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If the sampling frequency is increased by a factor k, the frequency range is increased

from its original f

S

to

S

fk

⋅

and the quantisation noise

12

q

is distributed across this

extended range

). This increase by the factor k is known as oversampling. If

the ADC then followed by a digital low-pass filter, most of the quantisation noise is

removed from the output signal, while theuseful signal is not affected by the filter. In this

way, the ENOB of a low resolution ADC can be improved when the sampling rate is

increased, followed by filtering.

Oversampling, digital filter andnoise shaping

Looking at a

Σ

/

∆

-ADC in terms of frequency behaviour, we get a simplified block

diagram as i

The integrator is represented as an analogue low-pass filter with the transfer functio

f

1 )f(H

=

. For the output signal A then:

(

)

1 f

Qf

1 f

E QAE

f

1 A

+

⋅

+

+

= + − ⋅ =

It can be seen from

that the output signal A always gets closer and closer to

the input signal E for lower frequencies, while at higher frequencies f, the quantisation

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The transfer function of a linear and time-invariant function is derived from its Laplace transform. The Laplace

transform converts a given function f(t) from the real time domain into a complex function F(s) that represents the

frequency range. This transform is named after theFrenchmathematicianPierre-SimonLaplace (1749 - 1827).

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