3 Digitization

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    Sampling First step in digitizing speech

    Establish a set of discrete times at which the input waveform is

    sampled Sampling Intervals

    Regular

    Irregular

    Minimum sampling frequency is given by Nyquist theorem.

    To reconstruct the original waveform from the sampled sequencethe sampling frequency must be at least twice the maximumfrequency of the original waveform.

    Fs 2H

    Fs=Sampling frequency or Nyquist rate

    H=maximum frequency component in the analog waveform

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    Sampling H is the bandwidth of the input waveform

    In this case the waveform is reconstructed by passing the sampled

    values through a low pass filter which smoothens out or interpolates

    the signal between sampled values

    vi(t) vo(t)

    T TT

    time time

    1

    0

    vi(t)

    Input Signal

    WaveformSampled Signal

    Waveform

    (i)(ii) Sampling (iii)

    ...011101010011010011...

    Samples are coded for transmission

    (iv)

    Analogue-to-digitalConverter

    Digital-to-analogue

    Converter

    Sampled signal is recovered

    (v)

    Vi(t)

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    PAM System

    Sampling is a process of

    multiplying a constant

    amplitude impulse train

    with the input signal

    Like an Amplitude

    modulation system where

    pulse train acts as the

    carrier

    Called Pulse Amplitude

    Modulation (PAM)

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    Foldover Distortion

    For a sine carrier

    Frequency range is Fc-H to Fc+H (Fc is carrier frequency)

    For PAM, the output spectrum contains the fundamental as well as

    the harmonics of the fundamentals.

    If the pulse train is square wave with 50% duty cycle, only the

    fundamental and odd harmonics are present. The low pass filter at

    the receiver end allows only the baseband component 0-H to pass.

    If Fs is less than twice H, portions of PAM spectrum overlaps

    This overlapping of the sidebands produces beat frequencies that

    interfere with the desired signal and such an interference is referred

    as aliasing or foldover distortion. The filter used for band limiting the

    input speech waveform is known as antialiasing filter..

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    Foldover Distortion

    In digital speech system speech is sampled as 8KHz.

    8KHz sampling results in oversampling.

    This oversampling provides for the nonideal filter

    characteristics such as lack of sharp cutoff.

    The sampled signal is sufficiently attenuated at the

    overlap frequency of 4 KHz. To adequately reduce the

    energy level of the foldover spectrum

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    Quantization and Binary Coding

    Pulse amplitude modulation systems are not useful over long

    distance, for the vulnerability of individual pulse amplitudes to noise,distortion and crosstalk.

    The susceptibility of amplitude may be eliminated by converting the

    PAM samples into a digital format. (Using regenerative repeaters) A finite number of bits are used for coding PAM samples.

    n bit number can represent 2n samples.

    PAM samples amplitude can take on an infinite range of values.

    The PAM sample amplitude is quantized to the nearest of a range of

    discrete amplitude levels.

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    Quantization Process Signal V is confined to a range of VL

    and VH. This range is divided into M(M=8) equal steps.

    The step size S is given by

    The center of each steps locate thequantization levels V0, V1V8.

    Quantized signal Vq takes any of thequantized level value

    A signal V is quantized to its nearestquantization level.

    ( )H LV VS =

    The convention followed to quantize the signal is

    Thus, the signal Vq makes quantum jump of step size S and at any instant of time thequantization error (V-Vq) has magnitude which is equal or less than S/2

    The quantization in which the step size is uniform is called linear or uniform quantization.

    q

    q

    V =V3 (if (V3-S/2) V< (V3+S/2)

    V =V4 (if (V4-S/2) V< (V4+S/2)

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    Quantization

    Quantization brings about a certain amount of noise in immunity to the

    signal.

    Repeaters with quantizers are used after certain distance to control the

    variation in instantaneous amplitude for attenuation and channel noise

    within S/2.

    If instantaneous noise level is larger than S/2, error occurs in the

    quantization level.

    The quantized signal is an approximate of the original signal. Quality can be increased by increasing the number of quantization levels

    Sometimes increased levels introduces noise in the repeaters.

    The susceptibility to noise can be greatly minimized by resorting the digital

    coding of the PAM sample amplitude Each quantized level is represented by a code number and transmitted

    instead of the level value.

    If binary arithmetic is used the number will be transmitted as a series of

    pulses.

    Such a system is called PCM System.

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    Binary PCM The analog signal is limited in

    its excursions to the range -4

    V to + 4V. The step size is 1 volt.

    Eight quantization levels are

    used and are located at -

    3.5V, -2.5V ., +3.5V. Code

    number 000 is assigned to -3.5V and so on.

    If the analog samples are

    transmitted the 1.3, 2.7, 0.5

    etc will be transmitted.

    If the quantized values are

    transmitted voltages 1.5, 2.5,

    0.5 etc will be transmitted

    In binary PCM the binary

    code patterns 101, 110,100are transmitted.

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    PCM System The functional diagram for PCM is shown in the next figure

    The analog input V is bandlimited to 3.4 KHz to prevent aliasing and

    sampled at 8 KHZ.

    Samples are quantized to produce PAM signals, and applied to encoder.

    Encoder generates a unique pulse pattern for each quantized sample level.

    The quantizer and encoder together work as Analog to Digital Converter

    (ADC)

    Receiver first separates the noise from the signals.

    A qunatizer does it by determining the two voltage levels of the pulse.

    Then it regenerates the appropriate pulse depending on the decision.

    The regenerated pulse train is now fed to a decoder which assembles the

    pulse pattern and generates a corresponding quantised voltage level. Qunatizer and decoder work together as a Digital to Analog converter

    (DAC)

    The quantized PAM is now passed through a filter which rejects the

    frequency components lying outside the baseband signal.

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    PCM System

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    Digital Data, Digital Signal

    Digital signal

    Discrete, discontinuous voltage pulses

    Each pulse is a signal element

    Binary data encoded into signal elements

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    Terms

    Unipolar

    All signal elements have same sign

    Polar

    One logic state represented by positivevoltage the other by negative voltage

    Data rate

    Rate of data transmission in bits per second

    Duration or length of a bit

    Time taken for transmitter to emit the bit

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    Terms

    Modulation rate

    Rate at which the signal level changes

    Measured in baud = signal elements per

    second

    Mark and Space

    Binary 1 and Binary 0 respectively

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    Interpreting Signals

    Need to know

    Timing of bits - when they start and end

    Signal levels

    Factors affecting successful interpreting ofsignals

    Signal to noise ratio

    Data rate Bandwidth

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    Analogue to Digital

    After sampling, the analogue amplitude value of each

    sampled (PAM) signal is quantized into one of a numberof L discrete levels. The result is a quantized PAM

    signal.

    A codeword can then be used to designate each level at

    each sample time. This procedure is referred to as Pulse Code Modulation .

    Low-pass

    Filter

    Encoder;

    Pulse

    modulate

    Sampler Quantizer

    Continuous-

    time

    message

    signal

    PCM

    wave

    Quantized

    PAM signal

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    Encoding

    After quantization, a digit is assigned to each of the

    quantized signal levels in such a way that each level hasa one-to-one correspondence with the set of real

    integers. This is called digitization of the waveform .

    Each integer is then expressed as an n-bit binary

    number, called codeword, or PCM word.

    The number of codewords, M , is related to n by: 2n = M

    Quantized

    PAM

    signal

    A real

    integer

    PCM

    codeword

    (bit stream)

    digitization To binary

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    Codeword

    Quantization followed by digitization maps input

    amplitudes into PCM words.

    A cell is the set of input amplitudes mapped to a

    codeword.There are M integers, PCM words, or codewords

    to correspond to the M allowed output

    amplitudes of the quantizer.

    Codebook is the set of all these M codewords.

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