How to Avoid Aliasing: Anti-Aliasing Filters and DAQ

How to Avoid Aliasing

1. Sample Above the Nyquist Rate

\(F_s > 2 F_{\text{max}}\)

2. Use an Anti-Aliasing Filter (Pre-Filter)

An analog lowpass filter before the ADC removes frequencies above $F_s/2$.

Analog Signal → Anti-Aliasing LPF → ADC (Sampling + Quantization) → Digital Signal
     x(t)           H(f) cutoff=Fs/2         Fs                          x[n]

3. Practical Design Margin

In practice, sample at 2.5× to 4× the highest frequency of interest to relax filter requirements.

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Same Sampling Rate, Different Reconstruction Outcomes

Signal	$F_{\text{max}}$	$F_s$	Result
$\cos(2\pi \cdot 100 t)$	100 Hz	250 Hz	✓ Perfect reconstruction
$\cos(2\pi \cdot 100 t)$	100 Hz	150 Hz	✗ Aliasing (appears as 50 Hz)

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Data Acquisition System (DAQ)

A complete analog-to-digital conversion chain:

Sensor → Signal Conditioning → Anti-Aliasing Filter → Sample & Hold → ADC → Digital Processor
         (amplify, filter)      (analog LPF)           (S/H)           (quantize)

Steps to Convert Continuous-Time to Digital:

1. Sample — capture $x(nT)$
2. Quantize — map to discrete levels
3. Encode — represent as binary words

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Quick Reference: Nyquist Rate Cheat Sheet

Signal Type	Highest Frequency	Minimum $F_s$
Speech (telephone)	3.4 kHz	8 kHz
Audio (CD quality)	20 kHz	44.1 kHz
ECG	100–150 Hz	250–300 Hz
EEG	100 Hz	250 Hz
Radar/Ultrasound	MHz–GHz	Application-specific

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