Fourier transform and its applications using Microsoft EXCEL®
Fourier transformations Transformations (Mathematics)
IOP Publishing
2018
EISBN 9781643272863
1. The principle of superposition and the Fourier series.
1.1. The principle of superposition.
1.2. Wave equations.
1.3. Fourier series.
1.4. Orthonormal basis
2. The Fourier transform.
2.1. From the Fourier series to the Fourier transform.
2.2. Practical computational issues of the Fourier transform.
2.3. Discrete Fourier transform and fast Fourier transform
3. The EXCEL-based Fourier transform.
3.1. Data acquisition.
3.2. Fourier transform.
3.3. The effect of windowing function.
3.4. Peak peeking.
3.5. 2N-point FFT from N-point FFTs.
3.6. Inverse Fourier transform
4. The Fourier transform in physics.
4.1. Examples of acoustic spectra.
4.2. Electronic circuits.
4.3. Telecommunication signals.
4.4. Spectroscopy.
4.5. Fourier transform in optics.
4.6. Quantum mechanics
5. Beyond the Fourier transform spectroscopy.
5.1. LP method.
5.2. ME method.
5.3. LPC examples.
5.4. LPC cepstrum.
This book demonstrates Microsoft EXCEL®-based Fourier transform of selected physics examples, as well as describing spectral density of the auto-regression process in relation to Fourier transform. Rather than offering rigorous mathematics, the book provides readers with an opportunity to gain an understanding of Fourier transform through the examples. They will acquire and analyze their own data following the step-by-step procedure outlined, and a hands-on acoustic spectral analysis is suggested as the ideal long-term student project.
1.1. The principle of superposition.
1.2. Wave equations.
1.3. Fourier series.
1.4. Orthonormal basis
2. The Fourier transform.
2.1. From the Fourier series to the Fourier transform.
2.2. Practical computational issues of the Fourier transform.
2.3. Discrete Fourier transform and fast Fourier transform
3. The EXCEL-based Fourier transform.
3.1. Data acquisition.
3.2. Fourier transform.
3.3. The effect of windowing function.
3.4. Peak peeking.
3.5. 2N-point FFT from N-point FFTs.
3.6. Inverse Fourier transform
4. The Fourier transform in physics.
4.1. Examples of acoustic spectra.
4.2. Electronic circuits.
4.3. Telecommunication signals.
4.4. Spectroscopy.
4.5. Fourier transform in optics.
4.6. Quantum mechanics
5. Beyond the Fourier transform spectroscopy.
5.1. LP method.
5.2. ME method.
5.3. LPC examples.
5.4. LPC cepstrum.
This book demonstrates Microsoft EXCEL®-based Fourier transform of selected physics examples, as well as describing spectral density of the auto-regression process in relation to Fourier transform. Rather than offering rigorous mathematics, the book provides readers with an opportunity to gain an understanding of Fourier transform through the examples. They will acquire and analyze their own data following the step-by-step procedure outlined, and a hands-on acoustic spectral analysis is suggested as the ideal long-term student project.
