Period of Signal

i am reading signals and system by oppenheim.There they shown way to found how to find period of a signal,but did not show to find the period of signal when it is in sum like x(t)= sin5t-4cos7t .Here i can find period of individual signal(i mean sin5t and cos7t) but with that how can find period of x(t).Thank you

You just have to assign values for your "t". Then there you can solve for your x(t). At least 5 values of "t" should be just fine.

Hi Nick,

Remember that the period of a signal is the reciprocal of the frequency. (T = 1/f). After you calculate the periods of the two sinusoids (T = 1/f), you need to find the least common multiple of the two periods in order to get the period of the overall signal.

I hope this helps,
Kevin

The period is the first non- zero value of t where both sin5t=0 and cos7t=1,
t=2npi/5 and t=2mpi/7 where n and m are integers. As Kevin states, this will be the least common multiple of 7 and 5.

bq). t=2npi/5 and t=2mpi/7

here least common multiple is 35 . is the period x(t)=2pi/35?

Remember that the period of a signal is the reciprocal of the frequency. (T = 1/f). However, if period1 and/or period2 are fractions, then you should first multiply both periods by their least common denominator, and then find the LCM. Afterwards, divide your answer by the number that you multipled the two periods, in order to make them integers.

f1 = 5 , f2= 7
T1 = 0.2 ,T2 =0.1428
multiplying both by LCD(35) to get 7 and 5.
LCM of 7 and 5 is 35
period = 35/35 =1

I hope this helps,

got it thanks
i like to add this for some viewers

lcm(a*x, b*x)=lcm(a,b)*x where for example x=Pi is possible.
Thank you