Calculate time period of a graph signal

Hello guys , i am new to matlab .

I have a signal graph that i want to find the time period of it and the time in which the amplitude gets half of its starting value.

The singal is below :

Any help will be appreciated !

Thanks

[Sam Chak]

Okay, please provide the data to plot this signal.

[Bill Kyriakidis]

Okey ,

I have 2 variables.The variable t ,which is time and zn which is amplitude .

The values of these two are in the text document i attach

Answer 1

[Star Strider]

Use findpeaks to get the peak indices and then use the associated time vector to calculate the period. Use the envelope function to return the upper envelope of the waveform that can then be used to determine the rate of the decrease in the amplitude.

Alternatively, use the procedure described in Curve Fitting of large Data Measurement? to get the relevant parameters, and use those values to calculate the desired results.

EDIT — (27 Mar 2022 at 19:35)

The envelope turns out not to be a single exponential, so while treating it as such may work, any results derived from that assumption may have some inaccuracies.

There are beginning and trailing parts of the signal that I removed by finding the appropriate indices and the using only that part of the signal for the regression.

T1 = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/942934/Signal_processing_Bill.txt', 'VariableNamingRule','preserve')

T1 = 1000×1 table
    Calculate time period of a graph signal
    _______________________________________

                    0.51485                
                   -0.47324                
                   -0.72355                
                    0.13836                
                    0.74797                
                    0.18449                
                   -0.66647                
                   -0.47968                
                    0.43007                
                      0.644                
                   -0.14748                
                   -0.70913                
                   -0.17036                
                    0.60437                
                     0.4239                
                   -0.41766                

x = linspace(0, numel(T1{:,1})-1, numel(T1{:,1}))';
[pks,locs] = findpeaks(T1{:,1});
Period = mean(diff(x(locs)))

Period = 4.6573

env = envelope(T1{:,1}, 5, 'peak');

figure
plot(x, T1{:,1})
hold on
plot(x,env)
hold off
grid
legend('Signal','Upper Envelope', 'Location','best')

yc(:,1) = T1{:,1};
[mv,ix] = max(yc);
lcs = find(islocalmax(yc(yc(:,1)>0), 'MinProminence',0.05));
lims = [ix max(lcs)];
yc = yc(lims(1):lims(2));
x = linspace(0, numel(yc)-1, numel(yc))';

vn = T1.Properties.VariableNames;                                                   % Variable Names
ttlstr = vn(1);                                                                 % Variable Names Used In The Code

for k = 1:size(yc,2)
    yk = yc(:,k);
    y = yk;
    % y = detrend(y);
    ym = mean(y);                                                                   % Estimate offset
    y = y - ym;
    yu = max(y);
    yl = min(y);
    yr = (yu-yl);                                                                   % Range of ‘y’
    yz = y-yu+(yr/2);
    zci = @(v) find(diff(sign(v)));                                                 % Returns Approximate Zero-Crossing Indices Of Argument Vector
    zt = x(zci(y));
    per = 2*mean(diff(zt))                                                         % Estimate period

    fit = @(b,x)  b(1) .* exp(b(2).*x) .* (sin(2*pi*x./b(3) + 2*pi/b(4))) + b(5);   % Objective Function to fit
    fcn = @(b) norm(fit(b,x) - yk);                                                 % Least-Squares cost function
    s0 = [yr; -1E-2;  per;  -1;  ym];                                               % Initial Parameter Estimates
    [s,nmrs] = fminsearch(fcn, s0)                                                  % Minimise Least-Squares

    xp = linspace(min(x),max(x), 500);

    figure
    plot(x,yk,':b', 'LineWidth',1.5)
    hold on
    plot(xp,fit(s,xp), '--r')
    hold off
    grid
    xlabel('Time (s)')
    ylabel('Amplitude')
    title(ttlstr{k})
    legend('Original Data',  'Fitted Curve')
    text(0.1*max(xlim),0.7*min(ylim), sprintf('$y = %.3f\\cdot e^{%.3f\\cdot x}\\cdot sin(2\\pi\\cdot x\\cdot %.3f%+.3f) %+.4f$', [s(1:2); 1./s(3:4); s(5)]), 'Interpreter','latex')
end

per = 4.6602

s = 5×1

0.6171 -0.0047 4.6593 -1.3232 -0.0003

nmrs = 0.5517

.

[Bill Kyriakidis]

Thank you very much!!

I apreciate your time spent for my problem !

[Star Strider]

As always, my pleasure!