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1<html><head><title>ezfft (Ezyfit Toolbox)</title>
2<!-- Help file for ezfft.m generated by makehtmldoc 1.22, 02-Jul-2012 09:32:07 -->
3<!-- makehtmldoc (F. Moisy, 2005-2006), see http://www.fast.u-psud.fr/~moisy/ml/ -->
4 
5<link rel=stylesheet href="docstyle1.css" type="text/css">
6</head>
7<body bgcolor=#ffffff>
8<table width="100%" border=0 cellpadding=0 cellspacing=0><tr><td valign=baseline bgcolor="#e7ebf7"><b>EzyFit Function Reference</b></td><td valign=baseline bgcolor="#e7ebf7" align=right><a href="evalfit.html"><b>&lt;&lt; Prev</b></a>&nbsp;|&nbsp;<a href="ezfit.html"><b>Next &gt;&gt;</b></a>&nbsp;</td></tr></table>
9<font size=+3 color="#990000">ezfft</font><br>
10Easy to use Power Spectrum<br>
11<br>
12 
13<font size=+1 color="#990000"><b>Description</b></font>
14<code><pre>
15<b>ezfft</b>(T,U) plots the power spectrum of the signal U(T) , where T is a
16'time' and U is a real signal (T can be considered as a space
17coordinate as well). If T is a scalar, then it is interpreted as the
18'sampling time' of the signal U.  If T is a vector, then it is
19interpreted as the 'time' itself. In this latter case, T must be
20equally spaced (as obtained by LINSPACE for instance), and it must
21have the same length as U. If T is not specified, then a 'sampling
22time' of unity (1 second for instance) is taken. Windowing
23(appodization) can be applied to reduce border effects (see below).
24 
25[W,E] = <b>ezfft</b>(T,U) returns the power spectrum E(W), where E is the
26energy density and W the pulsation 'omega'.  W is *NOT* the frequency:
27the frequency is W/(2*pi). If T is considered as a space coordinate,
28W is a wave number (usually noted K = 2*PI/LAMBDA, where LAMBDA is a
29wavelength).
30 
31<b>ezfft</b>(..., 'Property1', 'Property2', ...) specifies the properties:
32 'hann'    applies a Hann appodization window to the data (reduces
33           aliasing).
34 'disp'    displays the spectrum (by default if no output argument)
35 'freq'    the frequency f is displayed instead of the pulsation omega
36           (this applies for the display only: the output argument
37           remains the pulsation omega, not the frequency f).
38 'space'   the time series is considered as a space series. This simply
39           renames the label 'omega' by 'k' (wave number) in the plot,
40           but has no influence on the computation itself.
41 'handle'  returns a handle H instead of [W,E] - it works only if the
42           properties 'disp' is also specified. The handle H is useful
43           to change the line properties (color, thickness) of the
44           plot (see the example below).
45 
46The length of the vectors W and E is N/2, where N is the length of U
47(this is because U is assumed to be a real signal.) If N is odd, the
48last point of U and T are ignored. If U is not real, only its real part
49is considered.
50 
51    W(1) is always 0.  E(1) is the energy density of the average of U
52      (when plotted in log coordinates, the first point is W(2), E(2)).
53    W(2) is the increment of pulsation, Delta W, given by 2*PI/Tmax
54    W(end), the highest measurable pulsation, is PI/DT, where DT is the
55       sampling time (Nyquist theorem).
56 
57Parseval Theorem (Energy conservation):
58For every signal U, the 'energy' computed in the time domain and in the
59frequency domain are equal,
60    MEAN(U.^2) == SUM(E)*W(2)
61where W(2) is the pulsation increment Delta W.
62Note that, depending on the situation considered, the physical 'energy'
63is usually defined as 0.5*MEAN(U.^2). Energy conservation only applies
64if no appodization of the signal (windowing) is used. Otherwise, some
65energy is lost in  the appodization, so the spectral energy is lower
66than the actual one.
67 
68As for FFT, the execution time depends on the length of the signal.
69It is fastest for powers of two.
70 
71</pre>
72<font size=+1 color="#990000"><b>Example</b></font>
73<pre>
74  simple display of a power spectrum
75   t = linspace(0,400,2000);
76   u = 0.2 + 0.7*sin(2*pi*t/47) + cos(2*pi*t/11);
77   <b>ezfft</b>(t,u);
78 
79</pre>
80<font size=+1 color="#990000"><b>Example</b></font>
81<pre>
82  how to change the color of the plot
83   h = <b>ezfft</b>(t,u,'disp','handle');
84   set(h,'Color','red');
85 
86</pre>
87<font size=+1 color="#990000"><b>Example</b></font>
88<pre>
89  how to use the output of <b>ezfft</b> 
90   [w,e] = <b>ezfft</b>(t,u,'hann');
91   loglog(w,e,'b*');
92 
93</pre>
94<font size=+1 color="#990000"><b>See Also</b></font>
95<pre>
96FFT
97 
98Published output in the Help browser
99   showdemo <b>ezfft</b> 
100</pre></code>
101 
102<br>
103<table width="100%" border=0 cellspacing=0 bgcolor="#e7ebf7"><tr><td>&nbsp;<a href="evalfit.html"><b>Previous: evalfit</b></a></td><td align=right><a href="ezfit.html"><b>Next: ezfit</b></a>&nbsp;</td></tr></table><br>
1042005-2012 <a href="ezyfit.html">EzyFit Toolbox 2.41</a><br>
105<br>
106</body></html>
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