Finding Fundamental Period of x(t) with 2 Exponentials

Click For Summary
SUMMARY

The fundamental period of the signal x(t) = 2 cos(10t + 1) - sin(4t - 1) is determined by the angular frequencies of the cosine and sine components. The angular frequencies are 10 and 4, which share a greatest common factor (GCF) of 2. The correct fundamental period is calculated as the least common multiple (LCM) of the individual periods, leading to a fundamental period of π, not π/10. The phase shifts of +1 and -1 do not affect the fundamental period.

PREREQUISITES
  • Understanding of trigonometric functions and their properties
  • Knowledge of angular frequency and its relationship to periodicity
  • Familiarity with the concepts of least common multiple (LCM) and greatest common factor (GCF)
  • Basic skills in signal analysis and representation
NEXT STEPS
  • Study the relationship between angular frequency and period in trigonometric functions
  • Learn how to calculate the least common multiple (LCM) of multiple frequencies
  • Explore the effects of phase shifts on signal periodicity
  • Review examples of signal decomposition into sinusoidal components
USEFUL FOR

Students and professionals in electrical engineering, signal processing, and mathematics who are analyzing periodic signals and their properties.

EvLer
Messages
454
Reaction score
0
I can't get my answer match up with correct answer in the book:
i need to find fundamental period of this signal:

x(t) = 2 cos(10t + 1) - sin(4t -1)

i used formula for cosine Acos(wt + a) = ... that gives two exponentials... so I got pi/10 instead of pi for answer...
any help is appreciated
 
Physics news on Phys.org
x(t) = 2 cos(10t + 1) - sin(4t -1)

Is there an [itex]\omega[/itex] missing in this formula?

The +1 and -1 are phase shifts.

10 and 4 share a gcf of 2.

IIRC, there may be a relationship between gcf and the fundamental frequency.
 

Similar threads

Engineering Fourier transform of a shifted sine wave
  • · Replies 3 ·
Replies
3
Views
2K
Find maximum current in a coil using oscilloscopes and Faraday's Law?
  • · Replies 5 ·
Replies
5
Views
3K
Fourier Series Frequency, Period, and Coefficients
  • · Replies 5 ·
Replies
5
Views
3K
Engineering Sinusoidal steady state analysis using Laplace transform
  • · Replies 3 ·
Replies
3
Views
3K
Engineering Signals and Systems: Determine the convolution of x(t) and h(t)
  • · Replies 4 ·
Replies
4
Views
3K
Plotting a rotating ellipse trajectory (the Moon orbiting the Earth in 2D)
  • · Replies 2 ·
Replies
2
Views
2K
Frequencies for harmonic oscillator with multiple periodic solutions?
  • · Replies 6 ·
Replies
6
Views
1K
Engineering Filter Linear Phase Property for non-integer time delays
  • · Replies 3 ·
Replies
3
Views
2K
How should I find the following period ## T ## of this solution?
  • · Replies 5 ·
Replies
5
Views
3K
Engineering Continuous and discontinuous modes of series excited DC motors
  • · Replies 3 ·
Replies
3
Views
2K