Fertig
Dependencies: mbed
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GPA.cpp@3:769ce5f06d3e, 2018-04-09 (annotated)
- Committer:
- altb
- Date:
- Mon Apr 09 08:01:29 2018 +0000
- Revision:
- 3:769ce5f06d3e
- Parent:
- 0:78ca29b4c49e
- Child:
- 6:2cc56521aa16
Changes from pmic
Who changed what in which revision?
User | Revision | Line number | New contents of line |
---|---|---|---|
altb | 0:78ca29b4c49e | 1 | /* |
altb | 0:78ca29b4c49e | 2 | GPA: frequency point wise gain and phase analyser to measure the frequency |
altb | 3:769ce5f06d3e | 3 | respone of a dynamical system |
altb | 3:769ce5f06d3e | 4 | |
altb | 0:78ca29b4c49e | 5 | hint: the measurements should only be perfomed in closed loop |
altb | 0:78ca29b4c49e | 6 | assumption: the system is at the desired steady state of interest when |
altb | 0:78ca29b4c49e | 7 | the measurment starts |
altb | 3:769ce5f06d3e | 8 | |
altb | 0:78ca29b4c49e | 9 | exc(2) C: controller |
altb | 0:78ca29b4c49e | 10 | | P: plant |
altb | 3:769ce5f06d3e | 11 | v |
altb | 0:78ca29b4c49e | 12 | exc(1) --> o ->| C |--->o------->| P |----------> out |
altb | 0:78ca29b4c49e | 13 | ^ | | |
altb | 0:78ca29b4c49e | 14 | | --> inp | exc: excitation signal (E) |
altb | 0:78ca29b4c49e | 15 | | | inp: input plant (U) |
altb | 0:78ca29b4c49e | 16 | -------------------------------- out: output plant (Y) |
altb | 3:769ce5f06d3e | 17 | |
altb | 0:78ca29b4c49e | 18 | instantiate option 1: |
altb | 0:78ca29b4c49e | 19 | GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1) |
altb | 3:769ce5f06d3e | 20 | |
altb | 0:78ca29b4c49e | 21 | fMin: minimal desired frequency that should be measured in Hz |
altb | 0:78ca29b4c49e | 22 | fMax: maximal desired frequency that should be measured in Hz |
altb | 0:78ca29b4c49e | 23 | NfexcDes: number of logarithmic equaly spaced frequency points |
altb | 0:78ca29b4c49e | 24 | NperMin: minimal number of periods that are used for each frequency point |
altb | 3:769ce5f06d3e | 25 | NmeasMin: minimal number of samples that are used for each frequency point |
altb | 0:78ca29b4c49e | 26 | Ts: sampling time |
altb | 3:769ce5f06d3e | 27 | Aexc0: excitation amplitude at fMin |
altb | 0:78ca29b4c49e | 28 | Aexc1: excitation amplitude at fMax |
altb | 3:769ce5f06d3e | 29 | |
altb | 0:78ca29b4c49e | 30 | hints: the amplitude drops with 1/fexc, if you're using |
altb | 3:769ce5f06d3e | 31 | Axc1 = Aexc0/fMax then d/dt exc = const., this is recommended |
altb | 0:78ca29b4c49e | 32 | if your controller does not have a rolloff. |
altb | 0:78ca29b4c49e | 33 | if a desired frequency point is not measured try to increase Nmeas. |
altb | 3:769ce5f06d3e | 34 | |
altb | 3:769ce5f06d3e | 35 | pseudo code for a closed loop measurement with a controller C: |
altb | 3:769ce5f06d3e | 36 | |
altb | 0:78ca29b4c49e | 37 | excitation input at (1): |
altb | 3:769ce5f06d3e | 38 | |
altb | 3:769ce5f06d3e | 39 | - measuring the plant P and the closed loop tf T = PC/(1 + PC): |
altb | 3:769ce5f06d3e | 40 | desTorque = pi_w(omega_desired - omega + excWobble); |
altb | 3:769ce5f06d3e | 41 | inpWobble = desTorque; |
altb | 3:769ce5f06d3e | 42 | outWobble = omega; |
altb | 3:769ce5f06d3e | 43 | excWobble = Wobble(excWobble, outWobble); |
altb | 3:769ce5f06d3e | 44 | |
altb | 3:769ce5f06d3e | 45 | - measuring the controller C and the closed loop tf SC = C/(1 + PC) |
altb | 3:769ce5f06d3e | 46 | desTorque = pi_w(omega_desired - omega + excWobble); |
altb | 3:769ce5f06d3e | 47 | inpWobble = n_soll + excWobble - omega; |
altb | 3:769ce5f06d3e | 48 | outWobble = desTorque; |
altb | 3:769ce5f06d3e | 49 | excWobble = Wobble(inpWobble, outWobble); |
altb | 3:769ce5f06d3e | 50 | |
altb | 0:78ca29b4c49e | 51 | excitation input at (2): |
altb | 0:78ca29b4c49e | 52 | |
altb | 3:769ce5f06d3e | 53 | - measuring the plant P and the closed loop tf SP = P/(1 + PC): |
altb | 3:769ce5f06d3e | 54 | desTorque = pi_w(omega_desired - omega) + excWobble; |
altb | 3:769ce5f06d3e | 55 | inpWobble = desTorque; |
altb | 3:769ce5f06d3e | 56 | outWobble = omega; |
altb | 3:769ce5f06d3e | 57 | excWobble = Wobble(excWobble, outWobble); |
altb | 3:769ce5f06d3e | 58 | |
altb | 0:78ca29b4c49e | 59 | usage: |
altb | 3:769ce5f06d3e | 60 | exc(k+1) = myGPA(inp(k), out(k)) does update the internal states of the |
altb | 3:769ce5f06d3e | 61 | gpa at the timestep k and returns the excitation signal for the timestep |
altb | 3:769ce5f06d3e | 62 | k+1. the results are plotted to a terminal (putty) over a serial |
altb | 3:769ce5f06d3e | 63 | connection and look as follows: |
altb | 0:78ca29b4c49e | 64 | ----------------------------------------------------------------------------------------- |
altb | 0:78ca29b4c49e | 65 | fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y| |
altb | 0:78ca29b4c49e | 66 | ----------------------------------------------------------------------------------------- |
altb | 3:769ce5f06d3e | 67 | 1.000e+00 2.924e+01 -1.572e+00 1.017e+00 -4.983e-02 5.000e+00 1.739e-01 5.084e+00 |
altb | 3:769ce5f06d3e | 68 | |
altb | 0:78ca29b4c49e | 69 | in matlab you can use: |
altb | 0:78ca29b4c49e | 70 | dataNucleo = [... insert measurement data here ...]; |
altb | 0:78ca29b4c49e | 71 | g = frd(dataNucleo(:,2).*exp(1i*dataNucleo(:,3)), dataNucleo(:,1), Ts, 'Units', 'Hz'); |
altb | 0:78ca29b4c49e | 72 | gcl = frd(dataNucleo(:,4).*exp(1i*dataNucleo(:,5)), dataNucleo(:,1), Ts, 'Units', 'Hz'); |
altb | 3:769ce5f06d3e | 73 | |
altb | 0:78ca29b4c49e | 74 | if you're evaluating more than one measurement which contain equal frequency points try: |
altb | 0:78ca29b4c49e | 75 | dataNucleo = [dataNucleo1; dataNucleo2]; |
altb | 0:78ca29b4c49e | 76 | [~, ind] = unique(dataNucleo(:,1),'stable'); |
altb | 0:78ca29b4c49e | 77 | dataNucleo = dataNucleo(ind,:); |
altb | 3:769ce5f06d3e | 78 | |
altb | 0:78ca29b4c49e | 79 | autor: M.E. Peter |
altb | 3:769ce5f06d3e | 80 | */ |
altb | 0:78ca29b4c49e | 81 | |
altb | 0:78ca29b4c49e | 82 | #include "GPA.h" |
altb | 0:78ca29b4c49e | 83 | #include "mbed.h" |
altb | 0:78ca29b4c49e | 84 | #include "math.h" |
altb | 0:78ca29b4c49e | 85 | #define pi 3.1415927f |
altb | 0:78ca29b4c49e | 86 | |
altb | 0:78ca29b4c49e | 87 | using namespace std; |
altb | 0:78ca29b4c49e | 88 | |
altb | 0:78ca29b4c49e | 89 | GPA::GPA(float fMin, float fMax, int NfexcDes, int NperMin, int NmeasMin, float Ts, float Aexc0, float Aexc1) |
altb | 0:78ca29b4c49e | 90 | { |
altb | 0:78ca29b4c49e | 91 | this->NfexcDes = NfexcDes; |
altb | 0:78ca29b4c49e | 92 | this->NperMin = NperMin; |
altb | 0:78ca29b4c49e | 93 | this->NmeasMin = NmeasMin; |
altb | 0:78ca29b4c49e | 94 | this->Ts = Ts; |
altb | 0:78ca29b4c49e | 95 | |
altb | 0:78ca29b4c49e | 96 | // calculate logarithmic spaced frequency points |
altb | 0:78ca29b4c49e | 97 | fexcDes = (float*)malloc(NfexcDes*sizeof(float)); |
altb | 0:78ca29b4c49e | 98 | fexcDesLogspace(fMin, fMax, NfexcDes); |
altb | 0:78ca29b4c49e | 99 | |
altb | 0:78ca29b4c49e | 100 | // calculate coefficients for decreasing amplitude (1/fexc) |
altb | 0:78ca29b4c49e | 101 | this->aAexcDes = (Aexc1 - Aexc0)/(1.0f/fexcDes[NfexcDes-1] - 1.0f/fexcDes[0]); |
altb | 0:78ca29b4c49e | 102 | this->bAexcDes = Aexc0 - aAexcDes/fexcDes[0]; |
altb | 0:78ca29b4c49e | 103 | |
altb | 0:78ca29b4c49e | 104 | fnyq = 1/2.0f/Ts; |
altb | 0:78ca29b4c49e | 105 | pi2 = 2.0f*pi; |
altb | 0:78ca29b4c49e | 106 | pi2Ts = pi2*Ts; |
altb | 0:78ca29b4c49e | 107 | piDiv2 = pi/2.0f; |
altb | 0:78ca29b4c49e | 108 | |
altb | 0:78ca29b4c49e | 109 | sU = (float*)malloc(3*sizeof(float)); |
altb | 0:78ca29b4c49e | 110 | sY = (float*)malloc(3*sizeof(float)); |
altb | 0:78ca29b4c49e | 111 | reset(); |
altb | 0:78ca29b4c49e | 112 | } |
altb | 0:78ca29b4c49e | 113 | |
altb | 0:78ca29b4c49e | 114 | GPA::~GPA() {} |
altb | 0:78ca29b4c49e | 115 | |
altb | 0:78ca29b4c49e | 116 | void GPA::reset() |
altb | 0:78ca29b4c49e | 117 | { |
altb | 0:78ca29b4c49e | 118 | Nmeas = 0; |
altb | 0:78ca29b4c49e | 119 | Nper = 0; |
altb | 0:78ca29b4c49e | 120 | fexc = 0.0f; |
altb | 0:78ca29b4c49e | 121 | fexcPast = 0.0f; |
altb | 0:78ca29b4c49e | 122 | ii = 1; // iterating through desired frequency points |
altb | 0:78ca29b4c49e | 123 | jj = 1; // iterating through measurement points w.r.t. reachable frequency |
altb | 0:78ca29b4c49e | 124 | scaleG = 0.0f; |
altb | 0:78ca29b4c49e | 125 | cr = 0.0f; |
altb | 0:78ca29b4c49e | 126 | ci = 0.0f; |
altb | 0:78ca29b4c49e | 127 | for(int i = 0; i < 3; i++) { |
altb | 0:78ca29b4c49e | 128 | sU[i] = 0.0f; |
altb | 0:78ca29b4c49e | 129 | sY[i] = 0.0f; |
altb | 0:78ca29b4c49e | 130 | } |
altb | 0:78ca29b4c49e | 131 | sinarg = 0.0f; |
altb | 0:78ca29b4c49e | 132 | NmeasTotal = 0; |
altb | 0:78ca29b4c49e | 133 | Aexc = 0.0f; |
altb | 0:78ca29b4c49e | 134 | pi2Tsfexc = 0.0f; |
altb | 0:78ca29b4c49e | 135 | } |
altb | 0:78ca29b4c49e | 136 | |
altb | 0:78ca29b4c49e | 137 | float GPA::update(float inp, float out) |
altb | 0:78ca29b4c49e | 138 | { |
altb | 0:78ca29b4c49e | 139 | // a new frequency point has been reached |
altb | 0:78ca29b4c49e | 140 | if(jj == 1) { |
altb | 0:78ca29b4c49e | 141 | // get a new unique frequency point |
altb | 0:78ca29b4c49e | 142 | while(fexc == fexcPast) { |
altb | 0:78ca29b4c49e | 143 | // measurement finished |
altb | 0:78ca29b4c49e | 144 | if(ii > NfexcDes) { |
altb | 0:78ca29b4c49e | 145 | return 0.0f; |
altb | 0:78ca29b4c49e | 146 | } |
altb | 0:78ca29b4c49e | 147 | calcGPAmeasPara(fexcDes[ii - 1]); |
altb | 0:78ca29b4c49e | 148 | // secure fexc is not higher or equal to nyquist frequency |
altb | 0:78ca29b4c49e | 149 | if(fexc >= fnyq) { |
altb | 0:78ca29b4c49e | 150 | fexc = fexcPast; |
altb | 0:78ca29b4c49e | 151 | } |
altb | 0:78ca29b4c49e | 152 | // no frequency found |
altb | 0:78ca29b4c49e | 153 | if(fexc == fexcPast) { |
altb | 0:78ca29b4c49e | 154 | ii += 1; |
altb | 0:78ca29b4c49e | 155 | } else { |
altb | 0:78ca29b4c49e | 156 | Aexc = aAexcDes/fexc + bAexcDes; |
altb | 0:78ca29b4c49e | 157 | pi2Tsfexc = pi2Ts*fexc; |
altb | 0:78ca29b4c49e | 158 | } |
altb | 0:78ca29b4c49e | 159 | } |
altb | 3:769ce5f06d3e | 160 | // secure sinarg starts at 0 (numerically maybe not given) |
altb | 3:769ce5f06d3e | 161 | sinarg = 0.0f; |
altb | 0:78ca29b4c49e | 162 | // filter scaling |
altb | 0:78ca29b4c49e | 163 | scaleG = 1.0f/sqrt((float)Nmeas); |
altb | 0:78ca29b4c49e | 164 | // filter coefficients |
altb | 0:78ca29b4c49e | 165 | cr = cos(pi2Tsfexc); |
altb | 0:78ca29b4c49e | 166 | ci = sin(pi2Tsfexc); |
altb | 0:78ca29b4c49e | 167 | // filter storage |
altb | 0:78ca29b4c49e | 168 | for(int i = 0; i < 3; i++) { |
altb | 0:78ca29b4c49e | 169 | sU[i] = 0.0f; |
altb | 0:78ca29b4c49e | 170 | sY[i] = 0.0f; |
altb | 0:78ca29b4c49e | 171 | } |
altb | 0:78ca29b4c49e | 172 | } |
altb | 0:78ca29b4c49e | 173 | // filter step for signal su |
altb | 0:78ca29b4c49e | 174 | sU[0] = scaleG*inp + 2.0f*cr*sU[1] - sU[2]; |
altb | 0:78ca29b4c49e | 175 | sU[2] = sU[1]; |
altb | 0:78ca29b4c49e | 176 | sU[1] = sU[0]; |
altb | 0:78ca29b4c49e | 177 | // filter step for signal sy |
altb | 0:78ca29b4c49e | 178 | sY[0] = scaleG*out + 2.0f*cr*sY[1] - sY[2]; |
altb | 0:78ca29b4c49e | 179 | sY[2] = sY[1]; |
altb | 0:78ca29b4c49e | 180 | sY[1] = sY[0]; |
altb | 0:78ca29b4c49e | 181 | // measurement of frequencypoint is finished |
altb | 0:78ca29b4c49e | 182 | if(jj == Nmeas) { |
altb | 0:78ca29b4c49e | 183 | jj = 1; |
altb | 0:78ca29b4c49e | 184 | ii += 1; |
altb | 3:769ce5f06d3e | 185 | fexcPast = fexc; |
altb | 0:78ca29b4c49e | 186 | // calculate the one point dft |
altb | 0:78ca29b4c49e | 187 | float Ureal = 2.0f*scaleG*(cr*sU[1] - sU[2]); |
altb | 0:78ca29b4c49e | 188 | float Uimag = 2.0f*scaleG*ci*sU[1]; |
altb | 0:78ca29b4c49e | 189 | float Yreal = 2.0f*scaleG*(cr*sY[1] - sY[2]); |
altb | 0:78ca29b4c49e | 190 | float Yimag = 2.0f*scaleG*ci*sY[1]; |
altb | 0:78ca29b4c49e | 191 | // calculate magnitude and angle |
altb | 0:78ca29b4c49e | 192 | float Umag = sqrt(Ureal*Ureal + Uimag*Uimag); |
altb | 0:78ca29b4c49e | 193 | float Ymag = sqrt(Yreal*Yreal + Yimag*Yimag); |
altb | 0:78ca29b4c49e | 194 | float absGyu = Ymag/Umag; |
altb | 0:78ca29b4c49e | 195 | float angGyu = atan2(Yimag, Yreal) - atan2(Uimag, Ureal); |
altb | 0:78ca29b4c49e | 196 | float absGye = Ymag/Aexc; |
altb | 0:78ca29b4c49e | 197 | float angGye = (atan2(Yimag, Yreal) + piDiv2); |
altb | 0:78ca29b4c49e | 198 | // user info |
altb | 3:769ce5f06d3e | 199 | if(ii == 2) { |
altb | 0:78ca29b4c49e | 200 | printLine(); |
altb | 0:78ca29b4c49e | 201 | printf(" fexc[Hz] |Gyu| ang(Gyu) |Gye| ang(Gye) |E| |U| |Y|\r\n"); |
altb | 0:78ca29b4c49e | 202 | printLine(); |
altb | 0:78ca29b4c49e | 203 | } |
altb | 3:769ce5f06d3e | 204 | printf("%11.3e %10.3e %10.3e %10.3e %10.3e %10.3e %10.3e %10.3e\r\n", fexc, absGyu, angGyu, absGye, angGye, Aexc, Umag, Ymag); |
altb | 0:78ca29b4c49e | 205 | } else { |
altb | 0:78ca29b4c49e | 206 | jj += 1; |
altb | 0:78ca29b4c49e | 207 | } |
altb | 0:78ca29b4c49e | 208 | sinarg = fmod(sinarg + pi2Tsfexc, pi2); |
altb | 0:78ca29b4c49e | 209 | NmeasTotal += 1; |
altb | 0:78ca29b4c49e | 210 | return Aexc*sin(sinarg); |
altb | 0:78ca29b4c49e | 211 | } |
altb | 0:78ca29b4c49e | 212 | |
altb | 0:78ca29b4c49e | 213 | void GPA::fexcDesLogspace(float fMin, float fMax, int NfexcDes) |
altb | 0:78ca29b4c49e | 214 | { |
altb | 0:78ca29b4c49e | 215 | // calculate logarithmic spaced frequency points |
altb | 0:78ca29b4c49e | 216 | float Gain = log10(fMax/fMin)/((float)NfexcDes - 1.0f); |
altb | 0:78ca29b4c49e | 217 | float expon = 0.0f; |
altb | 0:78ca29b4c49e | 218 | for(int i = 0; i < NfexcDes; i++) { |
altb | 0:78ca29b4c49e | 219 | fexcDes[i] = fMin*pow(10.0f, expon); |
altb | 0:78ca29b4c49e | 220 | expon += Gain; |
altb | 0:78ca29b4c49e | 221 | } |
altb | 0:78ca29b4c49e | 222 | } |
altb | 0:78ca29b4c49e | 223 | |
altb | 0:78ca29b4c49e | 224 | void GPA::calcGPAmeasPara(float fexcDes_i) |
altb | 0:78ca29b4c49e | 225 | { |
altb | 0:78ca29b4c49e | 226 | // Nmeas has to be an integer |
altb | 0:78ca29b4c49e | 227 | Nper = NperMin; |
altb | 0:78ca29b4c49e | 228 | Nmeas = (int)floor((float)Nper/fexcDes_i/Ts + 0.5f); |
altb | 0:78ca29b4c49e | 229 | // secure that the minimal number of measurements is fullfilled |
altb | 0:78ca29b4c49e | 230 | int Ndelta = NmeasMin - Nmeas; |
altb | 0:78ca29b4c49e | 231 | if(Ndelta > 0) { |
altb | 0:78ca29b4c49e | 232 | Nper = (int)ceil((float)NmeasMin*fexcDes_i*Ts); |
altb | 0:78ca29b4c49e | 233 | Nmeas = (int)floor((float)Nper/fexcDes_i/Ts + 0.5f); |
altb | 0:78ca29b4c49e | 234 | } |
altb | 0:78ca29b4c49e | 235 | // evaluating reachable frequency |
altb | 0:78ca29b4c49e | 236 | fexc = (float)Nper/(float)Nmeas/Ts; |
altb | 0:78ca29b4c49e | 237 | } |
altb | 0:78ca29b4c49e | 238 | |
altb | 0:78ca29b4c49e | 239 | void GPA::printLine() |
altb | 0:78ca29b4c49e | 240 | { |
altb | 0:78ca29b4c49e | 241 | printf("-----------------------------------------------------------------------------------------\r\n"); |
altb | 0:78ca29b4c49e | 242 | } |
altb | 0:78ca29b4c49e | 243 | |
altb | 0:78ca29b4c49e | 244 | void GPA::printGPAfexcDes() |
altb | 0:78ca29b4c49e | 245 | { |
altb | 0:78ca29b4c49e | 246 | printLine(); |
altb | 0:78ca29b4c49e | 247 | for(int i = 0; i < NfexcDes; i++) { |
altb | 0:78ca29b4c49e | 248 | printf("%9.4f\r\n", fexcDes[i]); |
altb | 0:78ca29b4c49e | 249 | } |
altb | 0:78ca29b4c49e | 250 | } |
altb | 0:78ca29b4c49e | 251 | |
altb | 0:78ca29b4c49e | 252 | void GPA::printGPAmeasPara() |
altb | 0:78ca29b4c49e | 253 | { |
altb | 0:78ca29b4c49e | 254 | printLine(); |
altb | 0:78ca29b4c49e | 255 | printf(" fexcDes[Hz] fexc[Hz] Aexc Nmeas Nper\r\n"); |
altb | 0:78ca29b4c49e | 256 | printLine(); |
altb | 0:78ca29b4c49e | 257 | for(int i = 0; i < NfexcDes; i++) { |
altb | 0:78ca29b4c49e | 258 | calcGPAmeasPara(fexcDes[i]); |
altb | 0:78ca29b4c49e | 259 | if(fexc == fexcPast || fexc >= fnyq) { |
altb | 0:78ca29b4c49e | 260 | fexc = 0.0f; |
altb | 0:78ca29b4c49e | 261 | Nmeas = 0; |
altb | 0:78ca29b4c49e | 262 | Nper = 0; |
altb | 0:78ca29b4c49e | 263 | Aexc = 0; |
altb | 0:78ca29b4c49e | 264 | } else { |
altb | 0:78ca29b4c49e | 265 | Aexc = aAexcDes/fexc + bAexcDes; |
altb | 0:78ca29b4c49e | 266 | fexcPast = fexc; |
altb | 0:78ca29b4c49e | 267 | } |
altb | 0:78ca29b4c49e | 268 | NmeasTotal += Nmeas; |
altb | 0:78ca29b4c49e | 269 | printf("%12.2e %9.2e %10.2e %7i %6i \r\n", fexcDes[i], fexc, Aexc, Nmeas, Nper); |
altb | 0:78ca29b4c49e | 270 | } |
altb | 0:78ca29b4c49e | 271 | printGPAmeasTime(); |
altb | 0:78ca29b4c49e | 272 | reset(); |
altb | 0:78ca29b4c49e | 273 | } |
altb | 0:78ca29b4c49e | 274 | |
altb | 0:78ca29b4c49e | 275 | void GPA::printGPAmeasTime() |
altb | 0:78ca29b4c49e | 276 | { |
altb | 0:78ca29b4c49e | 277 | printLine(); |
altb | 0:78ca29b4c49e | 278 | printf(" number of data points: %9i\r\n", NmeasTotal); |
altb | 0:78ca29b4c49e | 279 | printf(" measurment time in sec: %9.2f\r\n", (float)NmeasTotal*Ts); |
altb | 0:78ca29b4c49e | 280 | } |