[SOLVED] What is fundamental frequency of signal x(t)

[moonnightingale]

If the signal is

x(t) =5+ 6cos(40xpixt) + 3cos(60xpixt) + 10 cos(120xpixt)

What is fundamental frequency of this signal

What we mean by fundamental frequency

 

[FvM]

https://en.wikipedia.org/wiki/Fundamental_frequency

In a sum of harmonic signals, the fundamental is the greatest common divisor of signal frequencies.

 

[moonnightingale]

Can anybody tell me the answer

is it w0 = 20 pi

Is this answer correct

the four options with me are

20 pi
40 pi
60 pi
120 pi

thanks

 

[dave9000]

20*pi is correct.
It makes sense because 40*pi is it's 2nd harmonic and 60*pi the 3rd.
Try and plot both your function and cos(20*pi*t) and you'll see they have the same repetition period.

 

[moonnightingale]

dave thanks
yes i also beleive so but one of my frd told me that
the max freq is fund freq which is 120 pi. so it means he is wrong

are u 100% sure abt answer of 20pi?

 

[errakeshpillai]

The fundamental frequency is the lowest frequency of any waveform, that is periodic of course. So I think the answer should be 40*pi

 

[enjunear]

dave thanks
yes i also beleive so but one of my frd told me that
the max freq is fund freq which is 120 pi. so it means he is wrong

are u 100% sure abt answer of 20pi?

From FvM's post:
In a sum of harmonic signals, the fundamental is the greatest common divisor of signal frequencies.

So, yes. 20*pi would be correct, and dave9k's analysis in the harmonic context is sound.

 

[moonnightingale]

The fundamental frequency is the lowest frequency of any waveform, that is periodic of course. So I think the answer should be 40*pi

yes this is the confusion

wikipedia also says

the fundamental frequency is the lowest frequency sinusoidal in the sum.

so what is correct answer ???????????

 

[dave9000]

You don't have to believe to anyone's theory, just fire up Matlab/excel, plot it and measure the repetition period.
You should find 10Hz:
cos(20*pi*t) = cos(10 * 2*pi*t) -> 10 Hz
cos(40*pi*t) = cos(20 * 2*pi*t) -> 20 Hz
cos(60*pi*t) = cos(30 * 2*pi*t) -> 30 Hz

 

[moonnightingale]

Dave u again confused me
What is the answer, is it now 10 HZ??????

previously u told me 20 HZ
plz just tell me correct answer now

is it 10 or 20

 

[DartPlayer170]

First of all the frequency is w/2Pi in the equation x(t)=VpSin(wt+o)
Secondly, the fundamental frequency is the smallest frequency by which all other harmonic frequencies are integer multiples of.
Note, the fundamental frequency does not necessarily exist in the transform. ie: it could be filtered out.

So, Dave's second answer of 10 is correct.
40 Pi t = 2 x wt
60 Pi t = 3 x wt
120 Pi t = 6 x wt

where w=2 Pi f
and f=10

The fundamental frequency of 10 is absent but 20 is incorrect because then 60 w t would equal 1.5 times the fundamental which is not part of a Fourier transform.
40 is even more incorrect because w=2 x Pi x f not just Pi x f plus it is not an integer of the fundamental.

 

[moonnightingale]

Thaks to all but 10 cannot be answer
the book says answer is among these 4

20 pi
40 pi
60 pi
120 pi

So plz provide correct answer. From discussion uptill now, i think 20pi is correct answer as
40pi,60pi and 120pi are all integral multiple of 20 pi

so plz guide me

 

[dave9000]

the thread is getting fun

I gave twice the same answer, because cos(20*pi*t) is a signal at 10Hz.
Just remember that you need 2*pi to complet a period, so cos(F * 2 * pi * t) is a signal at F Hz.
Hope it is more clear now ...

 

[moonnightingale]

Ok thanks dave
now i got it
answer is 20 pi


thanks to all

 

[DartPlayer170]

Thaks to all but 10 cannot be answer
the book says answer is among these 4

20 pi
40 pi
60 pi
120 pi

So plz provide correct answer. From discussion uptill now, i think 20pi is correct answer as
40pi,60pi and 120pi are all integral multiple of 20 pi

so plz guide me

You originally asked for the fundamental frequency. It is 10.
w=2*Pi*f = 20 * Pi - this is the angular frequency.
What is the question actually asking for? angular frequency or frequency? There is an important distinction!
If the choices of answers are in multiples of Pi then it should be asking for angular frequency ( also radian frequency ).

Note: the importance is not to get the answer correct, it is to understand the concept. How else will you answer the question on a final exam?