function x(t) = cos(2*t + pi/4) anyone know whether the signal is periodic, and if it is what's its period. can you show the working out cheers

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

function x(t) = cos(2*t + pi/4) anyone know whether the signal is periodic, and if it is what's its period. can you show the working out cheers

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

ok it's been a while since i did this. We know it's periodic because all cos functions are periodic, unless there is a discontinuity in there somewhere. (Usually by dividing by 0). Yours is fine. So the way we know its period, is from the angular frequency. The angular frequency is always multiplied by the variable. So in this case the 2 is multiplied by the (t) so the 2 is the angular frequency. The angular frequency is also always equal to 2 * pi* /T. (T= period, t= variable for time). In your case set the 2*pi/T = 2, and then solve for T = pi
I'm not sure on the diving by 0 and discontinuity can you explain a bit more thanks, i have another example x(t) = u(t)*cos(2*pi*t) apparently this is aperiodic
Ok so there is formal stuff on discontinuities, you should check with your teacher about them. I wouldn't worry about it unless this is for a calculus course. Also i am not entirely sure if i am correct on the discontinuity bit. Pretty much for a function to be periodic, it must be repeatable on some interval, and then go on forever. So cos(x) is. You can find out what it is from 0 to 2 pi, and then repeat that over and over again. The same can be said for any of the the other trig functions. This is shown by how cos(2 * pi) = 1 = cos(0) = cos (4pi)..... going on forever. I used 0 because it is easy, but in reality the same thing works for any cos(x). ie. cos(48.84*32* x) = cos(48.84*32*x+2*pi) ie. cos(x) = cos(x+2*pi). For your example of x(t) = u(t)*cos(2*pi*t). I am not sure exactly how to answer this because i was taught that, in order for this statement to be true then ALL function of u(t) multiplied by cos(2*pi*t) will make it non periodic. If you make u(t) = t then you get x(t) = t*cos(2*pi*t). This means that x(t) does not equal x(t+2*pi), which means that it is not periodic. The period doesn't have to be 2*pi, but it usually is. If you are stuck you can try graphing it, (either using your calculator or wolfram alpha). On the other hand, if you make u(t) = cos(2*pi*t) you will actually get a periodic function. The function is given by x(t) = cos(2*pi*t)^2, and this has a period of pi. I am not sure how to classify this one, you really need to check with your teacher. I am sure different mathematicians will give you different answers and you just need to regurgitate what yours wants. Hope this helps.

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Ok so there is formal stuff on discontinuities, you should check with your teacher about them. I wouldn't worry about it unless this is for a calculus course. Also i am not entirely sure if i am correct on the discontinuity bit. Pretty much for a function to be periodic, it must be repeatable on some interval, and then go on forever. So cos(x) is. You can find out what it is from 0 to 2 pi, and then repeat that over and over again. The same can be said for any of the the other trig functions. This is shown by how cos(2 * pi) = 1 = cos(0) = cos (4pi)..... going on forever. I used 0 because it is easy, but in reality the same thing works for any cos(x). ie. cos(48.84*32* x) = cos(48.84*32*x+2*pi) ie. cos(x) = cos(x+2*pi). For your example of x(t) = u(t)*cos(2*pi*t). I am not sure exactly how to answer this because i was taught that, in order for this statement to be true then ALL function of u(t) multiplied by cos(2*pi*t) will make it non periodic. If you make u(t) = t then you get x(t) = t*cos(2*pi*t). This means that x(t) does not equal x(t+2*pi), which means that it is not periodic. The period doesn't have to be 2*pi, but it usually is. If you are stuck you can try graphing it, (either using your calculator or wolfram alpha). On the other hand, if you make u(t) = cos(2*pi*t) you will actually get a periodic function. The function is given by x(t) = cos(2*pi*t)^2, and this has a period of pi. I am not sure how to classify this one, you really need to check with your teacher. I am sure different mathematicians will give you different answers and you just need to regurgitate what yours wants. Hope this helps.
Sorry about the multiple posts, i wasn't logged in and everytime i hit the 'enter' key, it posted it once i logged in.
No worries thank you for your help

Not the answer you are looking for?

Search for more explanations.

Ask your own question