Sinusoidal Signal Analysis
Let us use mathematical tools like Fourier series to do analysis of Sinusoidal signal
Frequency domain analysis of sinusoidal waves
Among all of the mathematical tools used for analysis in engineering, frequency domain analysis is arguably the most convenient and useful. Frequency domain analysis refers to the steady state response of a system when subjected to a sinusoidal input. In frequency domain methods, the frequency of the input signal is varied over a certain range and study the resulting response.
Let us do the frequency domain analysis of a linear system which is subjected to a sinusoidal input.
For an input r(t)= A sin((ωt) , the output of the linear system is:
c(t)=B sin(ωt + φ)
Hence we can say that when a sinusoidal input is fed to a linear system, the output generated is also a sinusoidal signal of the same frequency but different in magnitude and phase.
Fourier Analysis
Fourier analysis is a tool used in Signal Processing For the FT, both the time variable t and frequency variable ω are continuous-valued and vary from −∞ to ∞. The transform equations are
X(ω) = ∫x(t)e−jωt dt Forward transform
x(t) = 1/2π ∫ X(ω)ejωt dω Inverse transform
If X(ω) is the Fourier transform of a signal x(t) meaning x(t) is the inverse transform of X(ω)
x(t) ←→ X(ω)
x(t)= FT ←→ X(ω)
Using the above formula , we calculate the Fourier Transform of sin(ω0t)
F.T of sin(ω0t)= π/j[δ(ω − ω0) − δ(ω + ω0)]
Sinusoidal Signal
Sinusoidal Signal is an important tool in the electronic industry. They are ubiquitous in modern electronics and are almost used in every daily appliance for input as Voltage, Current, and power amplifiers. In this article, we will study what a sinusoidal signal, how does it look like. We will also represent the Sinusoidal signal mathematically. Later we will discuss the need of having Sinusoidal signal and some applications of Sinusoidal Electronic Signal. We will conclude the article by summing up what we have learned. The electronics industry especially the communication system uses these signals in various circuits and readers can read about these other signals as well.
Table of Content
- Sinusoidal Signal
- Primary Technologies
- Sinusoidal Signal Analysis
- Characteristics
- Importance
- Applications
- Solved Examples