D R . T A R E K T U T U N J I
P H I L A D E L P H I A U N I V E R S I T Y
2 0 1 4
Continuous-Time Signals
Continuous Signals
A continuous-time signal is a variable that changes with time
Continuous-Time Signals
Consider the signal: x(t) = 5 cos ( pt/2 + p/4)
This signal is: Deterministic: The value of the signal can be obtained for any
possible value for t
Analog: There is a continuous variation of time and amplitude
Of infinite support: The signal does not become zero outside any finite interval
The signals has Amplitude of 5
Frequency of p/2 rad/sec
Phase of p/4 rad
Basic Signals
A fundamental idea in signal processing is to attempt to represent signals in terms of basic signals, which we know how to process
The following basic signals will be considered:
Sinusoids
Complex Exponential
Impulse
Step
Ramp
Sinusoids
Sinewave Signal
Phase Shift
Complex Exponential Signals
Complex Exponential Signals
Impulse and Step
Ramp Signal
Basic Signal Operations
Adder
Delay
Constant Multiplier
Modulation
Basic Signal Operations
Example
Signal Classification
According to the predictability of their behavior, signals can be random or deterministic.
According to the variation of their time variable and their amplitude, signals can be
either continuous-time or discrete-time, analog or discrete amplitude, or digital. According to their energy content, signals can be characterized as finite- or infinite-
energy signals. According to whether the signals exhibit repetitive behavior or not as periodic or
aperiodic signals. According to the symmetry with respect to the time origin, signals can be even or
odd. According to the dimension of their support, signals can be of finite or of infinite
support.
Signal Classification: Even and Odd Signals
Periodic Signals
Example
Signal Classification: Energy and Power
Example
Conclusion
Continuous-time signals vary with time and its value is defined for all range
The basic signals are: sinusoid, exponential, pulse, unit, and ramp
The basic operations are: addition, multiplication , and delay
Signals can be classified as: Periodic / non-periodic, Odd/even, Energy/power
Reference
Chapter 1, Signals and Systems using MATLAB by Luis Chaparro. Elsevier Publisher 2011