Proof of Periodic Sinusoidal waveforms

In summary, the conversation is about proving the periodicity of a sinusoidal waveform. The given signal is x(t)=cos(2t+pi/4) and the goal is to prove that it is periodic. The user attempted to use the fact that cos(x)=sin(x+pi/2) to prove the periodicity, but encountered a non-zero answer. Another user suggested using the identity cos(A+2πn)=cosA to prove the periodicity, which was deemed helpful.
  • #1
tomh
1
0

Homework Statement


Hi,

Have completely forgotten how to prove that a sinusoidal waveform is periodic and can't seem to find it anywhere. So was hoping someone could here.

I've got the signal x(t)=cos(2t+pi/4)

and am trying to prove it is periodic.

Homework Equations



wt=theta

f(x+k)=f(x)

cos(x)=sin(x+pi/2)

The Attempt at a Solution



I know that it is periodic, but to prove I think I have to prove that x(t)=0

Have tried letting t=-pi/8 but with the phase change of pi/2 to convert it to a sine again it gives me a non zero answer.

Anyone with any help would be greatly appreciated.
 
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  • #2
welcome to pf!

hi tomh! welcome to pf! :smile:

(have a pi: π and a theta: θ :wink:)

cos(A + 2πn) = cosAcos2πn - sinAsin2πn = cosA

does that help?​
 

FAQ: Proof of Periodic Sinusoidal waveforms

What is a periodic sinusoidal waveform?

A periodic sinusoidal waveform is a type of wave that repeats itself over a certain period of time. It is characterized by its amplitude, frequency, and phase.

What is the mathematical representation of a periodic sinusoidal waveform?

The mathematical representation of a periodic sinusoidal waveform is given by the equation y = A sin (ωt + φ), where A is the amplitude, ω is the angular frequency, t is the time, and φ is the phase shift.

What is the period and frequency of a periodic sinusoidal waveform?

The period of a periodic sinusoidal waveform is the time it takes for one complete cycle to occur, and it is denoted by T. The frequency is the number of cycles per unit time, and it is denoted by f. The relationship between period and frequency is given by T = 1/f.

What is the significance of the amplitude, frequency, and phase in a periodic sinusoidal waveform?

The amplitude determines the maximum displacement of the waveform from its equilibrium position. The frequency determines how many cycles occur in a given time period. The phase represents the starting point of the waveform and determines its position in time.

What are some real-life applications of periodic sinusoidal waveforms?

Periodic sinusoidal waveforms have many practical applications, including in communication systems, electrical circuits, sound and music, and signal processing. They are also used in medical imaging, seismic data analysis, and many other fields of science and engineering.

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