià)格波動(dòng)在不同時(shí)間尺度和頻率上的特征為投資決策提供參考依據(jù)。總之MATLAB 環(huán)境下的一維時(shí)間序列信號(hào)同步壓縮小波包變換算法憑借其豐富可調(diào)節(jié)的參數(shù)和廣泛的適用性在眾多領(lǐng)域都有著巨大的應(yīng)用潛力值得我們深入探索和研究。