# Lecture 13 Blog, ECE438 Fall 2010, Prof. Boutin

Wednesday September 22, 2010.

In Lecture #13, we continued considering the sampling

$x_1[n]=x(T_1 n)$

of a continuous-time signal x(t). We obtained and discussed the relationship between the DT Fourier transform of $x_1[n]$ and that of a downsampling $y[n]=x_1[Dn]$, for some integer D>1. (Yes, I know it was a lot of math, but this is good for you, trust me!) We then obtained the relationship between the DT Fourier transform of $x_1[n]$ and that of an upsampling of x[n] by a factor D. From this relationship, we concluded that, under certain circumstances, a low-pass filter could be applied to this upsampling so to obtain the signal

$x_2[n]=x\left( n \frac{T_1}{D} \right)$.

Side notes:

Previous: Lecture 12; Next: Lecture 14

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