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Telecommunications Engineering, Schemes and Mind Maps of Telecommunications Engineering

Books and notes for telecommunications engineering.

Typology: Schemes and Mind Maps

2021/2022

Uploaded on 03/06/2022

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Sampling – The Cardinal Series
Sampling Theorem: Any physical waveform may be represented
over the interval byt fddf
where fsis a parameter assigned some convenient value
greater than zero
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Sampling – The Cardinal Series

Any physical waveform may be represented Sampling Theorem:

byfd t d f over the interval

is a parameter assigned some convenient value^ s where f
greater than zero

Sampling – The Cardinal Series

Nyquist Frequency^ B^2 min^ s^ f

Sampling – The Cardinal Series

Impulse Sampling

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Impulse Sampling

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n s

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t t t

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Impulse Sampling- text

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Impulse Sampling

The spectrum of the impuse sampled signal is the spectrum of the

is the^ s Hz, where f^ s unsampled signal that is repeated every f

sampling frequency or rate (samples/sec). This is one of the

basic principles of digital signal processing, DSP.

Note:

This technique of impulse sampling is often used to

translate the spectrum of a signal to another frequency band that

(^) .s is centered on a harmonic of the sampling frequency, f

(^) >=2B, (see fig 2-18), the replicated spectra arounds If f

do not overlap, and the original spectrum can^ s each harmonic of f

(^) /2.s be regenerated with an ideal LPF with a cutoff of f

Natural Sampling

Generation of PAM with natural sampling (gating).

Natural Sampling

Duty cycle =1/

Natural Sampling

s

f s
d
f
3 at Null

Demodulation of a PAM signal (naturally sampled). Figure 3–

Nyquist region recovery th n
Illustration of waveforms in a PCM system. Figure 3–

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q(x)

Quantization

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Quantization Noise

So we can define the mean squared error distortion as:

) ( The pdf of the error is uniformly distributed ~

X Q X X

)~x(f

2 '



2 '

x

Signal to Quantization Noise Ratio SQNR –

SQNR – Signal to Quantization Noise

Ratio

Example of SQNR for full scale sinewave done on board

SQNR – Linear Quantization

max
max

d

x

P

x X E

x

The SQNR decreases as

The input dynamic range

increases

-Law Nonuniform PCM U

, xmax, and n^ x used to increase SQNR for given P

255 U.S U=

-Law Nonuniform PCM a

87.56 U.S a=

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8 bit
is signal power^ xP
Relative to full scale

xP