Fundamentals of Signals

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Fundamentals of Signals

• power, energy, voltage
• decibels
• filters
• electromagnetic signals
• Fourier Analysis and Spectrum

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• Power, Energy, and Voltage
• Power P V2/R Watts Joules/Second
• Voltage V Joules/Coulomb
• Energy E Joules

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Decibels Represent power/voltage ratios over a
wide range
Ratio Power (dB) Voltage (dB)
½ -3 -6
2 3 6
10 10 20
100 20 40
1000 30 60
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Using Decibels addition for multiple stages
gain ranges from 36dB to 55dB
Decibels and Bandwidth (BW) 3dB BW range of
frequencies between -3dB response
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e.g. R 100k?, C 0.01uF
P
-3dB
f
160Hz
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Complex Filters
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Electromagnetic Signals

• c propagation velocity of light in a vacuum 3
  ? 108 m/s
• ci signal velocity of signal i
• pi propagation factor of signal i
• ci cpi
• for air 0.95 ? pi ? 0.98
• for wire 0.60 ? pi ? 0.85

fi frequency of signal i in Hz ( 2?w in
radians) ?i wavelength of signal i fi ci
/?i
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• ? impacts types of components that can be used
• antennas size
• types of cabling
• active components (filters, amplifiers)

wire signal is guided (confined) by transmission
media

• free space signal can reflect and refract
  depending on
• angle of incidence
• type of material
• signal frequency

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EM Spectrum
cellular spectrum
ELF VF VLF LF MF HF VHF UHF SHF EHF
visible light spectrum red 3.9 ? 1014 Hz ? ??
769 nm violet 7.9 ? 1014 Hz ? ?? 379 nm
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Fourier Analysis and Spectrum
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DC Waveform
Impulse
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Fourier Analysis and Phase (time delayed)

• f0 1/T

f0
f0
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f0 w0/2? is the fundamental frequency nf0, n
2,3,4 are harmonic of f0
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Fourier Transform convert general time domain
signal into frequency domain representation
FFT divide an conquer approach using
microprocessor
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Spectrum Analyzer graphical display of
spectrum (1) Series of Bandpass Filters (2)
Single Narrow Bandpass filter variable passband
defines resolution variable center frequency
scan spectrum of interest
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Spectrum of Square Wave Periodic Signal (? 0.5T
) x(t) A for 0 ? t ? T/2 0 for
T/2 lt t lt T
thus an 0 for all n
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Spectral (sinc) Envelope passes through 0 at n?
General Spectrum when ? ? 0.5T
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? T f0 ?/T
0.05 0.25 s 4 Hz 0.2
0.05 1 s 1 Hz 0.05
0.005 0.25s 4 Hz 0.02
? pulse width T pulse period ?/T duty cycle
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Superposition In a linear transmission medium
spectral components are additive