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| + | =[[Hw2ECE38F10|HW2]] Discussion, [[ECE438]], Fall 2010, Prof. [[user:mboutin|Boutin]] = | ||
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So, my understanding of this material is that X(f),X1(w) mainly differ on their X axis scaling, and same sort of thing X1 and X2? | So, my understanding of this material is that X(f),X1(w) mainly differ on their X axis scaling, and same sort of thing X1 and X2? | ||
Valid? ~AJFunche | Valid? ~AJFunche | ||
| − | ::It's a bit more complicated than a mere rescaling of the frequency axis. First, one must not forget that the DTFT is ALWAYS periodic with period <math>2\pi</math>. Second, the amplitude of the FT changes when sampling. Third, something called "aliasing" might occur. --[[User:Mboutin|Mboutin]] 08:56, 7 September 2010 (UTC) | + | ::It's a bit more complicated than a mere rescaling of the frequency axis. First, one must not forget that the DTFT is ALWAYS periodic with period <math>2\pi</math>. Second, the amplitude of the FT changes when sampling. Third, something called "aliasing" might occur. Can other students please try clarify this? I will step in if I notice obvious misconceptions/mistakes.--[[User:Mboutin|Mboutin]] 08:56, 7 September 2010 (UTC) |
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| + | I think the question is asking us to choose a sampling frequency greater than and less than half the natural frequency of the signal we choose (some note in the middle of the piano other than C), sample the signal at those frequencies, plot the two sampled signals and observe the differences. Also, take the CTFT of the original signal and compare it to the sampled signals. Is that correct? | ||
| + | ::Yes, that is the idea. But you should also note the similarities between the Fourier transforms (not just the differences). --[[User:Mboutin|Mboutin]] 12:07, 7 September 2010 (UTC) | ||
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| + | [[Hw2ECE38F10|Back to HW2 ECE438 Fall 2010]] | ||
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| + | [[2010_Fall_ECE_438_Boutin|Back to ECE438 Fall 2010 Prof. Boutin]] | ||
Latest revision as of 07:07, 7 September 2010
HW2 Discussion, ECE438, Fall 2010, Prof. Boutin
So, my understanding of this material is that X(f),X1(w) mainly differ on their X axis scaling, and same sort of thing X1 and X2?
Valid? ~AJFunche
- It's a bit more complicated than a mere rescaling of the frequency axis. First, one must not forget that the DTFT is ALWAYS periodic with period $ 2\pi $. Second, the amplitude of the FT changes when sampling. Third, something called "aliasing" might occur. Can other students please try clarify this? I will step in if I notice obvious misconceptions/mistakes.--Mboutin 08:56, 7 September 2010 (UTC)
I think the question is asking us to choose a sampling frequency greater than and less than half the natural frequency of the signal we choose (some note in the middle of the piano other than C), sample the signal at those frequencies, plot the two sampled signals and observe the differences. Also, take the CTFT of the original signal and compare it to the sampled signals. Is that correct?
- Yes, that is the idea. But you should also note the similarities between the Fourier transforms (not just the differences). --Mboutin 12:07, 7 September 2010 (UTC)
