hilbert2 1.0

HILBERT2 Extract instantaneous envelope and frequency from a bandlimited signal via Hilbert transform. [ENV FREQ] = HILBERT2(X,FS), for vectors X, returns estimates of the instantaneous envelope and frequency. X is assumed to be a band-limited signal sampled at a rate specified by FS (in units of Hz). If FS is not specified, HILBERT2 uses a sampling rate of 1 Hz. If X is a matrix, HILBERT2 operates along the columns of X. If the input X is complex, then only the real part is used: X=real(X) HILBERT2 returns the magnitude (ENV) and rate of change of the argument (FREQ) of the complex analytic signal corresponding to X. For a theoretical explication of this techinque and the formulas employed here, see:Ktonas & Papp (1980) Instantaneous envelope and phase extraction from real signals. Signal Processing 2:373-385. Be sure to visualize your results, as this technique may produce distortions when estimating the instantaneous envelope and frequency at the edges of the waveform. EXAMPLE: Create signal Fs = 500; T = 10; N = Fs*T; t = linspace(0,T,N)'; g = 2*pi*3*t + 75*normcdf(t,5,1); A = 5 - 15*normpdf(t,5,1.5); x = A.*cos(g); Extract instantaneous envelope and frequency [env freq] = hilbert2(x,Fs); Plot results figure(1); clf; subplot(2,1,1) plot(t,x,'LineWidth',2); hold on plot(t,[env -env],'LineWidth',2,'Color',[0 1 0.5]) xlim([1 9]); ylabel('Signal amplitude') title('Original signal with instantaneous envelope') subplot(2,1,2); plot(t,freq,'k','LineWidth',2); axis([1 9 0 10]); xlabel('Time (sec)'); ylabel('Hz') title('Instantaneous frequency'); Created by Scott McKinney, October 2010 http://www.mathworks.com/matlabcentral/fileexchange/authors/110216 See also HILBERT

Requirements:	No special requirements
Platforms:	Matlab
Keyword:	2pi3t,  Acosg,  Create,  Distortions,  Edges,  Env Linewidth Color,  Estimating,  Figure,  Hilbert Xfs,  Linspace,  Normcdft,  Normpdft,  Plottenv,  Plottx Linewidth,  Produce,  Results,  Subplot,  Technique,  Waveform
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