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DR. TAREK TUTUNJI PHILADELPHIA UNIVERSITY 2014 Continuous-Time Signals

Introduction to Signal Processing - Philadelphia University · 2014. 3. 8. · by Luis Chaparro. Elsevier Publisher 2011 . Title: Introduction to Signal Processing Author: PC Created

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  • 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