Lecture 20: Signal Measures

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Lecture 20Signal Measures

• Svetoslav NikolovØrstedDTU, Building 349

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Signal measures based on p-norm

• p1 Maximum value
• p2 used in the calculation of power and energy
• p1 mean value. Easy-to-build devices

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Power estimation
Sinusoidal signal
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Power estimation
Sinusoidal signal
Amplitude spectrum for x2(t)
w
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X(m)
Frequency Hz
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Power estimation
Periodic signal
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Power estimation
Periodic signal
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Power estimation unknown period
Sinusoidal signal
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Power estimation unknown period
Sinusoidal signal
Maaldemo increase T1
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Error in RMS measurement as a function of T1
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Signal measures of some periodic waves
Sine wave
Full-wave rectified sine
Half-wave rectified sine
Triangle wave
Square wave
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Power of random signals
Need to characterize the variation in p(t)
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Example
x(t) band-limited signal, white
filter
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Relative precision

• Relative precision
• Band-limited white noise
• Gaussian signal

Equivalent bandwidth
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Uncertainty
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Example of use
x(t)
h1(t)
z(t)
y(t)
z(t) y(t) x(t)h(t) x(t)h1(t)
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Summary

• Signal measures are single numbers characterizing
  a signal.
• They are used in comparing signals, for example
  in adaptive filtering or control systems.
• The longer we measure, the more precise the
  result is.