(New page: 1. Using the same value I used in HW1. <math>e^{\frac{1}{4}j\pi*n}</math> 2. Also using the same value I used in HW1. <math>e^{\sqrt{3}j\pi*n}</math> As we learned in class, any DT f...) |
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<math>e^{\frac{1}{4}j\pi*n}</math> | <math>e^{\frac{1}{4}j\pi*n}</math> | ||
| + | This function can be periodic or non-periodic depending on the sampling rate. It will be periodic for any multiple of <math>\frac{1}{8}</math> as calculated in HW1. Similarly, for any sampling rate not a multiple of <math>\frac{1}{8}</math>, the function will not be periodic. | ||
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<math>x[n]=\sum{inf}{k=-inf}{d[n-k]}</math> | <math>x[n]=\sum{inf}{k=-inf}{d[n-k]}</math> | ||
| + | |||
| + | By taking multiple unit impulses we can make a non-periodic function periodic. | ||
Latest revision as of 09:08, 12 September 2008
1. Using the same value I used in HW1.
$ e^{\frac{1}{4}j\pi*n} $
This function can be periodic or non-periodic depending on the sampling rate. It will be periodic for any multiple of $ \frac{1}{8} $ as calculated in HW1. Similarly, for any sampling rate not a multiple of $ \frac{1}{8} $, the function will not be periodic.
2. Also using the same value I used in HW1.
$ e^{\sqrt{3}j\pi*n} $
As we learned in class, any DT function x[n] can be written as:
$ x[n]=\sum{inf}{k=-inf}{d[n-k]} $
By taking multiple unit impulses we can make a non-periodic function periodic.
