# period of this signal

it could be a donkey question but I'm a little confused.

I have this signal $w(t)=sin({\pi}0.1f)$. I have to calculate the period of this signal.

$w(t)=sin(2{\pi}\frac{1}{20}f)$

the period of this signal is: $20s$ while the frequency is $\frac{1}{20}Hz$

is it correct?

You are mostly correct. The equation should be $w(t) = sin(2\pi\frac{1}{20}t)$. The variable in the sin should be $t$, not $f$. The frequency is determined by the $\frac{1}{20}$, not by the variable.

Other than that you are correct. The period is 20s, which makes it a $\frac{1}{20}$ Hz sin wave.

• I used $f$ variable because my sin function is domain of frequency and not in time domain – Mazzy Apr 14 '12 at 14:00
• @Mazzy Okay, but then it would be w(f), not w(t). – Jim Clay Apr 15 '12 at 2:37
• @Mazzy To add further to Jim Clay's response to your use of $f$, note that $w(f) = \sin(2\pi \frac{1}{20}f)$ is not the Fourier transform of a sinusoidal signal in the time domain. The Fourier transform of a sinusoidal time-domain signal is a pair of impulses in the frequency domain. – Dilip Sarwate Apr 15 '12 at 12:44

It's very important to write the equation properly. The way your equation is written originally there is no period at all. Your left side function of the variable "t". Since t doesn't show in the right side, the right side is a independent of t. Hence it's a constant and therefore the period is infinity.

Jim Clay already fixed that in his response. The other potential pitfall are units. If you write the equation as sin(2*pi*(1/20)*t), then t is a unit-less quantity since you cannot take the sin() of a quantity that has units. So the answer would be that the period is 20 (and not 20s). If you write the equation as sin(2*pi*(1/20s)*t), then the t is a time and the units of t cancel with the units in the term (1/20s). In this case the period would be 20s.

• Why infinity and not any value? – Rojo Apr 16 '12 at 1:29
• @Rojo: What's the frequency of the number 1? It has no frequency; it's not a sine wave. – endolith Apr 16 '12 at 16:06
• @endolith the concept of period far exceeds sine waves – Rojo Apr 16 '12 at 17:51
• @Rojo: What's the period of a constant, then? – endolith Apr 16 '12 at 17:52
• @endolith, formally I am not sure, I was asking. But it would make sense to me that any nonzero value is a possible period. f(t) = f(t+P) for any P if f is a constnat. Periods are not unique. In a sin(2*pi*t), 2 is a period too. Probably the prime period in a constant is undetermined, because there's no minimum period. But I'd say "infinity" is the period of signals that never repeat themselves, not constants – Rojo Apr 16 '12 at 18:41