28 Sampling and Aliasing: Nyquist and Filters

electronics-controller-design

analog

digital

nyquist

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mixed-signal

signal-chain

binary

sensors

firmware

When fast vibration becomes a false slow wave

Follow the continuous signal, its sample dots, and the wave those dots imply. Play follows the recorded narration with captions. Choose a beat or Reduced motion for a still. The motor arithmetic is exact; unlabeled rates and filter attenuation are schematic.

Full transcript — Nyquist and filters (8 beats)

B1 — Fast vibration, false reading
You are designing a motor vibration monitor for a factory. Your job is to detect bearing trouble before a breakdown. A fast vibration can turn into a slow false reading when sampling is too slow. The sampling error could make a bearing problem resemble normal motor vibration.

B2 — Readings over time
Sampling means taking readings from a changing signal. The sampling rate tells you how many readings you take each second. Aliasing is an error: a fast real wave appears slower in sampled data. The readings can describe a frequency the motor never produced.

B3 — Retain a bounded band
The Nyquist rule starts with a signal whose frequency range has been limited. Sample at more than twice the highest frequency you retain. Half the sampling rate is called the Nyquist frequency. Keep the retained signal frequencies lower than the Nyquist ceiling so the samples can represent them faithfully.

B4 — Exactly at the ceiling
For your motor monitor, suppose the bearing defect produces a peak at five hundred hertz. Hertz measures cycles per second. Consider taking one thousand readings per second. Half of one thousand is five hundred, so the wanted peak sits exactly at the Nyquist ceiling.

B5 — 800 Hz becomes 200 Hz
Include an unfiltered vibration component at eight hundred hertz. At one thousand readings per second, subtract eight hundred from one thousand to get two hundred hertz, the apparent frequency. Normal motor vibration in this example ranges up to two hundred hertz. The false component lands in that range and could hide a bearing problem.

B6 — The whole signal matters
A common mistake is to assume sampling at exactly twice the wanted frequency reliably captures the peak, but at one thousand readings per second, the five hundred hertz bearing peak sits exactly at the sampling ceiling. Its samples depend on where in the wave each reading falls, so they cannot reliably describe the peak. The eight hundred hertz component lies above that ceiling and appears as a false slower vibration. Both effects matter when choosing the sampling rate.

B7 — Filter before sampling
An analogue anti-alias filter reduces unwanted high frequencies before an analogue-to-digital converter turns the signal into numerical samples. A low-pass filter lets lower frequencies through while weakening higher ones. Set its cutoff below the Nyquist ceiling because the filter weakens frequencies gradually rather than stopping them all at once. Sampling faster leaves more room for that gradual filtering.

B8 — Rate and filter together
Choose the rate for the signal you keep, and filter unwanted fast components before they become false slow readings.

28.1 Start With the Decision

This section: Start With the Decision — A sensor can report a slow false wave when it samples a fast real signal.

A sensor can report a slow false wave when it samples a fast real signal. Sampling rate and filtering must protect the measurement before analysis begins.

28.2 Route Overview

This section: Route Overview — This is part 1 of 3.

This is part 1 of 3. Continue with Sampling Design: Product Scenarios.

28.3 Part Objectives

This section: Part Objectives

Apply the Nyquist condition to a bounded sensor signal.
Explain how aliasing and anti-alias filters change sampled evidence.

28.4 Start Simple

This section: Start Simple — Picture a vibration monitor that reports a gentle wobble while the machine is shaking much faster.

Prove a Fast Signal Does Not Become a Slow Lie

Picture a vibration monitor that reports a gentle wobble while the machine is shaking much faster. The stored trace may be neat and still be false.

Sampling rate means how many measurements are taken each second. State the fastest signal of interest and what the input filter removes before choosing that rate.

Apply a known slow tone, a near-limit tone, and one above the limit. Keep the source frequency, filter, sampling rate, raw samples, spectrum, and false component so another person can repeat the check.

This check covers chosen tones and one signal path, not every transient. The deeper sections develop aliasing, limits, filtering, oversampling, and reconstruction.

Imagine measuring vibration but sampling so slowly that a fast wobble appears as a slow false pattern. Nyquist sampling is the rule that prevents a changing signal from pretending to be something else. Start with the highest frequency you need to trust, then choose sample rate and filtering before collecting data.

In 60 Seconds

For a band-limited signal, sample above twice its highest retained frequency and use an anti-alias filter to make the reconstruction assumption practical. Sampling too slowly causes aliasing — high frequencies masquerade as lower ones, corrupting your data. In practice, IoT engineers oversample at 2.5-5x and add hardware anti-aliasing filters to ensure reliable sensor readings.

Key Concepts

Nyquist–Shannon Sampling Theorem: A band-limited continuous signal can be reconstructed from samples when fs is chosen above 2 × fmax with alias-producing components filtered before sampling.
Aliasing: The distortion that occurs when a signal is sampled below the Nyquist rate; high-frequency components above fs/2 fold back into the spectrum and appear as false low-frequency components that do not exist in the original signal
Nyquist Frequency: Half the sampling rate, fs/2. A component exactly at this limit is phase-ambiguous, so sample above twice the highest retained signal frequency and attenuate higher components before conversion.
Anti-Aliasing Filter: A low-pass filter applied before the ADC to attenuate signal components above the Nyquist frequency before sampling; prevents aliased components from entering the digital data; cutoff frequency is typically set to 0.4 x fs or below
Oversampling: Sampling above the Nyquist minimum can spread quantization noise over a wider band; with suitable uncorrelated noise and filtering, 4× oversampling followed by decimation can add about one effective bit.
Sample-and-Hold Circuit: The analog input circuit that captures (samples) the input voltage at a precise instant and holds it stable during the ADC conversion period; settling time of the S/H circuit limits the maximum usable sampling rate
Quantization Noise: The error introduced by representing a continuous voltage as one of 2^N discrete levels; quantization noise is approximately white noise with amplitude +-0.5 LSB; SNR improvement = 6.02 dB per additional bit of resolution
Signal Reconstruction: Recovering the original continuous signal from discrete samples using an ideal reconstruction (sinc interpolation) or practical low-pass filter; the reconstructed signal is an accurate replica of the original only if the Nyquist criterion was satisfied during sampling

28.5 Learning Objectives

This section: Learning Objectives

Apply Nyquist Theorem: Calculate minimum sampling rates for different signals
Diagnose Aliasing: Explain why undersampling causes incorrect frequency representation and predict aliased frequencies
Design Anti-Aliasing Filters: Specify hardware low-pass filter parameters to prevent high-frequency contamination before ADC
Evaluate Sampling-Power Trade-offs: Select optimal sampling rates that satisfy Nyquist while minimizing energy consumption in battery-powered IoT devices
Implement Oversampling: Use extra samples to improve effective resolution and reduce anti-aliasing filter complexity

For Beginners: Sampling Theory

Imagine trying to draw a smooth wave by only placing a dot every few seconds — if you place dots too infrequently, you get a distorted picture that looks nothing like the original wave. Sampling theory tells us exactly how often we need to measure a changing signal to capture it faithfully. The key rule is simple: sample at least twice as fast as the signal changes. This concept applies every time a sensor reads the physical world.

28.6 Prerequisites

This section: Prerequisites

Before diving into this chapter, you should be familiar with:

ADC Fundamentals: Understanding how ADCs convert analog to digital
Binary Fundamentals: Understanding of resolution and bit depth
Basic Signal Concepts: Understanding of frequency (Hz) and waveforms

28.7 Why This Chapter Matters

This section: Why This Chapter Matters — Follow these connections in order: Sampling theory sounds mathematical, but it answers a brutally practical question: how often do I need to read a sensor so the data still represents reality.

Follow these connections in order: Sampling theory sounds mathematical, but it answers a brutally practical question: how often do I need to read a sensor so the data still represents reality. In real IoT systems, bad sampling choices create fake signals, missed events, wasted battery, and misleading analytics. The device may still produce numbers, but the numbers no longer describe the real world. This chapter gives students a way to choose sampling rates intentionally instead of guessing.

28.8 How To Use This Chapter

This section: How To Use This Chapter

Start with the Nyquist rule and the aliasing examples. Those are the ideas you must keep.
Read the tables with real signal types slowly and compare them to devices you already know: temperature sensors, microphones, ECG signals, accelerometers, and vibration monitors.
When you finish a section, ask yourself what would happen in a real product if the sampling rate were cut in half.

Chapter Roadmap

Start Simple
In 60 Seconds
Key Concepts
For Beginners: Sampling Theory
Prerequisites
Why This Chapter Matters
How To Use This Chapter
Nyquist-Shannon Sampling Theorem
Phoebe’s Field Notes: Why Aliases Fold Back
Deep dive: Putting Numbers to It
Practical Sampling Rate Examples
Checkpoint: Rate Selection
Understanding Aliasing
Vibration Monitor Check
Sampling Tradeoffs for Vibration
Sampling Rate vs Power Consumption
Sampling Rate vs Power
Checkpoint: Aliasing and Power
Anti-Aliasing Filters
Anti-Aliasing Filter Strategies
Knowledge Check: Anti-Aliasing Filter Strategies
RC Anti-Aliasing Calculator
ADC Sampling and Aliasing Demo
Sampling Rate Design Calculator
Nyquist Rate Calculator
Checkpoint: Filters and Calculators

28.9 Nyquist-Shannon Sampling Theorem

This section: Nyquist-Shannon Sampling Theorem — Sampling means taking readings from a changing signal.

Sampling means taking readings from a changing signal. If the readings are too far apart, a fast real wave can look like a slow false one; that error is aliasing. Sampling rate is the number of readings each second. An input filter reduces fast parts that the chosen rate cannot represent. Check both before analysis begins.

The first design question is simple: what is the fastest part of the signal you must preserve. Nyquist turns that question into the minimum sampling rate.

To accurately digitize an analog signal, you must sample at least TWICE the highest frequency component.

$f_{sample} > 2 \times f_{max}$

Phoebe’s Field Notes: Why Aliases Fold Back

The mathematical gist. Sampling at $f_s$ gives a Nyquist ceiling $f_s/2$ . Keep the retained band below that ceiling with an anti-alias filter; a tone outside it can fold to $|f_{signal}-nf_s|$ . The chapter’s 800 Hz harmonic sampled at 1000 Hz appears at 200 Hz, while 2500 Hz leaves a 250 Hz gap above the named 1 kHz precursor.

Deep dive: Putting Numbers to It

For audio sampling human voice (max frequency $f_{max} = 3400$ Hz), Nyquist requires $f_{sample} \geq 2 \times 3400 = 6800$ Hz minimum. Telephony uses 8 kHz (18% margin). For music ( $f_{max} = 20$ kHz), CD audio samples at $44.1$ kHz = $2.205 \times f_{max}$ , providing a 10% guard band for the anti-aliasing filter’s roll-off. If you undersample a 1 kHz tone at 1.5 kHz (below Nyquist 2 kHz), it aliases to $|1000 - 1500| = 500$ Hz — you hear the wrong pitch. Power cost: sampling at 10 kHz vs 1 kHz increases ADC energy significantly (ESP32: ~2mA base + ~0.001mA per sample/s).

Inspect Figure 28.1 at this point because its depiction of nyquist-Shannon sampling theorem summary supplies the physical context for the prose.

Diagram summarizing the Nyquist-Shannon sampling theorem with the period and frequency conditions for reliable digital sampling — Figure 28.1: Nyquist-Shannon sampling theorem summary

Figure 28.1 gives separate roles to Nyquist-Shannon Sampling Theorem, pn = period of the “fastest” sine wave, and fn = frequency of the “fastest” sine wave. Following those roles reveals nyquist-Shannon sampling theorem summary. That reading provides the evidence needed for the section’s next calculation, comparison, or field check.

For verification, record the fastest sine-wave period pn, derive fn = 1/pn, and compare the sampling interval with half that period.

The theorem has direct implications for how we choose sampling rates in practice. Bare Nyquist is the mathematical minimum, but real devices usually need extra margin for noise, timing uncertainty, and anti-aliasing filter roll-off.

Trace Figure 28.2 before continuing. It turns how sample rate changes the reconstructed signal from a verbal claim into labelled evidence.

Three-step comparison showing undersampling, the bare Nyquist minimum, and practical oversampling, with the reconstructed waveform becoming more faithful as sample rate increases — Figure 28.2: How sample rate changes the reconstructed signal

Figure 28.2 gives separate roles to How Sample Rate Changes, Teal is the true signal, dots are the samples,, and 1. Undersampling. Following those roles reveals how sample rate changes the reconstructed signal. That reading provides the evidence needed for the section’s next calculation, comparison, or field check.

28.9.1 Why This Matters

Undersampling (too slow) causes aliasing - high frequencies appear as low frequencies!

Inspect Figure 28.3 before why this matters; its labelled elements make aliasing in a real sampling scenario concrete enough to test against the circuit narrative.

Comparison of real 50 Hz signal, undersampled (aliased) to 30 Hz, and properly sampled at 500 Hz with anti-alias filter. — Figure 28.3: Aliasing in a real sampling scenario

Anchor Figure 28.3 on True waveform: period = 20 ms, which corresponds to the stated Shaft speed = 3000 RPM. Under Signal Aliasing and Sampling, compare that real motion with the more slowly changing sample sequence. The mismatch shows how sparse observations can imply a false shaft speed or direction, connecting the sampling theorem to a concrete monitoring failure rather than an abstract waveform exercise.

28.10 Practical Sampling Rate Examples

This section: Practical Sampling Rate Examples — Compare the examples by moving from the stated input to the resulting electrical behavior: Maximum sample rate: ~9,600 Hz (9.6 kHz).

Signal Type	Frequency	Minimum Sample Rate	Typical Rate	Reason
Temperature	~0.01 Hz (slow)	0.02 Hz	1 Hz	Changes very slowly
Audio (human voice)	300-3,400 Hz	6,800 Hz	8,000 Hz	Phone quality
Audio (music)	20-20,000 Hz	40,000 Hz	44,100 Hz	CD quality
ECG (heart)	0.5-100 Hz	200 Hz	250-500 Hz	Medical-grade clarity
Vibration	10-1,000 Hz	2,000 Hz	5,000-10,000 Hz	Safety margin for harmonics
Accelerometer (gesture)	50 Hz	100 Hz	200 Hz	Oversampling for noise

Arduino Uno ADC:

Compare the examples by moving from the stated input to the resulting electrical behavior: Maximum sample rate: ~9,600 Hz (9.6 kHz). Practical rate: ~1-5 kHz for stable readings.

ESP32 ADC:

Compare the examples by moving from the stated input to the resulting electrical behavior: Maximum sample rate: ~83 kHz. Practical audio sampling: 16-48 kHz.

This section:

Voltage Vera, Electronics measurement and prototyping expert

Checkpoint: Rate Selection

You now know:

A 500 Hz signal needs at least 1000 Hz sampling.
A 500 Hz vibration design usually uses 1250-2500 Hz instead of the bare minimum.
A 3400 Hz voice band needs at least 6800 Hz; telephony uses 8 kHz.

28.11 Understanding Aliasing

This section: Understanding Aliasing — Meeting the minimum is only half the story.

Meeting the minimum is only half the story. Out-of-band frequencies can still make sampled data look clean but wrong.

Vibration Monitor Check

Real-World Scenario:

You’re designing a predictive maintenance system for a manufacturing plant. The system monitors motor vibrations to detect bearing failures before catastrophic breakdown. Motors typically vibrate at:

Normal operation: 0-200 Hz (fundamental frequency + harmonics)
Bearing defect signature: 500 Hz peak
Critical failure precursor: High-frequency components up to 1 kHz

Your ESP32-based vibration sensor uses an accelerometer with analog output. You need to decide the ADC sampling rate.

Customer Requirements:

Detect 500 Hz bearing defect signals reliably
Minimize false alarms from aliasing artifacts
Battery-powered operation (sampling consumes power)
Real-time processing on ESP32 (limited RAM for buffering)

Engineering proposes three options:

Option A: Sample at 500 Hz (same as defect frequency)
Option B: Sample at 1000 Hz (2x defect frequency, Nyquist minimum)
Option C: Sample at 2500 Hz (5x defect frequency, oversampling)

Analysis:

Sampling Tradeoffs for Vibration

Option A: 500 Hz Sampling (FAILS)

Nyquist minimum for 500 Hz signal: 2 x 500 Hz = 1000 Hz
Sampling at 500 Hz = exactly at signal frequency → aliasing occurs!
Aliasing: Nyquist frequency is only 250 Hz, so the 500 Hz component folds back to |500 - 500| = 0 Hz (DC) or nearby low frequencies depending on phase
Result: Cannot detect bearing defects reliably → UNACCEPTABLE for safety-critical application

Option B: 1000 Hz Sampling (RISKY)

Meets Nyquist minimum (1000 Hz >= 2 x 500 Hz)
But: Real motors have frequency components >500 Hz (harmonics, noise)
If motor has 800 Hz component (unfiltered), aliasing occurs:
- Aliased frequency = |800 Hz - 1000 Hz| = 200 Hz (false low-frequency artifact)
- Appears as normal vibration, masking actual bearing defect
Problem: No margin for real-world signal complexity

Option C: 2500 Hz Sampling (RECOMMENDED)

5x oversampling provides safety margin
Allows for anti-aliasing filter with gradual roll-off
Captures harmonics up to 1.25 kHz
Modeled current cost: 4.5 mA at 2.5 kHz versus 3 mA at 1 kHz is 1.5×, not 2.5×; measure both operating points on the target ESP32 board.
Benefit: Reliable defect detection, worth the power trade-off for predictive maintenance

Aliasing Example - Why Undersampling Fails:

Sampling 2 kHz signal at 3 kHz (below Nyquist 4 kHz):

Nyquist minimum: 2 x 2 kHz = 4 kHz
Actual sampling: 3 kHz < 4 kHz → aliasing!
Aliased frequency: |2 kHz - 3 kHz| = 1 kHz
Critical failure: 2 kHz bearing defect appears as harmless 1 kHz vibration
Maintenance team ignores “false” 1 kHz signal → bearing fails → $500K production downtime

28.12 Sampling Rate vs Power Consumption

This section: Sampling Rate vs Power Consumption — Once the signal is sampled honestly, every extra sample must justify its current, storage, and transmission cost.

Once the signal is sampled honestly, every extra sample must justify its current, storage, and transmission cost.

Sampling Rate vs Power

Option A: High-frequency sampling (1000 Hz): Captures fast transients below a practical bandwidth of 500 Hz after anti-alias guard band; assume ~5 mW continuous ADC-path power. At 32 bits per sample, 86.4 million samples/day require about 346 MB/day.

Option B: Low-frequency sampling (1 Hz): Adequate for slow environmental signals (temperature, humidity), power draw ~0.005mW with sleep between samples, generates 86,400 samples/day, requires 345 kB/day storage

Decision Factors: For battery-powered environmental sensors where signals change over minutes or hours, 1 Hz sampling can reduce sampling work while preserving relevant variation; battery-life gain depends on the full power budget. For vibration analysis, motor monitoring, or audio capture, 1000+ Hz is mandatory to avoid aliasing. A smart approach uses adaptive sampling: high rate during detected events, low rate during quiet periods.

Power vs Sampling Rate:

ESP32 ADC power: ~2mA base + 0.001mA per sample/sec
@ 100 Hz: 2.1mA
@ 1 kHz: 3mA
@ 10 kHz: 12mA
For battery-powered devices: Sample only as fast as needed!

Checkpoint: Aliasing and Power

You now know:

Sampling 500 Hz at 500 Hz fails: the Nyquist frequency is only 250 Hz, and the defect can fold to 0 Hz.
A 1000 Hz design has no margin for an 800 Hz harmonic, which can appear as 200 Hz.
Cost scales quickly: 1 Hz creates 86,400 samples/day and about 345 kB/day; 1000 Hz creates 86.4 million samples/day and about 345 MB/day.

28.13 Anti-Aliasing Filters

This section: Anti-Aliasing Filters — Why?

Anti-Aliasing Filter Strategies

Problem: Real-world signals have infinite frequency components (noise, harmonics). How to ensure f_max before ADC?

Solution: Hardware Anti-Aliasing Filter

Passive RC low-pass filter:
- R = 10k ohm, C = 1uF → f_cutoff = 15.9 Hz
- Attenuates 50 Hz by only about 10.4 dB before 100 Hz sampling; stronger rejection is needed if a 50 Hz component must not alias
- Cost: $0.15 (resistor + capacitor)
Active Sallen-Key filter:
- Op-amp based, sharp roll-off
- 4th-order Butterworth: -80 dB/decade above cutoff
- Cost: $1-2 (op-amp + passives)

Best Practice:

Specify the required stopband attenuation from the out-of-band signal level and allowed error; f_cutoff = f_sample / 4 is only a starting point
Sample at 2.5-5x desired f_max
Apply digital low-pass filter in software for extra margin

Example: 500 Hz vibration monitoring

Hardware filter: f_cutoff = 600 Hz (Sallen-Key 4th-order)
ADC sampling: 2500 Hz (5x oversampling)
Digital filter: 500 Hz FIR low-pass
Result: Check the 4th-order filter’s attenuation against the measured out-of-band vibration spectrum and the allowed in-band error; the stated rates alone do not quantify aliasing risk.

Anti-Aliasing Filter Design Rule:

Before the ADC, use a low-pass filter to attenuate frequencies above the Nyquist frequency ( $f_{sample}/2$ ). In practice, set the filter cutoff below Nyquist to allow for the filter’s gradual roll-off:

$f_{cutoff} \leq \frac{f_{sample}}{2}$

Setting $f_{cutoff} = f_{sample}/4$ creates transition bandwidth, but filter order and out-of-band signal levels still determine whether attenuation at and above $f_{sample}/2$ is adequate.

Why? If high-frequency noise (>f_sample/2) reaches the ADC, it aliases to lower frequencies, corrupting data.

Knowledge Check: Anti-Aliasing Filter Strategies

28.14 RC Anti-Aliasing Calculator

Design a passive RC low-pass filter for anti-aliasing. Enter the desired cutoff frequency or component values to calculate the filter response.

Example: 1 kHz accelerometer sampling without anti-aliasing filter

Motor emits 1.2 kHz vibration harmonic
Nyquist frequency: 1000 Hz / 2 = 500 Hz
1.2 kHz signal aliases to: |1200 Hz - 1000 Hz| = 200 Hz
False reading: 200 Hz vibration appears in data (doesn’t exist!)
Solution: Add RC low-pass filter with f_c = 400 Hz before ADC

28.15 ADC Sampling and Aliasing Demo

This section: ADC Sampling and Aliasing Demo

ADC Sampling and Aliasing Demo

Experiment with ADC sampling concepts: adjust signal frequency, sampling rate, and ADC resolution to see how they affect signal reconstruction and observe aliasing when the Nyquist criterion is violated.

How to Use This Demo:

Start with defaults (10 Hz signal, 100 Hz sampling) - observe clean sampling
Increase signal frequency past 50 Hz (half of sampling rate) to see aliasing occur
Watch the aliased frequency - a 60 Hz signal sampled at 100 Hz appears as 40 Hz!
Increase sampling rate to eliminate aliasing
Change ADC resolution to see how quantization levels affect the sampled values

Key Observations:

Nyquist Rule: When signal frequency > sampling rate / 2, aliasing occurs
Aliased Frequency: The signal “folds back” into the [0, fs/2] range
Quantization: Higher bit resolution = more voltage levels = finer measurements
Status Indicators: The dashboard above turns red when the Nyquist criterion is violated

Try These Experiments:

Experiment	Settings	What to Observe
Nyquist Limit	f=49 Hz, fs=100 Hz	Just under limit - OK
Aliasing	f=60 Hz, fs=100 Hz	60 Hz appears as 40 Hz
Severe Aliasing	f=90 Hz, fs=100 Hz	90 Hz appears as 10 Hz
More Samples	f=20 Hz, fs=200 Hz	Clean reconstruction
Low Resolution	Any, 8-bit	Visible quantization steps
High Resolution	Any, 12-bit	Smoother quantization

28.16 Sampling Rate Design Calculator

This section: Sampling Rate Design Calculator

Nyquist Rate Calculator

Use this calculator to determine the required sampling rate, storage needs, and estimated power draw for your IoT sensor design. Enter your signal parameters and the calculator will apply the Nyquist theorem with practical engineering margins.

How to use: Enter your signal’s highest frequency component, then choose a sampling margin for the anti-alias filter and timing requirements before setting ADC resolution, recording duration, and channel count. The calculator outputs the Nyquist minimum, practical recommended rate, required anti-aliasing filter cutoff, storage budget, data throughput rate, and estimated ESP32 ADC current draw.

This section:

Checkpoint: Filters and Calculators

You now know:

At 1 kHz sampling, a 1.2 kHz vibration harmonic can fold into a false 200 Hz reading.
A 500 Hz vibration monitor can sample at 2500 Hz, use a 600 Hz hardware filter, and apply a 500 Hz digital filter.
A first-order RC filter rolls off at -20 dB/decade; a 2nd-order Sallen-Key filter gives -40 dB/decade.

28.17 Continue to the Next Part

This section: Continue to the Next Part — Carry this evidence into Sampling Design: Product Scenarios, which begins with For Kids: Meet the Sensor Squad!.

Carry this evidence into Sampling Design: Product Scenarios, which begins with For Kids: Meet the Sensor Squad!.

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