# Harmonic components of a signal

1. Aug 23, 2011

### Jncik

1. The problem statement, all variables and given/known data

I have trouble understanding what the components are

suppose we have this discrete time signal

$$x[n] = e^{j \frac{2\pi}{3} n}$$

find the number of harmonic components

2. Relevant equations

3. The attempt at a solution

in my book it says that we have a set of harmonically related signals, that is signals that have a fundamental frequency that is multiple of $$\omega_{0}$$ where this omega is the fundamental frequency of x[n] in this case

so the set of this signals is $$x_{k}[n] = e^{j k \frac{2\pi}{3} n}$$

now,

for k = 0 we have a constant

for k = +1 and -1 we have the first harmonic component since the frequency is the smae
for k = +2 and -2 we have the second harmonic component
for k = +3 and -3 the third
for k = +4 and -4 the fourth which has frequency equal to the one where k = 0

now I don't understand the questions "how many harmonic components the signal has"

assuming that for k = +4, -4 and k = 0 we have the same frequency we can count this as one

for this reason can I say that we have 4 harmonic components?

the first for k = +1 and -1, the second for k = +2 and -2, the third for k = +3 and -3 and finally the fourth for k = +4 and -4?

last question: would it be the same if I started counting from k = 0, to k = 3,-3?