21-09-2013, 04:31 PM
Signal Processing and Modulation
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Static and Quasi-Static Signals
Static signals are by definition unchanging over a long period of time. Such signals
are essentially DC levels, while quasi-static signals are those that change very slowly
such as the drift on a sensor.
Periodic and Repetitive Signals
Periodic signals are those that repeat themselves on a regular basis. These include
sine, square and sawtooth waves. Their nature is such that each waveform is identical.
Repetitive signals are periodic in nature, but the exact shape may change slightly with
time. ECG signals are an example of this type.
Transient and Quasi Transient Signals
Transient signals are either one time only signals while quasi-transient signals are
those which are periodic but with a duration which is very short compared to the
period of the waveform. Pulsed radar signals are good examples of these.
Butterworth
This approximation to an ideal low pass filter is based on the assumption that a flat
response at zero-frequency is most important. The transfer function is an all-pole type
with roots that fall on the unit circle.
The Ear as a Filter Bank
In the ear, sound waves are transmitted into the cochlea which tapers in size like a
cone. Through the middle stretches the basilar membrane which gets wider as the
cochlea gets narrower.
The vibratory movement is transmitted as a standing wave in the basilar membrane
(much like a snapping rope) with the amplitude reaching a peak at a location
dependent on frequency due to the varying resonant characteristics of the membrane
as shown schematically in the following figure.
High frequency peaks occur toward the base (where the membrane is stiffest and
narrowest) while the low frequency peaks occur towards the apex. Hair cells rest on
the basilar membrane and convert these vibrations to electro-chemical signals which
are transmitted to the brain for interpretation.
Analog Modulation and Demodulation
A continuous unmodulated signal cannot be used to measure range as there is no way
of determining when the signal was transmitted.
For most sensor applications, the transmitted signal is “marked” in some way either
by altering its amplitude or frequency.
The round trip time from the moment that the “mark” is transmitted to when it is
received can then be used to determine the range to the target if the speed of
propagation is known.