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1. RAJARSHI SHAHU COLLEGE OF ENGINEERING TATHAWADE, PUNE Applications of Fourier series NAME: Nirasha Gajajan Kirme Div. : C (Electrical) Sub .: Engineering mathematics I Roll No. : 30

2. What Is The Fourier Series Used For? 

3. The Fourier series is a powerful mathematical tool for representing or analysing periodic signals. At first, the Fourier series can be difficult to comprehend as there is significant mathematics involved, but when you use the Fourier series in real-world applications, its function, importance and power become quickly clear

4. Typically, some real-world applications of the Fourier series include applications such as signal filtering, noise removal, identifying the resonant frequency of a structure, compression of audio signals and speech recognition.

5. 1. Selective Filtering The Fourier series can be used to design filters that remove specific frequency components from a signal while preserving others. This is known as selective filtering. For example, we often design audio filters using the Fourier series to remove unwanted noise from an audio signal while preserving the desired frequencies.

6. 2. Noise Filtering The Fourier series can be used to remove unwanted noise from a signal. This is known as noise reduction or noise cancellation. For example, active noise cancellation headphones use the Fourier series to remove unwanted background noise from an audio signal.

7. 3. Identifying Resonant Frequencies The Fourier series can be used. to identify the resonant frequency of a structure. This is known as resonance analysis. For example, the Fourier series can be used to analyse the resonance behaviour of a building or bridge. By Identifying the resonant frequencies of a structure, engineers can design the structure to avoid these frequencies or dampen them to prevent damage.

8. 4. Compression Of Signals The Fourier series can be used to compress signals by removing redundant information. For example, image compression algorithms often use the Fourier transform to remove high-frequency components that are not perceptible to human vision. This reduces the file size of the image without significantly degrading its quality.  The Fourier series can be used to compress audio signals. This is known as audio compression. For example, the mp3 audio format uses the Fourier series to compress audio files.

9. 5. Speech Recognition The Fourier series can be used for speech recognition. For example, the Fourier series can be used to process and recognise speech patterns

10. 6. Data Transmission The Fourier series can be used to encode and decode signals for transmission over a channel. This is known as data modulation. For example, the Fourier series can be used to modulate an audio signal for transmission over a telephone line.

11. THANK YOU…