A -bit converter is to digitise a signal band of to at

PHYSICS · Multi-part · Fermi University Physics · Electronics, Instrumentation & Communication · Digital electronics, embedded systems and data acquisition · Digital electronics, embedded systems and data acquisition

Electronics for Measurement, Ch Sampling, quantisation and the acquisition chain

Problem

10

-bit converter is to digitise a signal band of

0

2\,\mathrm{kHz}

f_s = 8\,\mathrm{kHz}

. Someone argues: "The rejection I need is

6.02(10) + 1.76 \approx 62\,\mathrm{dB}

f_s - f_{\max} = 6\,\mathrm{kHz}

. Rather than build an analogue filter, I will sample directly at

8\,\mathrm{kHz}

and then run a digital low-pass filter on the recorded numbers to remove everything above

2\,\mathrm{kHz}

; that gives the same

62\,\mathrm{dB}

of rejection without an extra component." ((a)) Find the error in this reasoning. ((b)) Calculate the order of Butterworth anti-alias filter actually needed, using the transition-ratio rule.

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