220 4 Structure of a Digital Airborne Camera
Apart from the signal-to-noise ratio, the FFT analysis provides additional tech-
nical data such as the total distortion factor (linearity) and spurious frequency
spacing, which will not be covered in detail here. The possibility of determining
the resulting number of bits of the actual resolution of the A-D converter is also
interesting.
The SNR value of a system is calculated as a ratio of the effective value of
excitation to the effective value of all noise components. Thus, by analogy with
(4.6-1),
SNR = U
Signal
(rms)/U
Noise
(rms) (4.6-3)
Or, in [dB],
SNR
dB
= 20 · log {U
Signal
(rms)/U
Noise
(rms)} (4.6-4)
The measured data acquisition time (start and end of acquisition), which is also
termed windowing, is limited. This rectangular window function has an effect in the
case of the FFT. The number N of FFT dots yields a correction factor for the y read-
ings. In logarithmic terms this yields the shift 10 ·log(N/2) in the case of windowing.
If the measured data underlying the FFT calculation were acquired asynchronously,
i.e., without a fixed phase and frequency correlation, then the measurement
should be evaluated with another windowing function (for example, Hanning,
Hamming, Blackmann-Harris et al.). In this way the error caused by the phase
position of the periodic sinusoidally shaped excitation relative to the window is
minimised.
Assuming coherent sampling with a rectangular windowing function, we obtain
the following noise floor:
U
Noise
[dB] = effective noise level +10 log(N/2) (4.6-5)
where N = number of FFT dots and N/2 = number of frequency positions.
Another important aspect for evaluating and/or selecting an A-D converter is
the sampling rate. According to the sampling theorem, an original signal can be
unequivocally restored only if the sampling rate fs of the converter is at least twice
as high as the highest frequency fc occurring in the signal, i.e., fs >2fc.
This holds true only, however, if the input signals are assumed to be sinusoidally
shaped. When A-D converters are used for digitising CCD signals, this statement
is compromised, since the input is not a sinusoid, but rather a quasi-discrete signal
which changes its value at equal intervals. It suffices (theoretically) if the converter’s
sampling rate of say 10 Msamples/s is identical to the CCD’s video frequency, in
this case namely 10 Mpixels/s. The basic condition here is, of course, that the A-D
converter has enough time to sample the quasi-stationary value (processed by CDS)
of the video signal. An example of such timing is shown in Fig. 4.6-10. Apart from
the CDS signals SHP and SHD, this timing shows the DATACLK signal. This is the
control pulse for the A-D converter, which is synchronous and staggered in time,
but with the frequency as the CCD video signal. It can be seen from the position