Question

Fundamental Frequency of Continuous Signals To identify the period T, the frequencyf= 1/T, or the angular frequency ω = 2nf= 2m/T of a given sinusoidal or complex exponential signal, it is always helpful to write it in any of the following forms: sin (gd-sin(2nf)-sin(2t/T) The fundamental frequency of a signal is the greatest common divisor (GCD) of all the frequency components contained in a signal, and, equivalently, the fundamental period is the least common multiple (LCM) of all individual periods of the components. Question 6: Find the fundamental frequency of the following continuous signal and rewrite in terms of the fundamental frequency: 37T r(t) = sinゃ+cos(3rt) + sin(動

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Answer #1

The given equation contains 3 terms. The first term is sin(5π /6t ) , the second term is cos(3π/4)t and the third term is sin(T/3)t .

Comparing all the three terms with the form sin(2π ft) or cos(2πft) , we get

The frequency of the first term is : 12

The frequency of the second term is : f2

The frequency of the third term is : 3 3

Now, we know that the fundamental frequency (f_{0}) is the GCD (Greatest common divisor) of f_{1} , , f_{2} and f_{3} :

So, 5 3 1 12 8 6 10 9 4 24 24 2424 (as GCD( 10.9.4 ) 1 )

And 24 12

So, the signal, in terms of fundamental frequency , can be written as

x(t) = sin left ( 10 imes rac{pi}{12} t ight ) + cos left ( 9 imes rac{pi}{12} t ight ) + sin left ( 4 imes rac{pi}{12} t ight )

or, 4π r(t) = sin (10π 12 12

For any doubt please comment and please give an up vote. Thank you.

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