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21
SIGNALS AND SYSTEMS EEE F243 / INSTR F243 BITS Pilani Pilani Campus Lecture 01 Introduction to Signals

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signals and system

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  • SIGNALS AND SYSTEMS

    EEE F243 / INSTR F243

    BITSPilaniPilani Campus

    Lecture 01

    Introduction to Signals

  • Todays Session

    Signals

    Size of a Signal

    Classification of Signals

    BITS Pilani, Pilani Campus

    Classification of Signals

    Useful Signal Operations

  • Signal

    Signal:

    Signal is a physical quantity which varies with time, space,

    frequency etc.

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    Examples: Electricity, Voice, Photons, Telephonic conversation, TV

    signal etc.

    Signal should be a function of an independent variable mainly time.

    Though others may be space, frequency etc.

  • Size of a Signal

    Signal Energy:

    It takes account of both amplitude and duration.

    = dttfE 2|)(|

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    V2s (A2s)

    Signal Power:

    Time average of the signal energy is the signal power.

    V2 (A2)

    = dttfE f2|)(|

    =2/

    2/

    2)(

    1lim

    T

    TTf dttf

    TP

  • Energy Signal: If and only if it has finite energy and zero

    average power.

    Power Signal: If and only if its power is finite and energy is

    infinite.

    Size of a Signal

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    Generally all periodic signals are power signals.

    A signal may not get classified as an energy or power signal, if it does

    not satisfy both the criteria. It is then called as neither energy nor

    power signal. Example: Ramp signal f(t) = t

    It increases indefinitely as t

  • Examples

    Find the energies of the following signals:

    0

    1

    t

    f(t) = sin t 1

    0 t1

    f(t) = t

    2

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    -2

    2

    8

    -8

    f(t) = t3

    Find the power of the following signal:

    12

  • Signal

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    Classification

  • Signal Classification

    Continuous Time / Discrete Time Signals:

    - Uniquely defined at all times / Defined at discrete intervals of time.

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  • Signal Classification

    Analog Signals Amplitude can take any value in continuous range.

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    Digital Signals Amplitude can take only finite number of values.

  • Signal Classification

    Periodic Signal: Repeats after finite intervals.

    for all t

    Smallest value of T satisfies above equation Period.

    )()( Ttftf +=

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    Aperiodic Signal: Does not repeat after regular intervals.

    for all t

    A periodic signal can be generated by its periodic extension.

    A periodic signal remains unchanged when time shifted by one

    period.

    )()( Ttftf +

  • Signal Classification

    Example of Periodic Signals:

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    Tt

  • Signal Classification

    Example of Aperiodic Signals:

    2

    f1(t)

    2

    f1(t)

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    1

    0

    0

    f2(t)

    t

    t

    1

    0

    0

    f2(t)

    t

    t

  • Signal Classification

    Causal Signal: A signal which does not start before t =0.

    0)( =tf 0

  • Signal Classification

    Deterministic Signal:

    A signal whose description is known completely either by

    mathematically or by graphically.

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    Random Signal:

    A signal which can only be predicted by probabilistic description.

  • Signal

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    Operations

  • Signal Operations

    Shifting: shifting of a signal certain time.

    )()( tfTt =+

    )()( Ttft =

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  • Signal Operations

    Scaling: The compression or expansion of a signal by time.

    Compression: )()( atft =

    1>a

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    Expansion:

    =a

    tft)(

    1>a

    f(t/2)

    f(2t)

  • Signal Operations

    Inversion (Reversal): Inverting or folding a signal.

    )()( tft =)()( tft =

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  • Combined Operations

    One operation for example is:

    First way: (1) Time shift:

    ( )batf

    ( )btf

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    (2) Time scaling:

    Second way: (1) Time scaling:

    (2) Time shift:

    ( )batf

    ( )atf

    ( )batfa

    btaf =

  • Examples

    Express following signals f2(t) and f3(t) in terms of f(t):

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    f3(t)

  • Examples

    For the following signal f(t): find (i) f(-t) (ii) f(t+6) (c) f(t/2)

    0.5

    f(t)

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    t0

    0.5

    -1

    6

    12 15 24