Question

How to calculate periodicity of a signal?

Answer 1

A sinsin signal has a period of 2π2π.Therefore you wanna know what nn has to be for 6π7n6π7n to equal 2π.2π.6π7n=2π⇔n=2π76π=146=736π7n=2π⇔n=2π76π=146=73Therefore the period is 7373You can check that way :y[n+73]=sin(6π7⋅(n+73)+1)=sin(6π7n+2π+1)=sin(6π7n+1)=y[n]y[n+73]=sin⁡(6π7⋅(n+73)+1)=sin⁡(6π7n+2π+1)=sin⁡(6π7n+1)=y[n]It works !shareciteimprove this answeranswered Jun 29 '14 at 15:27Hippalectryon4,14522251   Ok here we know that sin has 2pi as period, what if we didn't know? Another way to check? Or is my question non-sense =) – Anarkie Jun 29 '14 at 15:44   @Anarkie A function ff is periodic of period αα when f(x+α)=f(x)f(x+α)=f(x). Therefore if you find an αα that works, then it is periodic :) – Hippalectryon Jun 29 '14 at 16:03add a commentup vote1down voteA sinusoidal signal (such as sinsin) is indeed always periodic.The general form of a sine wave is:f(t)=Asin(2πft+ϕ)f(t)=Asin⁡(2πft+ϕ)Where ϕϕ (greek letter phi) is the phase shift, ff is the frequency (in Hertz, or Hz =1s=s−1=1s=s−1) and AAis the amplitude of the wave.You can use the formula ω=2πfω=2πf where ωω is the angular frequency (in radsrads), with the formula T=1fT=1f where TT is the period of the signal (in seconds, ss).The (general form) formula then becomes:f(t)=Asin(ωt+ϕ)f(t)=Asin⁡(ωt+ϕ)In your case (to make your formula fit the general form) you can say that t=nt=n, A=1A=1, ϕ=1ϕ=1 and the angular frequency ω=6π7ω=6π7, which means that the frequency is:f=ω2π=6π712π=37f=ω2π=6π712π=37.Now you can find out the period as follows:T=1f=137=73T=1f=137=73It's worthy to note that the term ϕϕ in the equation only offsets the wave (i.e. if ϕ≠2πk,k=[0,1,2,...]ϕ≠2πk,k=[0,1,2,...] then the wave is offset by ϕϕ) but does not affect its period/frequency.shareciteimprove this answeranswered Jun 30 '14 at 8:56aright1112   I think I will understand better if I see some non periodic signals after calculating its period, would you be able to give some examples for non-periodic case? Because then I think everything inside a sin() should be periodic? Or are non-periodic signals are addition of multiple sines and cosines? – Anarkie Jun 30 '14 at 10:07add a commentup vote0down voteSignal is periodic with period 7, not 7/3! Because we are talking about discrete case not continuous case. Here 'N' which is time period of discrete signal is always an integer.Because 'n' should be integer angular frequency(w) = 6π/7 So time period N = 2πm/(6π/7) = 7m/3 But N is always an integer in discrete case, hence we would multiply it with m = 3. Therefore, N = 7 'm' denoted the number of cycles continuous signal has to repeat to set 1 period of discrete case