Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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Fundamentals ofCommunications

(XE37ZKT), Part I

Pulse Code Modulation,Amplitude Shift Keying

Josef Dobes

6th

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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1. Outline

• Pulse Modulations

– Pulse Width Modulation (PWM)

– PAM, PPM, PCM, ...

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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1. Outline

• Pulse Modulations

– Pulse Width Modulation (PWM)

– PAM, PPM, PCM, ...

• Pulse Code Modulation (PCM)

• Examples of PCM Codes

• Nyquist Rate

• Quantization Noise

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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1. Outline

• Pulse Modulations

– Pulse Width Modulation (PWM)

– PAM, PPM, PCM, ...

• Pulse Code Modulation (PCM)

• Examples of PCM Codes

• Nyquist Rate

• Quantization Noise

• Three Types of Keying (ASK, FSK, PSK)

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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1. Outline

• Pulse Modulations

– Pulse Width Modulation (PWM)

– PAM, PPM, PCM, ...

• Pulse Code Modulation (PCM)

• Examples of PCM Codes

• Nyquist Rate

• Quantization Noise

• Three Types of Keying (ASK, FSK, PSK)

• Amplitude Shift Keying (ASK)

– LF/HF Spectra

– 4-ASK

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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2. Pulse Width Modulation

Signal is compared to a sawtooth wave producing a pulse widthproportional to amplitude.

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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2. Pulse Width Modulation

Signal is compared to a sawtooth wave producing a pulse widthproportional to amplitude.

There are many similar cases (PAM, PPM, ...). However, the mostimportant one is PCM. (See the sampling and quantization concept).

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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3. Pulse Code Modulation

3.1. Sampling and Quantization

−3.19 000

−2.28 001

−1.37 010

−0.455 011

0.455 100

1.37 101

2.28 110

3.19 111

Quan

tiza

tion

leve

ls

t

x(t) Sampled values Quantized values

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sampling period

−4

−3

−2

−1

0

1

2

3

4

110 110 111 110 011 010 011 100 100 011 010PCM sequence

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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4. Some PCM Codes

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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5. Nyquist Rate

Due to the sampling, the spectra are repeated with the samplingfrequency:

Thus, the spectra may overlay if fs < 2fm. In such a case, theoriginal signal cannot be completely reconstructed. To do so, thesampling frequency must fulfill the condition

fs = 2fm,

where fm is the maximum LF modulating frequency.

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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6. Quantization Noise

Average quantization noise power:

σ2 =q2

12,

where q is the quantization interval. (See the quantization errorconcept, where σ = 0.91 V).

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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6. Quantization Noise

Average quantization noise power:

σ2 =q2

12,

where q is the quantization interval. (See the quantization errorconcept, where σ = 0.91 V).

Signal peak power:

V2p =

L2q2

4,

where L is number of quantization intervals. (See the quantizationerror concept, where L = 7).

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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6. Quantization Noise

Average quantization noise power:

σ2 =q2

12,

where q is the quantization interval. (See the quantization errorconcept, where σ = 0.91 V).

Signal peak power:

V2p =

L2q2

4,

where L is number of quantization intervals. (See the quantizationerror concept, where L = 7).

Signal power to average quantization noise power:(S

N

)q

=V2

p

σ2= 3L2.

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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−3.19 000

−2.28 001

−1.37 010

−0.455 011

0.455 100

1.37 101

2.28 110

3.19 111

Quan

tiza

tion

leve

ls

t

x(t) Sampled values Quantized and Hold q(t)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sampling period

−4

−3

−2

−1

0

1

2

3

4

t

Quantization error q(t) − x(t)

ε(t

)

110 110 111 110 011 010 011 100 100 011 010

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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7. ASK/FSK/PSK Keying

7.1. Amplitude Shift Keying

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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7.2. Frequency Shift Keying

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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7.3. Phase Shift Keying

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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8. Amplitude Shift Keying

8.1. LF/HF Spectra

Outline

Pulse Width . . .

Pulse Code Modulation

Some PCM Codes

Nyquist Rate

Quantization Noise

ASK/FSK/PSK Keying

Amplitude Shift Keying

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8.2. 4-ASK

Actually, this is a form of combining the ASK and PSK...