Term
| Describe the relationship between DFT & DTFT. |
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Definition
X[k] = X(ejω)|ω=kω0
= X(ejkω0) , 0 ≤ k ≤ N-1
where... ω0 = 2Π/N |
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Term
| Describe the relationship between DFT & z-transform. |
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Definition
X[k] = X(z)|z=ejkω0 , 0 ≤ k ≤ N-1
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Term
| Describe the process of "zero padding". |
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Definition
| Increasing the value of N by "zero padding" the signal, increases the frequency repsonse of DFT. |
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Term
| Describe the relationship between DFT & DTFT. |
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Definition
This can be considered as the frequency resolution of the DFT.
If the actual length of signal x[n] is L, obviously, N must be ≥ L for the DFT to be useful. |
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Term
| How is DFT identical to DTFT? |
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Definition
| If the finite-length x[n] is considered as a periodic sequence /w period N. |
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Term
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Definition
DFT transform pair:
[image]
Both x[n] and X[k] are discrete and of the same finite length N. |
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Term
| Describe Discrete-time Fourier Series (DTFS). |
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Definition
- DTFS transforms a periodic discrete-time signal to discrete frequency representation.
- Both ˜x[n] and ˜X[k] are periodic sequences with period N.
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