Nyquist - shannon sampling theorem example

[Jncik]

Homework Statement

What sampling frequency would you use to sample the following signal

x(t) = 3sin(9πt) - 6cos(8πt)

Homework Equations

The Attempt at a Solution

let T1 be the period of 3sin(9πt) and T2 the period of 6cos(8πt)

T1 = 2π/9π = 2/9
Τ2 = 2π/8π = 2/8

thus, if f1 is the frequency of 3sin(9πt) and f2 the frequency of 6cos(8πt) we have

f1 = 1/T1 = 9/2 = 4.5
f2 = 1/T2 = 8/2 = 4

now about the niquist rate,

I'm not sure whether it will be 9(2*f1, since f1>f2) or the frequency that is 2 times larger than the overall frequency of x(t)

can you please remind this to me? thanks

 

[lewando]

I'm not sure whether it will be 9(2*f1, since f1>f2) or the frequency that is 2 times larger than the overall frequency of x(t)

Not sure what you mean by the "overall frequency of x(t)".

When you sample at the Nyquist frequency, you need to sample at twice the highest frequency component of the signal.

 

[Jncik]

thanks lewando

What I was meaning is that

x(t) may have two components but the overall frequency is the least common multiple of the frequencies of each of these 2 components right? so the result will be different

thus if I understand correctly the result should be 2*f1 = 9 because f1 > f2 right?

 

[lewando]

...the overall frequency is the least common multiple of the frequencies of each of these 2 components right?

Honestly, I have never seen the term "overall frequency", as you have defined, used anywhere.

thus if I understand correctly the result should be 2*f1 = 9 because f1 > f2 right?

Right!

 

[Jncik]

thanks a lot ;)