![Sinusoids
Input(-∝, +∝) Output [1,-1]](https://image.slidesharecdn.com/fourieranalysispresentationforthunderchasers-200712203354/85/Fourier-analysis-presentation-for-thunder-chasers-3-320.jpg)
Fourier analysis presentation for thunder chasers
- 1. Fourier Analysis An Intuitive Perspective A Basic Introductory Discussion Portraying how Fourier Series or Transformation Play Around Us
- 2. Axial Breakdown v cosx v sinx v x
- 3. Sinusoids Input(-∝, +∝) Output [1,-1]
- 4. Fourier Series 𝒇 𝒙 = 𝒂 𝟎 𝟐 + 𝒏=𝟏 ∞ 𝒂 𝒏 𝐜𝐨𝐬 𝟐𝒏𝝅𝒙 𝒃 − 𝒂 + 𝒃 𝒏 𝐬𝐢𝐧 𝟐𝒏𝝅𝒙 𝒃 − 𝒂 𝒂 𝟎 = 𝟐 𝒃 − 𝒂 𝒂 𝒃 𝒇 𝒙 ⅆ𝒙 𝒂 𝐧 = 𝟐 𝒃 − 𝒂 𝒂 𝒃 𝒇 𝒙 𝐜𝐨𝐬 𝟐𝒏𝝅𝒙 𝒃 − 𝒂 ⅆ𝒙 𝒃 𝐧 = 𝟐 𝒃 − 𝒂 𝒂 𝒃 𝒇 𝒙 𝐬𝐢𝐧 𝟐𝒏𝝅𝒙 𝒃 − 𝒂 ⅆ𝒙 𝒇 𝒕 = 𝒂 𝟎 𝟐 + 𝒏=𝟏 ∞ 𝒂 𝒏 𝐜𝐨𝐬 𝒏𝒘𝒕 + 𝒃 𝒏 𝐬𝐢𝐧 𝒏𝒘𝒕
- 5. 𝒚 = 𝒇 𝒙 = 𝒙 − 𝝅 𝑎0 = 2 2𝜋 0 2𝜋 𝑥 − 𝜋 𝑑𝑥 = 0 𝑏 𝑛 = 2 2𝜋 0 2𝜋 𝑥 − 𝜋 sin( 2𝜋𝑛𝑥 2𝜋 )𝑑𝑥 = − 2 𝑛 𝑎 𝑛 = 2 2𝜋 0 2𝜋 𝑥 − 𝜋 cos( 2𝜋𝑛𝑥 2𝜋 )𝑑𝑥 = 0 𝒇 𝒙 = −𝟐 𝒏=𝟏 ∞ 𝟏 𝒏 𝐬𝐢𝐧 𝒏𝒙 = −𝟐 (𝒔𝒊𝒏 𝒙 + 𝟏 𝟐 𝒔𝒊𝒏 𝟐𝒙 + 𝟏 𝟑 𝒔𝒊𝒏𝟑𝒙 + ⋯ . + 𝟏 𝒏 𝒔𝒊𝒏 𝒏𝒙 ) = 𝑭(𝒙) Fourier Series Ch. VI : Non-Sinusoidal Wave Example-1 Alternating Current Circuits by RM Kerchner & GF Corcoran
- 6. Sawtooth Wave Transformed Credit :Meyavuz
- 8. Straight Line with Sinusoids Credit :Mathloger
- 9. Have a Look ! Credit :Faviloo
- 10. Fourier in Exponential Form 𝒇 𝒕 = 𝒂 𝟎 𝟐 + 𝒏=𝟏 ∞ 𝒂 𝒏 𝐜𝐨𝐬 𝒏𝒘𝒕 + 𝒃 𝒏 𝐬𝐢𝐧 𝒏𝒘𝒕 sin 𝑛𝑤𝑡 = 1 2𝑖 (𝑒 𝑖𝑛𝑤𝑡 − 𝑒−𝑖𝑛𝑤𝑡) cos 𝑛𝑤𝑡 = 1 2 (𝑒 𝑖𝑛𝑤𝑡 + 𝑒−𝑖𝑛𝑤𝑡) 𝒇 𝝎 = 𝟏 𝟐𝝅 −∝ +∝ 𝒇(𝒕)𝒆−𝒊𝝎𝒕 𝒅𝒕 𝑓 𝑡 = 𝑎0 2 + 𝑛=1 ∞ ( 𝑎 𝑛 − 𝑖𝑏 𝑛 2 𝑒 𝑖𝑛𝜔𝑡 + 𝑎 𝑛 + 𝑖𝑏 𝑛 2 𝑒−𝑖𝑛𝜔𝑡) 𝑓 𝑡 = 𝑛=−∝ ∝ 𝑎 𝑛 𝑒 𝑖𝑛𝜔𝑡
- 11. Who cares about Fourier , huh ? Waves can be expressed as a sum of sines and cosines.
- 13. Who cares about Fourier , huh ? Shifting from Time Domain to Frequenc y Domain
- 14. Who cares about Fourier , huh ? Shifting from Time Domain to Frequenc y Domain
- 15. Frequency Domain Credit: RF Wireless World Credit: Pablo Puente Guillen
- 16. Applications Image Audio Filter Reconstruction Compression Compression Noise Exclusion Sound Synthesize
- 17. References & Resources https://www.quora.com/Why-are-Fourier-series- important-Are-there-any-real-life- applications-of-Fourier-series https://www.quora.com/What-are-the-applications -of-fourier-series-in-electrical-engineering https://en.wikipedia.org/wiki/Fourier_series https://www.youtube.com/watch?v=qS4H6PEcCCA Alternating Current Circuit by RM Kerchner & GF Corcoran Analysis of Linear Systems by D K Cheng https://www.youtube.com/watch?v=Mf8z3nm7prQ https://www.youtube.com/watch?v=wNwJOBmqBsc Special thanks to Aninda Nandy
- 18. T hank You Mohammad Iftekher Ebne Jalal (Iftu) ID : 1802119 Department of Electrical & Electronic Engineering, Chittagong University of Engineering & Technology I only intended to make you feel excited about Fourier Series. Feel free to learn more on this.