PULSE SIGNALING AND BASEBAND DIGITAL SIGNALING (PART 1)

PULSE PULSE MODULATIONMODULATIONPulse Modulation is a process of sampling analog signal and then converting them into discrete pulses and transporting the pulses from a source to a destination over a transmission medium. A device to perform this is called ADC (Analog-to-Digital Converter) & DAC (Digital-to-Analog Converter).

PULSE PULSE MODULATIONMODULATION1. PAM (Pulse Amplitude Modulation)2. PWM (Pulse Width Modulation) 3. PPM (Pulse Position Modulation)4. PCM (Pulse Code Modulation)

PAM (Pulse Amplitude Modulation)PAM (Pulse Amplitude Modulation)

It is used to describe the conversion of analog signal to pulse-type signal in which the amplitude of the pulse denotes the analog information.

In addition, it is a series of pulses in which the amplitude of each pulse represents the amplitude of the information signal at a given time.

PWM (Pulse Width Modulation) PWM (Pulse Width Modulation)

It is a pulse duration modulation (PDM) or pulse length modulation. The width of pulse is varied proportional to the Amplitude of the analog signal at the time signal is sampled.

PPM (Pulse Position Modulation)PPM (Pulse Position Modulation)

It is a series of pulses in which the timing of each pulse represents the amplitude of the information signal at a given time.

PCM (Pulse Code Modulation)PCM (Pulse Code Modulation)

It is a series of pulse in which the amplitude of the information signal at a given time is coded as a binary number. The pulses are of fixed length and fixed amplitude.

PCM is generated by 3 processes; Sampling, Quantization & Encoding.

Analog signal

Sample pulse

Pulse width modulation

Pulse position modulation

Pulse amplitude modulation

Pulse code modulation

A method used to represent an analog signal in terms of digital word

Constitutes 3 process:

1. Sampling the analog signal

2. Quantization of the amplitude of the sampled signal

3. Coding of the quantized sample into digital signal

Sampling Quantization Coding

An analog signal must be sampled at Nyquist rate to avoid aliasing

Quantization & Coding • Quantization : Process of Mapping samples of a

continuous amplitude waveform to a finite set of amplitudes.

• A fixed number of levels including the maximum and minimum value of the analog signal

• Number of levels is determined by the number of bits used for coding

• Coding : translate the quantized sample into a code number.

Is a process of taking a periodic samples of the waveform to be transmitted

Makes the signal discrete in time

fs ≥ 2 fm

fs = minimum Nyquist sample rate (Hertz) fm = maximum frequency to be sampled (Hertz)

• If fs is less than two times fm, distortion will result.• This distortion is called aliasing or foldover distortion.

• Quantization level, L = 2n

Quantization level depends on the number of binary bits, n used to represent each sample.

For example:For = 3; Quantization level, L = 23 = 8 level.

In this example, first level (level 0) is represented by 000, whereas bit 111 represents the eigth level

• Quantization Interval (ΔV)

Represent the voltage value for each quantized level

For example: For a sampled signal(mp) that has 5V amplitude, Vpp = 10 V divide by the quantized level, L = 8 level,

Therefore, quantized interval ,

V 25.18

V 102

L

mV p

The difference between the analog signal and the quantized signal is the quantization error.

(a) 5-bit resolution;

(a) 8-bit resolution.

As the number of bits per sample increases the quantization error decreases and picture resolution improves.

Folded PCM code = sample voltage resolution

For input at 2.6 V, the PCM code is therefore: 2.6/1 = 2.6 But since there is no code for +2.6, the magnitude is rounded off to the nearest valid code, which is 111 (+3V)

Thus there is difference of 0.4

QUANTIZATION ERROR (Qe)or also known as quantization noise (Qn)

Qe =sample voltage - original analog signal

Maximum magnitude Qe is equal to one-half a quantum

Low Resolution , more accurate the quantized signal will resemble the original analog sample

resolution

2eQ

Occurs when the input signal is at its minimum amplitude

SQR (dB) = 10 log V2/(q2/12)SQR (dB) = 10.8 + 20 log V/q

where V = rms signal voltage ΔV = q = quantization interval

Ratio of the largest possible magnitude to the smallest (other than 0) magnitude that can be decoded by the digital-to-analog converter (DAC) in the receiver

max max

min

2 1resolution

nV VDR

V

20log 2 1ndBDR

DR = dynamic range (unitless)Vmin = the quantum valueVmax = the maximum voltage magnitude of the DACsn = number of bits in a PCM code (excl. sign bit)

Number of bits used for a PCM code depends on the dynamic rangeDR = 2n -1

Thus 2n = DR + 1And therefore, The minimum number of bit used:

n = log ( DR + 1 ) n = excluding sign bitlog 2

For n > 42 1 2n nDR

20log 2 1 20 log 2 6ndBDR n n

No of Bits No of Levels DR (dB)

1 2 6.02

2 4 12

3 8 18.1

4 16 24.1

5 32 30.1

6 62 36.1

7 128 42.1

8 256 48.2

9 512 54.2

10 1024 60.2

11 2048 66.2

12 4096 72.2

13 8192 78.3

14 16348 84.3

15 32768 90.3

16 65536 96.3

Coding efficiency is a numerical indication of how efficiently a PCMcode is utilized

* Including sign bit

minimum number of bitscoding efficiency= 100

actual number of bits

A PCM systems has the following specification:Maximum Analog Input Frequency = 4 kHzMaximum decoded voltage at the receiver = 2.55 VThe dynamic range = 46 dB Determine the following : (a) Minimum Sampling Rate (b) Minimum number of bits used in PCM code (c) Resolution (d) Quantization Error (e) Coding Efficiency

(a) The minimum sampling rate: fs = 2fa = 2(4 kHz) = 8 kHz

(b) Calculate the Dynamic range : 46 = 20log(Vmax / Vmin) Vmax / Vmin = antilog (46/20) = 199.5 Thus, the minimum number of bit used: n = log (199.5 + 1) / Log 2 = 7.67

≈ 8 bits (c) Resolution is defined as: Vmax / 2n - 1 = 0.01 V

(d) Quantization Error : Q = resolution / 2 = 0.01 V / 2 = 0.005 V

(e) Coding Efficiency

Coding efficiency = (8.67/9)(100)= 96.3%

For a sinusoidal modulating signal with amplitude 2Vrms and theoutput signal to quantization noise ratio is to be held to 30.8dB.Determine: a. The quantization intervalb. The quantization levelc. Actual DRd. The coding efficiencye. The voltage level for 10110 and 00101

The process of compressing and expanding is called Companding.

Companding => Compress - Expanding

Input signal is compressed at the transmitter and expanded at the receiver

2 Popular companding system (standardized by 2 Popular companding system (standardized by ITU)ITU)

• EUROPE => A - Law

• USA/NORTH AMERICA => - Law

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xA

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MAX

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11

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max/ln1

max/ln(1

A - compressor paramater. Usually the value of A is 87.6.

max

maxln 1

ln 1

in

out

VV VV

Vmax = max uncompressed analog (volts)Vin = amplitude of the input signal at a particular instant of time (volts)µ = parameter used to define the amount of

compression (unitless)Vout = compressed output amplitude (volts)

2200 2300 2400 2500 2600 2700 2800 2900 3000-1

-0.5

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1

2200 2300 2400 2500 2600 2700 2800 2900 3000-1

-0.5

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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000-1

-0.5

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x[n]=speech /song/

y[n]=C(x[n])Companded Signal

Segment of x[n]

Segment of y[n]Companded Signal

Close View of the Signal

The maximum input voltage to the compressor using European standard is 2.5V. Determine the compressed output amplitude of this compressor for the input values of 0.01V, 0.05V, 1V, 1.8V and 2.5V. (A=87.6, µ = 100)