Time Domain: Classification Flashcards
Part 1A of the Signals and Systems unit, describing fundamental classifications of signals.
What is a continuous time (CT) signal?
A signal that has values for all points in time in some interval. It is denoted as x(t), where t = time
What is a discrete time (DT) signal?
A discrete time signal has values for only discrete points in time. Effectively, it is a sequence of samples. It is denoted as x[n], where n Is an integer defined over some time interval.
When is a signal considered analogue?
A signal (CT or DT) is considered analogue if the values that the signal can have vary continuously.
When is a signal considered digital?
A signal (CT or DT) is considered digital if it can only have a finite set of possible values.
These signals are considered continuous time - continuous variable signals.
Analogue signals
These signals are considered to be discrete time - discrete variable signals.
Digital signals
When is a continuous time signal considered to be periodic?
A CT signal, x(t) is considered to be periodic with period T if:
x[t] = x(t+T), for all t
where T is a positive real constant
What is the fundamental period?
The smallest value of T that satisfies periodicity
What is the fundamental frequency of a periodic signal?
f = 1/T
What is the angular frequency of a periodic signal (CT and DT)?
ω = 2π/T, for a CT signal
ω = 2π/N, for a DT signal
When do we consider a discrete-time signal to be periodic?
A discrete-time signal is said to be periodic with period N if:
x[n] = x[n+N], for all n
where N is a positive integer constant
What are the 3 ways of representing power?
Instantaneous power, average power, total average power
How do we find the instantaneous power of a signal?
The magnitude of the signal squared at time t
What is an energy signal?
For the energy to be finite the amplitude of the signal should tend to zero as t tends to infinity, signals for which this is true are called energy signals.
What is a power signal?
A signal in which the function e.g. x(t) does not tend to 0 as t tends to infinity. This signal has infinite energy so we use power to quantify the signal instead.
What is the simple equation for power?
Power = Energy/Time
What is an odd signal?
A signal that is antisymmetric about the origin.
This means that x(t) = -x(-t) for all t for CT signal
or x[n] = -x[-n]
e.g. (2,-3) -> (-2, 3)
(1,1) -> (-1,-1)
Odd signals have a value of 0 at the origin
What is an even signal?
A signal which when plotted is symmetrical about the origin. This means:
x(t) = x(-t), for all t of a CT signal
x[n] = x[-n] for all n of a DT signal
e.g. (2, 3) -> (-2, 3)
(1, 1) -> (-1, 1)
What is the importance of odd and even signals?
Every signal can be expressed as a sum of odd and even components as follows:
x(t) = xe(t) + xo(t)
How can we express an even signal as a function of x and t?
xe(t) = 1/2[x(t)+x(-t)]
How can we express an odd signal as a function of x and t?
Xo(t) = 1/2[x(t) - x(-t)]
What is a causal signal?
Causal signals are non-zero only for t greater than or equal to zero.
The signal only has some value at and after time 0.
What is a non-causal signal?
A non-causal signal are non-zero before time t.
The signal will have some value before time 0.
What are deterministic signals?
Signals that can be computed beforehand at any instant of time (i.e signals fully described by a mathematical expression)
What is a random signal?
A signal that cannot be described by a mathematical equation due to uncertainity with respect to its value at some instant of time. Hence, they are modelled in probabilistic terms.
Also known as non-deterministic signals
