How to level shift a sine wave mathematically?

Hello MatLab users,

Im currently working on a small program that gives me a certain number of values of a 60 Hz sine wave signal but unfortunately I was only able to create a sine wave that has positive and negative values, but what I really want is to get only positive values so I would need my sine wave to be level shifted up (for example 0 to 3). Is there any way to do this? I want to do this mathematically only. Help is appreciated, thank you all. I leave my code below and picture of plot of the sine wave.

f = 60;
fs = 1e4;                    % samples per second
t=0:1/fs:0.017;               % 1/fs is seconds per sample
x = sin(2*3.14*f*t);
plot(t,x)
x(:)

[Aquatris]

After you apply the suggestion of Geoff, you will get a sine wave that is between 0 and 2. Then you can change the range by simple multiplication;

   x = (1 + sin(2*pi*f*t))*n/2; % sine wave values between 0 and n

[Alex Avila]

Thank you Aquatris, your suggestion worked but what if I wanted the min not to be 0 and instead have a range between 0.5 and 3? and who is "Geoff" if you don't mind me asking? Thank you for your time and advice.

[dpb]

"_min not to be 0"_

That's what I showed in Answer is general scaling.

It's just mx+b applied to the function range...

[Aquatris]

Geoff did have a comment at the time I wrote mine. dqp gave you the answer below but if you need further explanation here it is;

First you create your sine wave that is between -1 and +1;

x = sin(2*pi*f*t);

You want this [-1,1] range to be [a,b] range instead, which is a simple linear mapping. This can be done by;

x_scaled = (x-(-1))*(b-a)/(1-(-1))+ a

So an example is;

t = 0:0.001:10;
x = sin(t);
a = 0.5; b = 3;
x_scaled = (x-(-1))*(b-a)/(1-(-1))+ a;
plot(t,x,t,x_scaled)

[Alex Avila]

Thank you Aquatris for helping me out as well, your explantation was very clear.

Answer 1

[dpb]

Sure, it's just a linear scaling from the [-1,1] interval to [minV,maxV]

x = sin(2*3.14*f*t);
M=[maxV-minV]/2;            % slope --> [maxV-minV]/[1-(-1)]
B=1+minV;                   % intercept
z=M*(x+B);                  % scale

for your min,max of [0,3] then

M=(3-0)/2;
B=1+0;

[Alex Avila]

Thank you dpb for taking your time and helping me out with this, your answer was very helpful.