Fourier principles

Fourier principles


Welcome to the principle of Fourier series.

Now, "wave" to trigonometric (circular functions) can be approximated by summing of the Fourier series from the principles and mechanisms, we can understand intuitively explained.
(The calculation does not only uses addition and subtraction and multiplication and fractions. Please believe in the power of your own intuition.)


"Trigonometric functions with (circular functions) represented by the sum of."
This idea, "Egypt's mysterious country" is likely to leave were obtained.
Accompanied Napoleon's expedition to Egypt, we made a mathematical study various archaeological years 1801 - 1798.
Take home to France to discover the Rosetta Stone at this time has seen the age of 12 was Champollion.
Speaking of ancient Egypt, Pythagoras endowed 思I浮Kabemasu a priest of the mysteries of time.

Egypt is the wisdom of the "Pythagorean theorem" Knowing, "Principles of Fourier series," I can understand.

Sure to cite the cycle (series) increases the overall resolution.
However, the Fourier series itself, the shape of the wave is not close.
Only minor variation of the wave (total) are close to but just.
On behalf of the wave position, the amount of change in a limited period if they are watching as a wave.
Rather than deterministic, but the convergence is in fact an agnostic.
(If you explore the Fourier series as a deterministic, Achilles and the Tortoise comes into the head.)
※ Fourier series, you have what looks like a wave of interest, I will never know.
Integration with Datte, has a total area of ​​overlap. In the differential never that way.


○ rotation on wave
① For Waves
Relationship with the rotational movement of the wave generation and ②
③ about invisible to the eye rotation

○ proof of Pythagorean theorem
Pythagorean Theorem
For a right triangle equal sides ① 2
② If the public right-angled triangle

For information on how to deal with several waves ①
① For a right triangle and rectangular coordinates
Pythagorean theorem and Cartesian ②
Be expressed in Cartesian coordinates for the wave ③

② How to deal with the number of rotational motion
For a right triangle and circular functions ①
② relationship Pythagorean theorem and circular functions
Represented by a circle rotation function ③

How to bridge the gap between waves and rotational movement ③
Cartesian motion of the waves about ①
② rotation for the circular functions
Combining movement and rotational movement of the waves ③



Synthesis and synthesis of rotational movement of the waves ④
Synthesis of a square wave with wave ①
Synthesis of waves by circular functions ②
③ Preparation of rotation due to circular motion
Bridge directly to the rotational motion of waves ④


⑤ mechanisms and principles of Fourier series
Relationship between the yen and the square wave function ①
② square wave with circular motion relationship
③ The principle of superposition of waves
Synthesis of rotation of the wave components ④
⑤ rotation and wave generation
⑥ orthonormal functions and function spaces



Recent changes:
「⑤フーリエ級数の仕組みと原理」の「⑥関数空間と正規直交関数について」の解説図の差し替え。
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About Fourier principles
Welcome to the principle of Fourier series.

Now, "wave" to trigonometric (circular functions) can be approximated by summing of the Fourier series from the principles and mechanisms, we can understand intuitively explained.
(The calculation does not only uses addition and subtraction and multiplication and fractions. Please believe in the power of your own intuition.)


"Trigonometric functions with (circular functions) represented by the sum of."
This idea, "Egypt's mysterious country" is likely to leave were obtained.
Accompanied Napoleon's expedition to Egypt, we made a mathematical study various archaeological years 1801 - 1798.
Take home to France to discover the Rosetta Stone at this time has seen the age of 12 was Champollion.
Speaking of ancient Egypt, Pythagoras endowed 思I浮Kabemasu a priest of the mysteries of time.

Egypt is the wisdom of the "Pythagorean theorem" Knowing, "Principles of Fourier series," I can understand.

Sure to cite the cycle (series) increases the overall resolution.
However, the Fourier series itself, the shape of the wave is not close.
Only minor variation of the wave (total) are close to but just.
On behalf of the wave position, the amount of change in a limited period if they are watching as a wave.
Rather than deterministic, but the convergence is in fact an agnostic.
(If you explore the Fourier series as a deterministic, Achilles and the Tortoise comes into the head.)
※ Fourier series, you have what looks like a wave of interest, I will never know.
Integration with Datte, has a total area of ​​overlap. In the differential never that way.


○ rotation on wave
① For Waves
Relationship with the rotational movement of the wave generation and ②
③ about invisible to the eye rotation

○ proof of Pythagorean theorem
Pythagorean Theorem
For a right triangle equal sides ① 2
② If the public right-angled triangle

For information on how to deal with several waves ①
① For a right triangle and rectangular coordinates
Pythagorean theorem and Cartesian ②
Be expressed in Cartesian coordinates for the wave ③

② How to deal with the number of rotational motion
For a right triangle and circular functions ①
② relationship Pythagorean theorem and circular functions
Represented by a circle rotation function ③

How to bridge the gap between waves and rotational movement ③
Cartesian motion of the waves about ①
② rotation for the circular functions
Combining movement and rotational movement of the waves ③



Synthesis and synthesis of rotational movement of the waves ④
Synthesis of a square wave with wave ①
Synthesis of waves by circular functions ②
③ Preparation of rotation due to circular motion
Bridge directly to the rotational motion of waves ④


⑤ mechanisms and principles of Fourier series
Relationship between the yen and the square wave function ①
② square wave with circular motion relationship
③ The principle of superposition of waves
Synthesis of rotation of the wave components ④
⑤ rotation and wave generation
⑥ orthonormal functions and function spaces



Recent changes:
「⑤フーリエ級数の仕組みと原理」の「⑥関数空間と正規直交関数について」の解説図の差し替え。

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