The function runs from -π to +π. As yourself: is the function even in x or odd in x? If it is odd in x, then you only need to include the sin terms in the Fourier Series. if it is odd in x, then you only need to include the constant term and the cosine terms in the Fourier Series. What is the argument of sin or cosine going to be if the function runs from -π to +π?Agata 78 said:Homework Statement
Determine the Fourier series for the periodic function of period 2∏ defined by:
-2 when (-∏ ) ∠ x ∠ (-∏/2)
f(x)= 2 when ( -∏/2) ∠ x ∠ (∏ /2)
-2 when (∏/2) ∠ x ∠ (∏)
how to start i?. I have already drawn it but what next.
thank you
Homework Equations
The Attempt at a Solution
Agata 78 said:yes, the function runs from -∏ to ∏. its from (-∏ to ∏/2) ( -∏/2 to ∏/2) and ( ∏/2 to ∏). There is no period in it, it doesn't repeat. Than it has to be even in. even in is cosinus than yes?
Agata 78 said:dont know what you mean by argument?
Agata 78 said:yes, the function runs from -∏ to ∏. its from (-∏ to ∏/2) ( -∏/2 to ∏/2) and ( ∏/2 to ∏). There is no period in it, it doesn't repeat. Than it has to be even in. even in is cosinus than yes?
I was thinking that the terms in the Fourier Series should be Ancos(nx) where x runs from -π to +π, and n is the sequence of integers 1,2,3,... So, the argument is nx.Agata 78 said:dont know what you mean by argument?
Chestermiller said:I was thinking that the terms in the Fourier Series should be Ancos(nx) where x runs from -π to +π, and n is the sequence of integers 1,2,3,... So, the argument is nx.
No apology necessary RM. You're the man!rude man said:You're right, the argument of each of the harmonics is nx, not x.
I wanted to say that his function was an even function of x, x being the argument of f(x).
Sorry Chet!
Agata 78 said:Is this function is odd or even, cause I am confused. When it repeats itself its called odd when its not its even.
This one repeats it self then its odd yes?
And using co- efficient formulae with 2L= 2π, than L= π.
after calculating
[a][/0] =0
[a][/ 1] = 0
dont know how to calculate [/0] ?
Agata 78 said:∞ n∏x n∏x
Sf(x) = a0 +Ʃ [ an cos L + bn sin L ]
n=1
1 ∏
a0= 2∏ ∫ f(x) dx =O
-∏
1 ∏
a1= ∏ ∫ f(x) cos nx dx= 0,
-∏
what happenes if even times even = is it odd? I know when odd times odd = even.
Im sorry i don't have a clue how to use latex, i tried so many times and still doesn't work. Its hard
Agata 78 said:I don't know how to do that, could you please help me?
Agata 78 said:It looks complicated, wouldn't know where to start!
The Fourier series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is named after the French mathematician Joseph Fourier and is used to analyze and approximate various types of signals and waveforms.
The Fourier series is a powerful mathematical tool that is used in various fields such as physics, engineering, and signal processing. It allows us to break down complex functions into simpler components, making it easier to analyze and understand them. It also allows us to approximate any periodic function with a combination of sinusoidal functions.
The coefficients of the Fourier series can be determined by using the Fourier series formula, which involves integrating the given function with respect to the variable of interest. The coefficients represent the amplitudes and frequencies of the sinusoidal functions that make up the Fourier series.
The Fourier series is used to represent a periodic function, while the Fourier transform is used to represent a non-periodic function. The Fourier series uses discrete frequencies, while the Fourier transform uses continuous frequencies. Additionally, the Fourier transform is more general and can be applied to a wider range of functions.
The Fourier series has numerous applications in various fields, such as audio and image processing, telecommunications, and signal analysis. It is used to compress audio and image files, filter out noise from signals, and analyze the frequency components of a signal. It is also used in the design of electronic circuits and in solving differential equations.