Multimedia Systems & InterfacesImagesAffine TransformsPowerPoint PresentationSlide 5Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21SamplingSlide 23UpsamplingSlide 25Slide 26Multimedia Systems &InterfacesSlides adapted from material created by Chris Wren and Paris SmaragdisImages•Transforms (cont.)•Sampling (cont.)•Filter examplesAffine TransformsSamplingDownsampling•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 thisTimeFrequency0 0.5 1 1.5 2 2.5 3 3.5 4x 10400.10.20.30.40.50.60.70.80.911 2 3 4 5 6 7 8 9 10-1.5-1-0.500.511.5Upsampling•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 i nterp 1 2 3 4 5 6 7 8 9 10 11-20210 20 30 40 50 60 70 80 90 100-2020 10 20 30 40 50 60 70 80 90 100-101What if the ratio is not integer?•Describe it using two integers–E.g. to go from 44.1kHz to 48kHz–Upsample by 1.0884–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 resample44.1kHzUpsample by 480Downsample by 44121168 kHz21168 kHz48 kHzAs we recall from last class, we should consider the Nyquist rate when sampling.A very good example can be found in wikipedia under
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