determine period of given signal

Question

i would like to compute Fourier coefficients from given signal,and i have following picture

enter image description here

i need to know period,just to make sure that i am not making mistake,period should be $\frac {T} {2}$ right?because starting from $0$ point,it repeats again peak after $\frac {T}{2}$ second am i right or i am making some mistake?thanks in advance

aa ,i see,so fourier coeficients i should take from $0$ to $T$ right? — dato datuashvili, Jul 05 '14 at 11:30
by the way DC coefficient of the Fourier series should be $1$ right?because we would have $\frac {1}{T} \int^{T}_{0} 1dt$ — dato datuashvili, Jul 05 '14 at 11:34
could you help me please to calculate fourier coefficients,i am lost — dato datuashvili, Jul 05 '14 at 11:42

score 1 · Answer 1 · answered Jul 05 '14 at 11:28

1

the period is T here, as it takes T to reach the same phase in your signal

answered Jul 05 '14 at 11:28

asdmin

111

Ömer · Accepted Answer · 2014-07-05T12:00:09.317

1

You can take your period as $[-T/2,T/2]$ and over a period your function can be written as $$ x(t)=\begin{cases} 1, & \frac{-T}{4}\leq t\leq\frac{T}{4}\\ 0, & else \end{cases} $$ So the coefficient $a_0$ is: $$a_{0}=\frac{1}{T}\int_{-T/2}^{T/2}1dt=\frac{1}{T}\int_{-T/4}^{T/4}1dt=\frac{1}{2}$$

edited Jul 05 '14 at 12:00

answered Jul 05 '14 at 11:48

Ömer

2,038

why half of period ? – dato datuashvili Jul 05 '14 at 11:51
yes that i have got for $a_0$,for $a_k$? – dato datuashvili Jul 05 '14 at 11:52
For $a_k$ evaluate the integral $\frac{2}{T}\int_{-T/4}^{T/4}cos(\frac{2\pi.t.n}{T})dt$ – Ömer Jul 05 '14 at 11:56

determine period of given signal

2 Answers2