ABSTRACT
Although already discussed in Chapter 2, sampling will be briefly revisited. In the simplest case, a SODAR transmits a signal
Asin(2πfTt)
at a frequency fT. The received signal is continuous, has reduced amplitude, in general is Doppler shifted and has modified phase
p t A f f tT( )= + +( )∗ sin 2π φ∆
This signal can be sampled using an analog-to-digital converter (ADC) at times
t m t m
f mm
s = = =∆ 0 1, ,…
The sampling frequency is fs. The sampled signal has discrete values
p A m f f fm
s = + +
∗ sin 2π φ∆
(6.1)
For simplicity, write
f f f
+ = +∆ δ
where n is an integer 0, 1, …, and δ is a fraction. Then
p A mm = +( )∗ sin 2π δ φ
since sin(θ±2πmn) = sin(θ). As an example, assume fs = 960 Hz: a signal component having frequency 960 + 960/3 = 1280 Hz gives the same digitized values as if it had
frequency 960/3 = 320 Hz. The same is true for negative δ. This means that higher frequency components can add into the lower frequency spectrum. This is called aliasing. This means that all frequency components outside of nfs ± fs/2 should be excluded from the signal before digitizing. This is called the Nyquist criterion. Usually this is interpreted as using anti-aliasing low-pass filters to remove all frequency components outside of ±fs/2, but in fact the criterion is satisfied if band-pass filters remove all components within a ±fs/2 bandwidth of nfs.
