My answer which I have got is :
The function is periodic with Fundamental Period, T = 6(pi)..
Is that right??
The function is periodic with Fundamental Period, T = 6(pi)..
Is that right??
I am not getting you, are you saying both are right?? 6(pi) and 2(pi) also? And I am unable to see what carrier you are referring to..Here is a plot of the waveform.
Your value of 6pi can clearly be seen as the modulating envelope repeat frequency.
Your book is referring to the timing between peaks on the underlying 'carrier', which I assume it means by the fundamental.
In the second diagram I havve stripped out the 2 and 3 multiplying factors as they push the peaks up and down but do not alter their timing.
This allows the carrier to be more clearly identified.
Remember the x axis is in radian measure.
You can tell the periodicity because the peaks alternate either side of the x axis although they are vary in height.
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Do you say this to everyone who uses this website or forum for very first time ??You time on forum is short as are your posts so I am not sure in what context you have met this question.
No but you were asked by two separate responders for more information.Do you say this to everyone who uses this website or forum for very first time ??
It means exactly what it says.Now the fundamental is not necessarily the lowest frequency (longest period) present.
This is a common misconception.
What does this mean??
Hi,What do you mean by Fundamental??
So if I pluck a guitar string so it vibrates with one central node and two end nodes is the fundamental present?The fundamental is the lowest frequency present
Hi,So if I pluck a guitar string so it vibrates with one central node and two end nodes is the fundamental present?
Or if I broadcast a suppressed carrier wireless transmission, is the fundamental present?
I think this is exactly right we really need more knowledge of what the book actually said.Yeah it would be better to know more about the 'book' in question here just to see what their general idea is about harmonics.
Sometimes seeing the actual question the way it was originally worded helps in cases like these, and sometimes we have to look at other questions and examples to see how they handle the other questions that involve the same concepts.
Hey, Mr Al there is no need to mock. The missing fundamental is a recognised phenomenon.
http://en.wikipedia.org/wiki/Missing_fundamental.
I think this is exactly right we really need more knowledge of what the book actually said.
Here is my understand ing of the maths involved in the Wolfram Alpha link.
A Harmonic analysis of a function y(t) can represent y(t) by a Fourier cosince series
\(y(t) = {A_0} + {A_1}\cos ({\omega _f}t + {\phi _1}) + {A_2}\cos (2{\omega _f}t + {\phi _2}) + {A_3}\cos (3{\omega _f}t + {\phi _3}) + .....\)
Where
\({\omega _f} = \frac{{2\pi }}{\tau }\)
Tau is the fundamental period and omega_f the angular frequency of the fundamental
and phi_n the phase angles of each component.
If we consider the original function y(t) as the output of a Fourier cosine analysis and compare coefficients we find immediately that
\({A_0} = {\phi _n} = 0\)
That is the fiorst term and all the phase angles phi are zero.
Now the original function had two terms so trying each one in turn as a proposed second term we have either
\(2\cos (t) = {A_1}\cos ({\omega _f}t)\) and \(3\cos \left( {\frac{t}{3}} \right) = {A_3}\cos (3{\omega _f}t)\)
Which yields Tau = 2pi and 18 pi ie a contradiction
or
\(2\cos (t) = {A_3}\cos (3{\omega _f}t)\) and \(3\cos \left( {\frac{t}{3}} \right) = {A_1}\cos ({\omega _f}t)\)
which yields tau = 6pi as the OP says.
by Jake Hertz
by Jake Hertz
by Jake Hertz
by Jake Hertz