How to Generate 5 Sine-waves each at 72° apart but every wave starting at 0.

How to generate a waveform as shown in figure?

[dpb]

Something else going on besides just a phase shift, though, in the figure.

There's some sort of transient in the first cycle that ramps up the amplitude with some overshoot of the steady-state magnitudes. W/O knowing what that was/is it's a shot in the dark.

A simple phase shift alone would be easy enough...

Answer 1

[Ameer Hamza]

One of the easiest ways I can think of is to use a continuous-time filter, with initial conditions set to zero. The only caveat is the attenuation in the magnitude of the sine wave and a bit of shift in the absolute phase. The relative phase difference is still 72 degrees. The magnitude attenuation can be corrected by multiplying it with a factor as done in the following code.

This code requires the control system toolbox. The same can be done with ode45.

t = linspace(0, 3, 1000); % time vector
freq = 1; % 1 Hz
phases = 0:deg2rad(72):deg2rad(72)*5; % phase shifts, multiple of 
y = sin(2*pi*freq*t + phases.'); % each row is a sine wave

% create and apply the filter
filter_freq = 3;
fil = tf(2*pi*filter_freq, [1 2*pi*filter_freq]); % create a filter
y_fil = zeros(size(y));
for i=1:size(y,1)
    y_fil(i, :) = lsim(fil, y(i,:), t);
end
mul_factor = sqrt((2*pi*freq)^2+(2*pi*filter_freq)^2)/(2*pi*filter_freq); % filter attenuation factor
y_fil = mul_factor*y_fil;

plot(t, y_fil)