Question

Create a discrete series of the signal

y(t) = 5 + 2cos10πt + sin20πt + 3cos30πt

[V]. Use 256 data points so as to contain exactly two complete periods of the fundamental frequency.

this question is for an experimental measures class which is similar to statistics and probability.

Create a discrete series of the signal

y(t) = 5 + 2cos10πt + sin20πt + 3cos30πt

[V]. Use 256 data points so as to contain exactly two complete periods of the fundamental frequency.

this is all the info i have for this question it is from my experimental measures and instruments class.

Answer 1

given function y(t) = 5 + 2cos10πt + sin20πt + 3cos30πt

firstly let us find the period of this function

period of cos10πt is 2π/10π = 1/5

period of sin20πt is 2π/20π = 1/10

period of cos30πt is 2π/30π = 1/15

the period of y is lcm of periods of cos10πt, sin20πt, cos30πt (i.e, lcm of 1/5,1/10,1/15 = 1/5)

period of y is 1/5.

in 256 data points we need 2 complete periods (2*1/5 sec)

gap between two datapoints is 2/(5*256).

so t-coordinates of discrete signal are i*(2/(5*256)) where 0 i 255

in y(t) we t = i*(2/(5*256)) where 0 i 255 gives 256 data points with 2 complete periods