Signals and Basic Operations

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Questions and Answers

Match the basic operations on dependent variables with their definitions:

Amplitude Scaling = Multiply the signal by a constant Addition = Sum two signals Differentiation = Rate of change of a signal Integration = Accumulation of a signal over time

Match the operations performed on independent variables with their definitions:

Time-shifting = Shift the signal in time Time-reversal = Reverse the time direction of the signal Time-scaling = Change the speed of the signal Time-dilation = Stretch the time duration of the signal

Match the classification of systems with their descriptions:

Linear system = Superposition applies Non-linear system = Superposition does not apply Time-invariant system = Response does not change over time Time-variant system = Response changes over time

Match the operations on signals with their corresponding mathematical representation:

<p>Differentiation = $ rac{dy(t)}{dt}$ Integration = $y(t) = , \int g(t) , dt$ Addition = $y(t) = g_1(t) + g_2(t)$ Multiplication = $y(t) = g_1(t) , g_2(t)$</p>
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Match the following signal types with their descriptions:

<p>Continuous-value signal = May have any value within a continuum of allowed values Discrete-value signal = Can only have values taken from a finite set Continuous-time signal = Defined for all time t Discrete-time signal = Defined only at discrete instants of time n</p>
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Match the following examples with their corresponding signal type:

<p>Analog speech transmission = Continuous-value signal Temperature readings at set intervals = Discrete-time signal Digital audio files = Discrete-value signal Light wave signals = Continuous-time signal</p>
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Match the following signal characteristics with their appropriate type:

<p>Continuous-time signals = Arise naturally from physical signals Discrete-value signals = Values derived from quantization of continuous signals Analog signals = Continuous amplitude over time Digital signals = Values represented by discrete levels</p>
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Match the following terms with their definitions:

<p>Quantized signal = Derived from a continuous-value signal Sampling process = Method of obtaining discrete-time signals from continuous-time signals Finite set = A limited number of distinct values Photoelectric cell = Transducer for converting light to electrical signals</p>
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Match the following properties with their corresponding signal types:

<p>Continuous signals = Can have zero value at certain instants Discrete signals = Do not have values at non-integer time instants Analog signals = Characterized by continuous amplitude Digital signals = Characterized by discrete amplitude levels</p>
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Study Notes

Signals

  • Any time-varying physical phenomenon that conveys information
  • Signals can be useful (human voices, music, images) or useless (noise, interference)

Basic Signal Operations

  • Dependent Variable Operations:

    • Amplitude Scaling: Multiplying the signal by a constant
    • Addition: Adding two signals together
    • Multiplication: Multiplying two signals together
    • Differentiation: Rate of change of the signal
    • Integration: Accumulation of the signal over time

  • Independent Variable Operations:

    • Time-Shifting: Shifting the signal in time
    • Time-Reversal: Reversing the signal in time
    • Time-Scaling: Compressing or stretching the signal in time

Signal Classification

  • Continuous-Value: Signal can have any value within a range
  • Discrete-Value: Signal can only take values from a finite set
  • Continuous-Time: Signal is defined for all time
  • Discrete-Time: Signal is defined only at specific instants of time (usually integer values)
  • Analog: Signal amplitude can take any value, continuous with time
  • Digital: Signal amplitude is quantized, belonging to a finite set of values, continuous with time
  • Deterministic: Signal's value can be predicted with certainty
  • Random: Signal's value cannot be predicted with certainty
  • Real: Signal's value is a real number
  • Complex: Signal's value is a complex number
  • Periodic: Signal repeats itself over time
  • Nonperiodic: Signal does not repeat itself
  • Even: Signal is symmetrical around the vertical axis
  • Odd: Signal is symmetrical around the origin (rotational symmetry)
  • Causal: Signal is zero for all negative time
  • Noncausal: Signal can have non-zero values before time zero

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