| Line 56: | Line 56: | ||
\begin{array}{l l} | \begin{array}{l l} | ||
n/2 & \quad \mbox{if n/D \in Z}\\ | n/2 & \quad \mbox{if n/D \in Z}\\ | ||
| − | 0 & \quad \mbox{else}\\ \end{array} \right. \] | + | 0 & \quad \mbox{else}\\ \end{array} \right. \],<\math> |
Revision as of 22:48, 22 September 2009
Discrete Time Interpolation
Mathematically, sure. Realistically? Let's find out.
Introduction
My fascination with the concept of discrete time interpolation began, when I asked Prof. Boutin if a discrete time interpolator, can ideally make a low-resolution image, a high resolution one.
The answer was, yes. Ideally, it can.
The equations that led to the concept seemed impeccable and mathematically, it seemed to make perfect sense.
But essentially, all we are doing is:
- adding zeros in between samples (the result of which looks horrible by the way)
- Low pass filtering,
and Voila! hi-res image. Impossible right?
After 6 hours of coding, and processing the image of my dog "Milo"(shown below), countless times, I am proud to say, that it is
"Almost Possible in the Real World"
Page Map
This page contains
- A mathematical basis for discrete time interpolation
- Application to a simple 1-D signal
- Application to an actual real-world image
Mathematical Basis
Discrete Time Interpolation looks at what happens if I take a signal x[n], originally sampled at rate T1, and I fill in zeros between the samples.
The number of zeros between each sample is D
where D is defined:
$ D = \frac{T2}{T_1} $
Then we can define $ x_2[n] $ as:
$ \[x_2(n) = \left\{ \begin{array}{l l} n/2 & \quad \mbox{if n/D \in Z}\\ 0 & \quad \mbox{else}\\ \end{array} \right. \],<\math> $
