# 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 $$w_2$$.

• How do I choose the weights? Are they depending on the frequency? – Pulz Dec 19 '18 at 22:29
• @Pulz That question should probably be posed to your instructor. – MBaz Dec 19 '18 at 22:48
• "Create a linear combination ..." doesn't say anything about the weights, does it? So just choose what you fancy. – Matt L. Dec 20 '18 at 8:12
• $w_1 = w_2 = 0$ 😂🤣😂 – Peter K. Feb 19 at 2:44
• If the instructor gives you that freedom, I would definitely use the comment from @PeterK. and set both weights to zero! I'd also include an example with weights like 1 and 0.5 just for extra credit ;-) – Dave C Feb 19 at 23:02

A linear combination simply means addition of the two signals.

And weights are just the amplitudes of your signals. There are no "standard" amplitudes. Even assuming it as one will be wrong