i want to know about periodicity of discrete and analog signals and difference between them
2006-12-06 17:12:07 · 5 answers · asked by ranjith 1 in Science & Mathematics ➔ Mathematics
If this is what you mean:
cos(t) + cos(2πt)
Then the answer is:
periodicity of cos(t) is 2π
Now we know that periodicity of cos(kt)....where k is constant is
2π/k
So, periodicity of cos(2πt) is 2π/2π=1
Now to combine these we take LCM of both
But LCM of 1 and 2π not possible as anything multiplied by 1 is 1 only.
=>Function is non-periodic!
2006-12-07 21:42:30 · answer #1 · answered by Anonymous · 0⤊ 0⤋
The *s in the function are confusing. If it is cos(t) + cos(2*pi*t), then it is not periodic at all. Cos(t) has a period = 2pi, and cos(2*pi*t) has period of 1, because you cannot have any real number that is an exact multiple of both 2Pi and 1.
If the second term is cos^2(pi*t), then this will have a period pi, so the sum will have the period 2Pi.
2006-12-07 02:44:19 · answer #2 · answered by Seshagiri 3 · 0⤊ 0⤋
This does not have a period. The reason is periodicity of cost t is 2pi and of cor 2pi t is 1
actually the period should be LCM of both but as 1 is rational and 2pi is irrational no LCM so non periodic
2006-12-07 10:38:14 · answer #3 · answered by Mein Hoon Na 7 · 0⤊ 0⤋
Period is defined as the time it takes a function to repeat itself. The cos function repeats every 2Ï radians, so
The period of cos(t) is 2Ï
The period of cos(2Ït) is 1
2006-12-07 01:30:40 · answer #4 · answered by Helmut 7 · 0⤊ 0⤋
period shud be 2pi
as lcm of both the periods(2pi and 1) is 2pi
2006-12-07 03:50:06 · answer #5 · answered by devil_b 2 · 0⤊ 1⤋