Fourier Series of: 2sin(4000*pi*t)*sin(46000*pi*t)

In summary, the conversation discusses how to find the magnitude spectra of a function with two sine waves. The person is unsure of the method and asks for help. They mention a shortcut method for finding Fourier coefficients for a square wave, but are uncertain if it can be applied to this question. They also ask for hints on a trigonometric identity related to the sines of two angles.
  • #1
zonedestruct
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Homework Statement



How can i find the magnitude spectra of 2sin(4000*pi*t)*sin(46000*pi*t)



The Attempt at a Solution



im not sure how to go about this question, can someone please give me some help on what i should do. I know that for a square wave i can find the Fourier series coefficients of it by finding the Fourier transform of one period (which is the Fourier transform of standard rect function) and then use Gn = f0G1(nf0). But this question I am not sure if i can do this shortcut method.
please help, thanks.
 
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  • #2
someone please give me some hints
 
  • #3
Given angles x and y, what is the trigonometric identity relating the sines of these angles to the sum and difference of these angles?
 

Related to Fourier Series of: 2sin(4000*pi*t)*sin(46000*pi*t)

1. What is a Fourier series?

A Fourier series is a mathematical tool used to represent a periodic function as a sum of simple sine and cosine functions. It allows us to analyze and understand complex patterns and signals by breaking them down into simpler components.

2. How is a Fourier series calculated?

To calculate a Fourier series, we use a mathematical formula called the Fourier transform. This involves breaking down a function into its individual frequency components and then representing it as a sum of sine and cosine functions.

3. What does the "2sin(4000*pi*t)*sin(46000*pi*t)" in this Fourier series represent?

The "2sin(4000*pi*t)*sin(46000*pi*t)" represents the original function that we are trying to represent using a Fourier series. In this case, it is a complex periodic function with two frequencies (4000 and 46000) multiplied together.

4. Why is the Fourier series of this function useful?

The Fourier series of this function allows us to analyze and understand the behavior of this complex function in a simpler way. It helps us to identify the individual frequency components and their contributions to the overall function.

5. In what fields is the Fourier series commonly used?

The Fourier series is commonly used in fields such as mathematics, physics, engineering, signal processing, and many other scientific disciplines. It has applications in areas such as image and sound processing, vibration analysis, and data compression.

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