What Is the Amplitude of a Harmonic Load in the Frequency Domain?

In summary, the conversation is about calculating the Fourier transformation of a harmonic load represented by the function f(t) = A * sin(ωt) in the time-domain. The person is asking for help in determining the amplitude of this function in the frequency domain. The response is that the amplitude is a delta function at ω with amplitude A.
  • #1
Mazzletov
3
0
Hello,

I am having a bit of trouble with calculating the Fourier transformation of a harmonic load.

I have the function f(t) = A * sin(ωt) in the time-domain.

I would like to represent this function in the frequency domain.

What would be its amplitude?

Thank you
 
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  • #2
Welcome to PF;
Please show your best effort so we can see where you are having trouble and so know how to best help you.
Thank you.
 
  • #3
Mazzletov said:
Hello,

I am having a bit of trouble with calculating the Fourier transformation of a harmonic load.

I have the function f(t) = A * sin(ωt) in the time-domain.

I would like to represent this function in the frequency domain.

What would be its amplitude?

Thank you
It is a delta function at ω with amplitude A.
 

Related to What Is the Amplitude of a Harmonic Load in the Frequency Domain?

1. What is an Exact Fourier Transformation?

An Exact Fourier Transformation is a mathematical function that converts a time-domain signal into its equivalent frequency-domain representation. It is used to analyze the frequency components of a signal and is commonly used in signal processing and data analysis.

2. How is an Exact Fourier Transformation different from a Discrete Fourier Transformation?

An Exact Fourier Transformation is a continuous function that can be applied to any signal, while a Discrete Fourier Transformation is a discrete function that can only be applied to a finite set of data points. This means that an Exact Fourier Transformation provides a more accurate representation of the frequency components of a signal.

3. What is the mathematical formula for an Exact Fourier Transformation?

The mathematical formula for an Exact Fourier Transformation is F(w) = ∫f(t)e^-iwt dt, where F(w) is the frequency-domain representation of the signal, f(t) is the time-domain signal, w is the angular frequency, and i is the imaginary unit.

4. What are some real-world applications of Exact Fourier Transformation?

Exact Fourier Transformation has many applications in fields such as engineering, physics, and data analysis. Some examples include signal processing in telecommunication systems, image and sound processing in media technology, and analysis of financial data in economics and finance.

5. Are there any limitations to using Exact Fourier Transformation?

One limitation of Exact Fourier Transformation is that it assumes the signal is periodic, which may not be true for all signals. Additionally, the transformation may not accurately represent high-frequency components of a signal if the sampling rate is not high enough. These limitations can be addressed by using more advanced techniques, such as windowing and zero-padding, in the Fourier transformation process.

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