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