function?varargout?=?vkf（yfsfpbwmultiorder）
%VKF?2nd?Generation?Vold-Kalman?Order?Filtering.
%???x?=?VKF（yfsf）?extracts?the?order?with?frequency?vector?f?from?signal?
%???y?with?samplerate?fs?using?a?2-pole?filter?with?a?-3dB?bandwidth?of?
%???1?percent?of?the?sample?rate.?The?output?is?a?single?waveform?x.
%
%???[...]?=?VKF（yfsfp）?uses?a?p-order?filter?（typically?between?1?or?4）.
%???Every?order?increases?the?roll-off?by?-40dB?per?decade.?By?specifying
%???additional?lower-order?coefficients?zero?boundary?conditions?are?
%???added.?For?instance:?p?=?[2?0?1]?applies?2nd?order?filtering?and
%???forces?the?envelope?amplitude?and?its?first?derivative?to?zero?at?t_1?
%???and?t_N.
%
%???[...]?=?VKF（yfsfpbw）?uses?a?bandwidth?in?Hertz?specified?by?bw.?If?
%???bw?is?a?scalar?a?constant?bandwidth?is?used;?if?bw?is?a?vector?with?
%???the?same?length?as?y?a?time-varying?instantaneous?bandwidth?is?
%???realised.
%
%???X?=?VKF（yfsF...）?with?[NK]?=?size（F）?performs?simultaneous?
%???extraction?of?K?orders?with?frequency?vectors?[f_1...f_K]?in?array?
%???F.?In?case?of?crossing?orders?this?method?tries?to?reveal?the?correct
%???order?amplitudes.?The?output?is?an?array?of?K?waveforms?[x_1...x_K].
%
%???X?=?VKF（yfsFpbw0）?switches?to?a?single-order?algorithm.?K?orders
%???are?still?extracted?but?the?single-order?algorithm?is?computationally
%???less?demanding.?This?is?suggested?for?high?sample?rates?and/or?long
%???timeseries.
%
%???[ac]?=?VKF（...）?returns?the?complex?envelope（s）?a?and?phasor（s）?c?
%???such?that?the?order?waveform（s）?can?be?reconstructed?by?x?=?real（a.*c）.
%
%???[acr]?=?VKF（...）?ouputs?an?additional?selectivity?vector?r?used?
%???to?realise?the?bandwidth?given?by?bw.
%
%???Note:?Filter?orders?>?4?usually?result?in?ill?conditioning?and?should?
%???be?avoided.?The?filter?bandwidth?determination?was?implemented?for?
%???arbitrary?order?but?was?not?verified?for?orders?higher?than?3.
%
%???Demo:
%???Calling?VKF?without?arguments?shows?a?small?demonstration?of?multi-
%???order?filtering?with?two?crossing?orders?in?the?presence?of?white?
%???noise.?Note?that?the?demo?uses?the?spectrogram?function?from?the?Signal
%???Processing?Toolbox.
%
%???Example:
%???????fs?=?4000;
%???????T?=?5;
%???????dt?=?1/fs;
%???????t?=?（0:dt:（T-dt））‘;
%???????N?=?numel（t）;
%?
%???????%?Instationary?component
%???????A1?=?[linspace（0.51floor（N/2））?linspace（10.5ceil（N/2））]‘;
%???????f1?=?0.2*fs?-?0.1*fs*cos（pi*t/T）;
%???????phi1?=?2*pi*cumsum（f1）*dt;
%???????y1?=?A1.*cos（phi1）;
%?
%???????%?Stationary?component
%???????A2?=?ones（N1）;
%???????f2?=?0.2*fs*ones（N1）;
%???????phi2?=?2*pi*cumsum（f2）*dt;
%???????y2?=?A2.*sin（phi2）;
%?
%???????%?White?noise
%???????e?=?2*rand（size（y1））;
%?
%???????%?Mixed?signal
%???????y?=?y1?+?y2?+?e;
%?
%???????%?Perform?VKF?on?periodic?components
%???????p?=?2;
%???????bw?=?1;
%???????[ac]?=?vkf（yfs[f1?f2]pbw）;
%???????x?=?real（a

?屬性????????????大小?????日期????時間???名稱
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?????文件????????8940??2013-05-03?15:16??vkf.m
?????文件????????1321??2014-02-12?14:24??license.txt