Additional Material on Digitization: Aliasing By Rick Pitchford
The Nyquist Theorem: 140 130 120 110 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. 98 100 90 m p 83 80 l 70 70 A i 60 t 57 50 u 42 40 30 20 Time 10 1 2 3 4 5 6 7 8 9 10 11 12 13 14 d e
Nyquist Theorum: 14 13 12 11 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. 10 A m 9 p 8 l 7 i 6 t 5 u 4 d e 3 2 Time 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14
Nyquist Theorum: 14 13 12 11 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. 10 A m 9 p 8 l 7 i 6 t 5 u 4 d e 3 2 Time 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14
CCDs - Sampled Analog: 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 fullresolution still images, causing moiré patterns.
DSLR Spatial Aliasing: images from www. bealecorner. org/red/test-patterns/ and the Great Camera Shootout 2011, Pt 2
Spatial Aliasing in the Wild: This is from footage shot with a Canon T 2 i, 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. video from B+U Steinmueller and nofilmschool. com
An Aftermarket Anti-aliasing Filter: 1080 p/24 video from http: //www. cinema 5 d. com/news/? p=11684
Frames and Temporal Aliasing: 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. Clip from Mitsubishi Motor Corp at http: //www. youtube. com/watch? v=5 wc. Qjvi 9 J 38
Block Diagram of a “Typical” Digital Device: analog in The input is low-pass filtered to remove frequencies anti-aliasing filter at or above 1/2 sampling rate; levels are constrained & level control to match the limitations of the quantization stage. A/D The analog signal is sampled and quantized. Processing/ Storage The data is converted back to analog form. The desired process is performed or the data stored. D/A The reconstructed analog signal is lowpass filtered to round out waveforms. smoothing filter analog out based on diagram from Broadcast Engineering, May, 2004
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