Signal Surasak Sanguanpong nguan@ku.ac.th - - PDF document

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Signal

Surasak Sanguanpong nguan@ku.ac.th http://www.cpe.ku.ac.th/~nguan

Last updated: 25 November 2004

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Analog and Digital Signal

Analog Digital

Amplitude Amplitude Time Time

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Time Domain

Th signal intensity varies in a smooth fashion over time.

Amplitude Time Amplitude Time

The signal intensity maintains a constant level for some period of time and then changes to another constant level.

lim s(t) = s(a)

for all a t a

Continuous signal Discrete signal

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Periodic and Aperiodic signals

T T T T

Amplitude Time Amplitude Time Time Amplitude Amplitude Time

T T T T

Periodic signals Aperiodic signals

Analog Analog Digital Digital

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Signal components

• Amplitude : strength of the signal
• Frequency : rate at which the signal repeats (in Hertz[Hz])
• Phase : position of the signal relative to time zero

Amplitude Time tn 1 second 1 second Max Amplitude Min Amplitude Beginning phase

φ = 0 degree

Period T = 1/3 s 3 periods in one second f = 3 Hertz Amplitude at time tn

T=1/f

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Phase different

0 degree 90 degree 180 degree 270 degree

s(t) = sin(2πft) s(t) = sin(2πft+π/2) s(t) = sin(2πft+π) s(t) = sin(2πft+3π/2)

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Changes in Amplitude and Frequency

Amplitude change Frequency change

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Phase Changes

No phase change 90 degree phase change 180 degree phase change 270 degree phase change

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Time and Frequency Domain

1 second 10

frequency f = 4 Hz

• 10

10

4

Frequency Amplitude 10

frequency f = 8 Hz

• 10

10

4 8

Frequency Amplitude 1 second Amplitude Amplitude Time Time

Time Domain Frequency Domain

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DC Component

1 second 10 10 10 10 8 15 1 second

frequency f = 8 Hz frequency f = 0 Hz

Amplitude Amplitude Frequency Frequency Amplitude Time Amplitude Time 5

Time Domain Frequency Domain

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Frequency Components

f 3f 3f f

s1(t) = sin(2πft ) s2(t) = 1/3sin(2π(3f)t) s3(t) = sin(2πft ) +1/3sin(2π(3f)t) ω

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Harmonics

s(t) = a0 +Σ [an cos(n2π t/T)]+ bn sin(n2π t/T)]

n=1

ฅ

1 and 3 harmonics 1,3 and 5 harmonics 1,3,5 and 7 harmonics infinite number of harmonics

• Any periodic waveform can be mathematically expressed as

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Bandwidth

1000 6000

Bandwidth = 6000-1000 = 5000 Hz

100 200 300 400 500 600 700 800

Bandwidth = 800-100 = 700 Hz

• Bandwidth is the width of

the frequency spectrum fh= the highest frequency fl= the lowest frequency B=fh-fl

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Bit rate

1 0 1 0 1 1 0 1

Bit rate = 8 bps

1 second

Bit duration = 1/8 s

bit interval = time to sent one bit bit rate = number of bits in one second

Amplitude Time

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Bit rate and Frequency

• Transmission medium has a

limited bandwidth

• Digital signal has infinite

bandwidth

• Selection of transmission

medium relies on the cost of investment and the quality of transmitted signal.

Signal before transmission with bit rate: 2 Kbps

Bandwidth: 500 Hz Bandwidth: 2.5 KHz Bandwidth: 4 KHz

Signal after transmission with various bandwidth