1. Additional Material on Digitization: Aliasing By Rick Pitchford

2. The Nyquist Theorem: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 AmplitudeAmplitude A signal must be sampled at a rate more than twice its frequency - more than two samples per cycle. Why? If sampled at exactly twice the signal’s frequency, the data becomes indeterminate. Time 140 130 120 110 100 90 80 70 60 50 40 30 20 10 83 42 57 98 70

3. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Time AmplitudeAmplitude At frequencies greater than half the sampling rate - less than two samples per cycle - aliases are formed. Aliases are reconstructed analog signals that didn’t exist in the original. Nyquist Theorum:

4. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Time AmplitudeAmplitude In order to prevent aliases, analog signals are run through very steep low-pass anti-aliasing filters to eliminate the signals at and above one half the sampling frequency. Nyquist Theorum:

5. CCD and CMOS camera pickups are analog devices - each photo site generates a continuously varying signal - but are sampled spatially by the nature of their row and column layout. To eliminate spatial aliases from fine detail, all chip cameras use a fog-type anti-aliasing filter to limit the high frequency details passing through the lens and onto the transducer surface. DSLRs subsample their imagers, using only every fourth or fifth row and column to produce HD video but only have an anti-alias filter designed for full- resolution still images, causing moiré patterns. CCDs - Sampled Analog:

6. images from www.bealecorner.org/red/test-patterns/ and the Great Camera Shootout 2011, Pt 2 DSLR Spatial Aliasing:

7. video from B+U Steinmueller and nofilmschool.com This is from footage shot with a Canon T2i, but any DSLRs without an anti-aliasing filter specifically for the version of HD video being shot will show the same type of artifacts on the roof. Spatial Aliasing in the Wild:

8. video from http://www.cinema5d.com/news/?p=11684 An Aftermarket Anti-aliasing Filter: 1080p/24

9. Clip from Mitsubishi Motor Corp at http://www.youtube.com/watch?v=5wcQjvi9J38 Film is also a sampled system, using a rate of 24 frames per second. Low frame rates cause artifacts in rapid camera movements plus the infamous “reverse rotating wheel spokes” seen in many car commercials and westerns Increasing the frame rate will allow faster moves and rotation before aliases appear. Frames and Temporal Aliasing:

10. analog in Block Diagram of a “Typical” Digital Device: analog out anti-aliasing filter & level control A/D Processing/ Storage D/A smoothing filter based on diagram from Broadcast Engineering, May, 2004 The input is low-pass filtered to remove frequencies at or above 1/2 sampling rate; levels are constrained to match the limitations of the quantization stage. The analog signal is sampled and quantized. The data is converted back to analog form. The desired process is performed or the data stored. The reconstructed analog signal is low- pass filtered to round out waveforms.

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