difficulty in understanding amplitude, frequency and period

Question

I have difficulty in understanding of some fundamental terms as amplitude. Can be there more than one amplitude for a signal? The following expression is combination of 3 sinusoidal signal, so are there 3 different amplitudes, periods or frequencies?

$h(x) = \sin\frac{2\pi x}{23} + \sin\frac{2\pi x}{28} + \sin\frac{2\pi x}{33}$

Answer 1

Are you possibly confused by what's known as Fourier analysis of signals, which decompose a given signal into multiple frequencies and amplitudes. What it essentially does is to find the individual components in the right hand side, given the signal in the left hand side. So it does not mean that the signal has multiple amplitudes or fundamental periods per given $x$.

Answer 2

On amplitudes, there are two terms here that need to be clarified:

• The peak amplitude, (or often called amplitude), is the non-negative value of your signal’s peak. This is for the whole duration. In most cases you have one.
• The instantaneous amplitude is the value of the localized peak amplitude at instant $t$. This is depending on the time $t$ you’re looking at. Here it’s simply the $y$-value of your time signal when at instant $t$

On period and frequency, see my answer here on finding the fundamental period/frequency. I see you have two nice prime numbers there 23 and 33, good luck.