Hamming Window
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The 12 Term Fourier Series of a Square Wave with a Hamming Window N=12 |
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| Amplitude | Frequency (rad/sec) | Phase (degrees) | |
| [0.54 + 0.46cos (pi × 1/12)] × 1 | 1 | 0 | |
| [0.54 + 0.46cos (pi × 3/12)] × 1/3 | 3 | 0 | |
| [0.54 + 0.46cos (pi × 5/12)] × 1/5 | 5 | 0 | |
| [0.54 + 0.46cos (pi × 7/12)] × 1/7 | 7 | 0 | |
| [0.54 + 0.46cos (pi × 9/12)] × 1/9 | 9 | 0 | |
| [0.54 + 0.46cos (pi × 11/12)] × 1/11 | 11 | 0 | |
The Hamming window creates a smoother signal at the top of the square wave approximation. Add more harmonics creates an accurate approximation.
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The 24 Term Fourier Series of a Square Wave with a Hamming Window N=24 |
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| Amplitude | Frequency (rad/sec) | Phase (degrees) | |
| [0.54 + 0.46cos (pi × 1/24)] × 1 | 1 | 0 | |
| [0.54 + 0.46cos (pi × 3/24)] × 1/3 | 3 | 0 | |
| : | : | : | |
| : | : | : | |
| [0.54 + 0.46cos (pi × 21/24)] × 1/21 | 21 | 0 | |
| [0.54 + 0.46cos (pi × 23/24)] × 1/23 | 23 | 0 | |
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