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

Answer 1

The given equation contains 3 terms. The first term is
The given equation contains 3 terms. The first term is sin (5 pi/6)t, the second term is cos (3 pi/4) t and the third term is sin (pi/3)t. Comparing all the three terms with the form sin (2 pi ft) or cos (2 pi ft), we get The frequency of the first term is: f_1 = 5/12 The frequency of the second term is: f_2 = 3/8 The frequency of the third term is: f_3 = 1/6 Now, we know that the fundamental frequency (f_0) is the GCD (Greatest common divisor) of f_1, f_2 and f_3 so, f_0 = GCD (5/12, 3/8, 1/6) = GCD (10/24, 9/24, 4/24) = 1/24 Hz (as GCD (01, 9, 4) = 1) And w_0 = 2 pi f_0 = 2 pi times 1/24 = pi/12 So, the signal, in terms of fundamental frequency, can be written as x(t) = sin (10 times pi/12 t) +
, the second term is and the third term is .

Comparing all the three terms with the form , we get

The frequency of the first term is :

The frequency of the second term is :

The frequency of the third term is :

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

So, (as )

And

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

or,

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