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[[Category:Hw3ECE438F09boutin]] | [[Category:Hw3ECE438F09boutin]] | ||
| − | =HW3_Signal Reconstruction_Interpolation= | + | =HW3_Signal Reconstruction_Interpolation (Band-limited)= |
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| + | After having creating a sampled version of your original function, '''<math>X_{s}</math>''', we need to reconstruct the original function '''<math>x(t)</math>'''. To do this, the Whittaker-Shannon interpolation formula is utilized. | ||
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| + | The sampling theorem says that given a function that meets two requirements: | ||
| + | :1) It is band-limited. This means that the Fourier transform of the original signal, also known as the spectrum, is 0 for |f| > B, where B is the bandwidth. | ||
| + | :2) It is sampled at the Nyquist frequency, <math>f_s > 2B</math> | ||
| + | |||
| + | it can be exactly reconstructed from its samples. | ||
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Revision as of 18:28, 22 September 2009
HW3_Signal Reconstruction_Interpolation (Band-limited)
After having creating a sampled version of your original function, $ X_{s} $, we need to reconstruct the original function $ x(t) $. To do this, the Whittaker-Shannon interpolation formula is utilized.
The sampling theorem says that given a function that meets two requirements:
- 1) It is band-limited. This means that the Fourier transform of the original signal, also known as the spectrum, is 0 for |f| > B, where B is the bandwidth.
- 2) It is sampled at the Nyquist frequency, $ f_s > 2B $
it can be exactly reconstructed from its samples.
