added deadtime and calculation of overall uncertainty

package/propagateSysUncToFreqDomain.m

@@ -60,21 +60,21 @@ defaultHys = 0;
 defaultFreq = [];
 
 p = inputParser;
-validScalarPosNum = @(x) isnumeric(x) && (x > 0);
+validScalarPosNum = @(x) isnumeric(x) && (x >= 0);
 
 addOptional(p, 'bias', defaultBias, validScalarPosNum);
-addOptional(p, 'slope', defaultSlope, validScalarPosNum);
-addOptional(p, 'lin', defaultLin, validScalarPosNum);
-addOptional(p, 'hys', defaultHys, validScalarPosNum);
+addOptional(p, 'sensitivity', defaultSlope, validScalarPosNum);
+addOptional(p, 'linearity', defaultLin, validScalarPosNum);
+addOptional(p, 'hysteresis', defaultHys, validScalarPosNum);
 addOptional(p, 'excitation_frequency', defaultFreq, validScalarPosNum)
 
 parse(p, varargin{:})
 
 %% Generate the uncertainty data structure with the given input arguments
 data.uncertainty.systematic.bias = p.Results.bias;
-data.uncertainty.systematic.slope = p.Results.slope;
-data.uncertainty.systematic.lin = p.Results.lin;
-data.uncertainty.systematic.hys = p.Results.hys;
+data.uncertainty.systematic.slope = p.Results.sensitivity;
+data.uncertainty.systematic.lin = p.Results.linearity;
+data.uncertainty.systematic.hys = p.Results.hysteresis;
 result_struct.excitation_frequency = p.Results.excitation_frequency;
 
 %% Pre Process the data
@@ -107,11 +107,14 @@ result_struct.number_of_cycles = getNumberOfCycles(time_vector, result_struct.ex
 result_struct.FFT.N_data_points_in_FFT = length(result_struct.value_mean_vector);
 result_struct.FFT.value = fft(result_struct.value_mean_vector);
 
+% result_struct.FFT.N_data_points_in_FFT = length(value_vector);
+% result_struct.FFT.value = fft(value_vector);
+
 % Calculate the statistical uncertainty
 % TODO: Maybe also write a test for the statistical uncertainty
-temp_term1 = result_struct.value_standartdeviation_vector * tinv(1 - (0.05/2), result_struct.number_of_cycles-1);
-temp_term2 = (sqrt(result_struct.number_of_cycles))^2 * result_struct.FFT.N_data_points_in_FFT;
-data.uncertainty.statistical = sqrt(sum(temp_term1 / temp_term2));
+temp_term1 = result_struct.value_standartdeviation_vector * tinv(1 - (0.05/2), result_struct.number_of_cycles-1)/sqrt(result_struct.number_of_cycles);
+temp_term2 = result_struct.FFT.N_data_points_in_FFT;
+data.uncertainty.statistical = sqrt(sum(temp_term1.^2) / temp_term2);
 clearvars temp_term1 temp_term2
 
 % Scale coefficients of the FFT
@@ -135,6 +138,14 @@ clearvars temp_term1 temp_term2
     data.uncertainty.systematic.hys, ...
     result_struct.FFT.value);
 
+%% Calculate uncertainty rising from sampling rate
+% Asumption: the actually measured value can is inbetween two sample points 
+% therefore we ad an deadtime uncertainty of +- sampletime 
+% This affects only the phase of the measurement in frequency domain
+
+result_struct.FFT.uncertainty.deadtime.phase = 0.5*0.95*sampletime*2*pi*result_struct.FFT.frequencies;    
+result_struct.FFT.uncertainty.deadtime.absolute = 0*result_struct.FFT.frequencies;
+
 %% Calculate resulting overall uncertainty
 
 % random uncertainty
@@ -150,22 +161,35 @@ result_struct.FFT.uncertainty.statistical.phase(1) = 0;
 % sum up
 result_struct.FFT.uncertainty.absolute = sqrt(...
     result_struct.FFT.uncertainty.statistical.absolute.^2 +...
-    result_struct.FFT.uncertainty.systematic.absolute.^2 );
+    result_struct.FFT.uncertainty.systematic.absolute.^2 +...
+    result_struct.FFT.uncertainty.deadtime.absolute.^2);
 result_struct.FFT.uncertainty.phase = sqrt(...
     result_struct.FFT.uncertainty.statistical.phase.^2 +...
-    result_struct.FFT.uncertainty.systematic.phase.^2 );
-
-% conversion
-temp1=atan(result_struct.FFT.uncertainty.phase).*abs(result_struct.FFT.value);
-temp2= result_struct.FFT.uncertainty.absolute.*cos(angle(result_struct.FFT.value))+...
-    1i*result_struct.FFT.uncertainty.absolute.*sin(angle(result_struct.FFT.value));
-temp1=temp1.*cos(angle(result_struct.FFT.value)+pi/2)+...
-    1i*temp1.*sin(angle(result_struct.FFT.value)+pi/2);
-
-result_struct.FFT.uncertainty.complex = ...
-   abs(real(temp1))+abs(real(temp2))+...
-   1i*(abs(imag(temp1))+abs(imag(temp2)));
-clear temp1 temp2
+    result_struct.FFT.uncertainty.systematic.phase.^2 +...
+    result_struct.FFT.uncertainty.deadtime.phase.^2 );
+
+% conversion from abs and phase to real and imag (complex number)
+
+% Ansatz: gausian uncertaintypropagation
+result_struct.FFT.uncertainty.real = sqrt(cos(angle(result_struct.FFT.value)).^2.*result_struct.FFT.uncertainty.absolute.^2+...
+   abs(result_struct.FFT.value).^2.*sin(angle(result_struct.FFT.value)).^2.*result_struct.FFT.uncertainty.phase.^2);
+
+result_struct.FFT.uncertainty.imag = sqrt(sin(angle(result_struct.FFT.value)).^2.*result_struct.FFT.uncertainty.absolute.^2+...
+   abs(result_struct.FFT.value).^2.*cos(angle(result_struct.FFT.value)).^2.*result_struct.FFT.uncertainty.phase.^2);
+
+result_struct.FFT.uncertainty.complex = result_struct.FFT.uncertainty.real+1i*result_struct.FFT.uncertainty.imag;
+
+% Maximum estimation according to Rexer, not realy sutable
+% temp1=atan(result_struct.FFT.uncertainty.phase).*abs(result_struct.FFT.value);
+% temp2= result_struct.FFT.uncertainty.absolute.*cos(angle(result_struct.FFT.value))+...
+%     1i*result_struct.FFT.uncertainty.absolute.*sin(angle(result_struct.FFT.value));
+% temp1=temp1.*cos(angle(result_struct.FFT.value)+pi/2)+...
+%     1i*temp1.*sin(angle(result_struct.FFT.value)+pi/2);
+% 
+% result_struct.FFT.uncertainty.complex = ...
+%    abs(real(temp1))+abs(real(temp2))+...
+%    1i*(abs(imag(temp1))+abs(imag(temp2)));
+% clear temp1 temp2
 
 
 % Mapping

package/underlying_functions/calculateSysUncInFreqDomain.m

@@ -34,13 +34,13 @@ function [systematic_uncertainty_absolute, ...
 %   (not always given)* obtained from the data sheet of the sensor that was
 %   used for the measurement or from calibration protocols. 
 %   Use 0 if there isn't a given value for your sensor.  
-
+%
 %   -- sysunc_hysteresis  scalar (1-by-1) real number of type double that
 %   represents the *hysteresis* systematic uncertainty and can be
 %   *sometimes (not always given)* obtained from the data sheet of the
 %   sensor that was used for the measurement or from calibration protocols.
 %   Use 0 if there isn't a given value for your sensor.
-
+%
 %   -- FFT_Mean  FFT of the mean value vector of the "statistic
 %   oscillation".
 %
@@ -56,8 +56,12 @@ function [systematic_uncertainty_absolute, ...
 %   given sensor. 
 
 
-systematic_uncertainty_absolute = sysunc_bias + sysunc_slope + (0.608 * sysunc_linearity);
-systematic_uncertainty_phase = atan(0.681 * sysunc_hysteresis ./ abs(FFT_Mean));
+systematic_uncertainty_absolute = ones(1,length(FFT_Mean)).*...
+    ((0.95*sysunc_slope.*abs(FFT_Mean)) + (0.263 * sysunc_linearity));
+systematic_uncertainty_absolute(1) = (0.95*sysunc_bias) + (0.95*sysunc_slope.*abs(FFT_Mean(1))) + (0.263 * sysunc_linearity); 
+
+systematic_uncertainty_phase = atan(0.235 * sysunc_hysteresis ./ abs(FFT_Mean));
+systematic_uncertainty_phase (1) = 0;
 
 end