--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/m-toolbox/test/test_ao_diff.m	Wed Nov 23 19:22:13 2011 +0100
@@ -0,0 +1,90 @@
+clear all
+
+%% Make test AO
+fs    = 10;
+Nsecs = 10;
+a = ao(plist('waveform', 'sine wave', 'A', 1, 'f', .3, 'phi', 0, 'fs', fs, 'nsecs', Nsecs, 'yunits', 'm'));
+b = ao(plist('waveform', 'sine wave', 'A', 2*pi*0.3, 'f', .3, 'phi', 90, 'fs', fs, 'nsecs', Nsecs, 'yunits', 'm')); % Theoretical first derivative
+b2 = -1*((2*pi*0.3)^2).*a; % Theoretical second derivative
+
+%% Test first derivative
+c = diff(a, plist('method', '2POINT'));
+d = diff(a, plist('method', 'ORDER2'));
+e = diff(a, plist('method', 'ORDER2SMOOTH'));
+f = diff(a, plist('method', '3POINT'));
+g = diff(a, plist('method', '5POINT'));
+h = diff(a, plist('method', 'FPS', 'ORDER', 'FIRST', 'COEFF', -1/5));
+
+pl = plist('Legends', {'Original','2POINT','ORDER2','ORDER2SMOOTH','3POINT','5POINT','FPS PAR','Theory'},...
+  'Markers', {'x', 's', '^', 'p', '+', '<', 'o',''});
+iplot(a,c,d,e,f,g,h,b, pl)
+
+%% Use noise and measure TFs for First Derivatives
+
+Nsecs = 1000;
+
+a = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', Nsecs));
+b = diff(a, plist('method', '2POINT'));
+c = diff(a, plist('method', 'ORDER2'));
+d = diff(a, plist('method', 'ORDER2SMOOTH'));
+e = diff(a, plist('method', '3POINT'));
+f = diff(a, plist('method', '5POINT'));
+g = diff(a, plist('method', 'FPS', 'ORDER', 'FIRST', 'COEFF', -1/5));
+h = diff(a, plist('method', 'FPS', 'ORDER', 'FIRST', 'COEFF', 1/12));
+
+pl  = plist('Nfft', fs*100);
+tf1 = tfe(a,b,pl);
+tf2 = tfe(a,c,pl);
+tf3 = tfe(a,d,pl);
+tf4 = tfe(a,e,pl);
+tf5 = tfe(a,f,pl);
+tf6 = tfe(a,g,pl);
+tf7 = tfe(a,h,pl);
+
+freq = tf1(1,2).data.x;
+tfthy = 2.*pi.*1i.*freq;
+tfth = ao(fsdata(freq,tfthy));
+
+pl = plist('Legends', {'2POINT','ORDER2','ORDER2SMOOTH','3POINT',...
+  '5POINT', 'FPS PAR', 'FPS SER','Theory',});
+iplot(tf1(1,2), tf2(1,2), tf3(1,2), tf4(1,2), tf5(1,2), tf6(1,2), tf7(1,2), tfth, pl)
+
+%% Make test AO for second derivative
+
+fs    = 10;
+Nsecs = 10;
+a = ao(plist('waveform', 'sine wave', 'A', 1, 'f', .3, 'phi', 0, 'fs', fs, 'nsecs', Nsecs, 'yunits', 'm'));
+b = ao(plist('waveform', 'sine wave', 'A', 2*pi*0.3, 'f', .3, 'phi', 90, 'fs', fs, 'nsecs', Nsecs, 'yunits', 'm')); % Theoretical first derivative
+b2 = -1*((2*pi*0.3)^2).*a; % Theoretical second derivative
+
+%% Test second derivatives
+
+c = diff(a, plist('method', 'FPS', 'ORDER', 'SECOND', 'COEFF', 2/7));
+d = diff(a, plist('method', 'FPS', 'ORDER', 'SECOND', 'COEFF', -1/12));
+e = diff(a, plist('method', 'FPS', 'ORDER', 'SECOND', 'COEFF', 1/4));
+
+pl = plist('Legends', {'Original','FPS PAR','FPS SER','FPS PI','Theory'},...
+  'Markers', {'x', 'o', 's', '^', ''});
+iplot(a,c,d,e,b2, pl)
+
+%% Use noise and measure TFs for SECOND Derivatives
+
+Nsecs = 1000;
+
+a = ao(plist('tsfcn', 'randn(size(t))', 'fs', fs, 'nsecs', Nsecs));
+c = diff(a, plist('method', 'FPS', 'ORDER', 'SECOND', 'COEFF', 2/7));
+d = diff(a, plist('method', 'FPS', 'ORDER', 'SECOND', 'COEFF', -1/12));
+e = diff(a, plist('method', 'FPS', 'ORDER', 'SECOND', 'COEFF', 1/4));
+
+pl  = plist('Nfft', fs*100);
+
+tf1 = tfe(a,c,pl);
+tf2 = tfe(a,d,pl);
+tf3 = tfe(a,e,pl);
+
+freq = tf1(1,2).data.x;
+tfthy = abs((2.*pi.*1i.*freq).^2);
+tfth = ao(fsdata(freq,tfthy));
+
+pl = plist('Legends', {'Theory','FPS PAR', 'FPS PI', 'FPS SER',});
+iplot(tfth, tf1(1,2), tf3(1,2), tf2(1,2), pl)