1. Multimedia Systems & Interfaces
Slides adapted from material created by Chris Wren and Paris Smaragdis

2. Images
Transforms (cont.)
Sampling (cont.)
Filter examples

3. Affine Transforms

22. Sampling

23. Downsampling From high sample rate to low Downsampling by 2
If we pick one out of two samples we will introduce aliasing
In order to get around it we can remove the high frequencies first and then pick samples
For downsampling by M
Lowpass to 1/M
Then pick one out of M samples
Only works for integer M
Loss of information (high freqs)
We can double up as well
To downsample by M = 8 we can downsample three times by M = 2
Use MATLAB’s decimate for this

24. Upsampling We can combine multiple upsamplers
From low sample rate to high
For upsampling by L
Put L-1 zeros between each sample
Lowpass filter to 1/L
Only works for integer L
Without filtering we get these noisy clicks
No loss of information
We can combine multiple upsamplers
To upsample by L=8 we can upsample three times by L=2
Use MATLAB’s interp

25. What if the ratio is not integer?
Describe it using two integers
E.g. to go from 44.1kHz to 48kHz
Upsample by
This is 480/441
We can upsample by 480 and downsample by 441!
Efficiency
There are ways to deal with not having to upsample by 480
Using tricky bookkeeping we can consolidate the two operations into one
For huge inputs it can be brutal otherwise!
That’s why CDs are 44.1kHz and DATs are 48kHz, to make resampling a pain
For nasty ratios we might get to lose a little bit of information
But it all sounds good pretty much always
Use MATLAB’s resample
44.1kHz
21168 kHz
Upsample by 480
21168 kHz
Downsample by 441
48 kHz

26. As we recall from last class, we should consider the Nyquist rate when sampling.
A very good example can be found in wikipedia under Nyquist.