Fourier series and parseval's theorem

In summary, a Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It is calculated using Fourier coefficients, which are obtained by integrating the function over one period and dividing by the period. Parseval's theorem relates the energy of a function in the time domain to its frequency components in the frequency domain, and is used in signal processing to analyze signals and determine their energy or power. Fourier series and Parseval's theorem have numerous applications in mathematics, physics, and engineering, including signal processing, image and sound compression, and solving differential equations.
  • #1
marshmallow
4
0
A square wave has amplitude 3 and period 5. calculate its power?

Using Fourier series for this square wave and Parseval’s
theorem, calculate the power in a signal obtained by cutting out frequencies
above 1 Hz in the square wave?

i am able to obtain the Fourier series for the square wave but i am unsure about the power and the power by cutting out frequencies above 1Hz?

Help would be much appreciated.
 
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  • #2
Write down Parseval's theorem. What does it mean? How might it apply to your problem?
 

1. What is a Fourier series?

A Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions. It allows us to break down a complex function into simpler sinusoidal components.

2. How is a Fourier series calculated?

A Fourier series can be calculated using the Fourier coefficients, which are obtained by integrating the function over one period and dividing by the period. These coefficients are then used in the Fourier series formula to express the function as a sum of sine and cosine terms.

3. What is Parseval's theorem?

Parseval's theorem states that the total energy of a function can be calculated as the sum of the squares of its Fourier coefficients. In other words, it relates the energy of a function in the time domain to its frequency components in the frequency domain.

4. How is Parseval's theorem used in signal processing?

Parseval's theorem is used to analyze signals in the frequency domain. It allows us to determine the energy or power of a signal by analyzing its frequency components. This is useful in applications such as noise reduction and filtering.

5. What are the applications of Fourier series and Parseval's theorem?

Fourier series and Parseval's theorem have many applications in mathematics, physics, and engineering. They are used in signal processing, image and sound compression, solving differential equations, and analyzing physical systems, among others.

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