# Foorier represtaion of this function

• nhrock3
In summary, the conversation is about finding the Fourier representation of the given function, f(x)=\sin(\frac{px}{2}). The conversation includes discussions about using trigonometric identities, integrating with the appropriate factors, and choosing the interval for the periodic extension. It is also mentioned that there may be discontinuities depending on the value of p and that the problem needs to be stated more clearly.
nhrock3
$$f(x)=\sin(\frac{px}{2})\\$$

$$a_0=0$$

$$a_n=0$$

$$b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}\(\sin(\frac{px}{2}))\sin(nx)dx=\frac{1}{2\pi}[\sin(\frac{p\pi}{2}-n\pi)-\sin(\frac{-p\pi}{2}+n\pi)]+\frac{1}{2\pi}[\sin(\frac{p\pi}{2}+n\pi)-\sin(\frac{-p\pi}{2}-n\pi)]$$

i used trig identetied to splt into two cosines

andi solved

but i got sines

i need an expression of cosines to do cos nx=(-1)^n

i need to have a simple linear fracture without cosines or sines

i can't transform it here in the needed form

?

and if thinking thurely then i see that i have a trig function on a simetric period
so its zero

so the foorier representation of the given function is zero
?

where is the mistake
it can't be zero

Hi nhrock3!

These trigonometric identities need a factor of 1/2 inside the RHS brackets.

i took the 0.5 out side of the integral

i'm getting confused

let's start again … shouldn't there be factors of 1/(p/2 ± n) after the integration?

foorier... Really? Did you really just do that? I'd attempt a response but I can't read whatever the hell you typed.

You need to state your problem more clearly. Are you trying to find a Fourier series that represents your function for all x? If not that, on what interval? Why are you choosing $(-\pi,\pi)$? Depending on the value of p, the periodic extension of your function from that interval may have discontinuities. Do your care about that? Do you want a half range expansion? A more careful statement of the problem please.

And what is "a simple linear fracture without sines or cosines?"

## 1. What is a Fourier representation of a function?

A Fourier representation of a function is a mathematical method used to decompose a function into a combination of sine and cosine waves of different frequencies. This allows us to analyze the frequency components of a function and study its behavior.

## 2. Why is Fourier representation important?

Fourier representation is important because it allows us to study the behavior of a function in terms of its frequency components. This is useful in many fields such as signal processing, data analysis, and image processing.

## 3. How is Fourier representation calculated?

Fourier representation is calculated using the Fourier transform, which is a mathematical operation that converts a function from the time or spatial domain to the frequency domain. The inverse Fourier transform can then be used to convert back to the time or spatial domain.

## 4. What is the difference between Fourier series and Fourier transform?

Fourier series is used to represent a periodic function as a combination of sine and cosine waves, while Fourier transform is used to represent a non-periodic function as a sum of sine and cosine waves of different frequencies.

## 5. What are some applications of Fourier representation?

Fourier representation has many applications in engineering, physics, and mathematics. It is used in signal processing to analyze and filter signals, in image processing to enhance images, and in data analysis to identify patterns and trends. It is also used in the study of heat transfer, vibrations, and quantum mechanics.

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