When I wrote the April
2008 column entitled, "Mama
Don't Take My Kodachrome Away," I focused on how the image sensor of a
digital camera was replacing film, never thinking that in 2011, even if you had
a roll of that film, you could not get it developed anywhere in the world! Yet,
that is what has happened. On Dec. 30, 2010, at Dwayne's Photo in Parsons, KS,
the last rolls of Kodachrome film in the entire world were processed. It
dramatically shows how digital the world has become.
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The
diagram shows a computer-controlled system and the interface between the analog
power domain and the digital information domain. Digitization (A/D conversion)
is the act of converting an analog signal - continuous in both time and
amplitude - to a digital signal - discrete in both time and amplitude. Discrete
values in time are the result of sampling an analog signal and discrete values
in amplitude are the result of representing those values using a finite number
of bits (quantization). Fourier showed that any waveform that exists in the
real world can be generated by adding up sine waves of different amplitudes,
frequencies and phases, and that representation is unique. And Nyquist showed
that a sampled signal can be converted back to its original analog signal (D/A
conversion) without any error if the sampling rate is more than twice as large
as the highest frequency of the signal.
If this Nyquist Sampling Theorem
is violated, an inevitable, irreversible effect called aliasing results.
Aliasing cannot be completely eliminated, only reduced with an anti-aliasing
analog filter before sampling takes place. The effect of aliasing is that
frequencies above the Nyquist frequency (Β½ the sampling frequency, also called
the folding frequency) are folded back into the useful frequency range and
appear indistinguishable from the real signals. For example, a tone 1 KHz above
the Nyquist frequency will fold back to 1 KHz below, while a tone 1 KHz below
the sampling frequency will appear at 1 KHz. The control system will respond to
both signals - real and fictitious. The anti-aliasing filter will limit performance
because of time delay, but the effects of aliasing are much worse.
The accuracy achieved in a digital
memory device depends on the number of bits used for storage of each sample.
Quantization is the process of changing the sample values to discrete levels
and results in errors called quantization noise. The measure of the relative
size of quantization noise is called the signal-to-noise ratio (SNR) and it is
given by the simple formula SNR = 2
B, where B is the number of bits
used to store samples.
Yes, everything is going digital,
but like Kodachrome film, I hope all these digital devices can "make you think
all the world's a sunny day." We all need that!
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