# Linear Combination of Two Signals

In my signal processing class I have some basic tasks working with sinus signals in Matlab. I have two sinusoidal signals with 1kHz and 3kHz and sampling rate of 16kHz. The next task says 'Create a linear combination of the two signals and save the result in a new vector'.

I don't really understand what's meant by the linear combination. I remember something vague about having to add them with weights but I'm don't quite comprehend what that does or how to do it.

As you said, a linear combination of two signals $$x_1[n]$$ and $$x_2[n]$$ is simply
$$y[n]=w_1x_1[n]+w_2x_2[n]$$
with real-valued weights $$w_1$$ and $$w_2$$.