Dr. Fred J. Taylor, Professor
Lesson Title: Continuous-Time Signal and
Lesson Number: 25 (Section 9-1 to 9-4)
signals and systems are known to the general public as
They have always been a part of man’s natural world in which our analog sensory
systems are presumed to process analog signals. A bridge between discrete-time signal and
system domains, studied to this point (Chapters 1-8), has been constructed using the Sampling
Theorem, z-transforms, and similar tools.
They are, however, differences between continuous-
and discrete-time signal and system models that should be understood.
The studies presented
in Chapter 9 develop these ideas and builds a framework in which the study of continuous-time
signal and systems can take place.
Continuous-time signals x(t) persist over an interval of time called the signal’s
interval of time can be
], also called “right sided”), or
Over the signal’s support, the continuous-time signal is continuously resolved in time
and amplitude (meaning that the time and amplitude values of x(t) are known with infinite
Over their support, continuous-time signals maybe
(e.g., noise) or
They maybe 1-
(e.g., x(t)=speech), 2-
)=2-D image), or multi-
, … , k
) = mechanical
system with n-degrees of freedom).
Signals may also be
(e.g., A cos(
Two-sided are assumed to exist for all time.
For example, a common sinusoidal test signal:
can be used to mathematically study the dynamic behavior of continuous-time systems. The
signal model assumes that the signal has always been present and will always be present.
raises questions of physical realizably which are often ignored.
Two-sided signals can also be
), a property that a one-side or finite support signal can not
One-sided signals are generally assume to be
For example, a common
test signal shown below: