4.3 Signal Processing: Filters, Sampling Rates & Display Parameters

4.3 Signal Processing: Filters, Sampling Rates & Display Parameters

In modern digital polysomnography, physiological bioelectric potentials (microvolts to millivolts) generated by the brain, eyes, muscles, and heart are amplified, filtered, digitized, and rendered on computer displays. On the Certified Polysomnographic Technician (CPSGT) examination, technicians must possess a deep operational knowledge of filter physics, time constants, sampling rates, display sensitivities, and epoch time bases as mandated by the American Academy of Sleep Medicine (AASM).

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1. AASM Master Filter Settings Matrix

Analog and digital filters allow specific frequency bands of physiological interest to pass through while attenuating unwanted high-frequency noise, muscle artifact, or slow baseline drift.

+-----------------------------------------------------------------------------+
|                   AASM FILTER BANDWIDTH VISUALIZER                          |
|                                                                             |
|   FREQUENCY (Hz)  0.03  0.1   0.3   1.0    10    15    35    70   100  500|
|                   ───┼────┼─────┼─────┼─────┼─────┼─────┼─────┼─────┼────┼──|
|   EEG / EOG:             [======= 0.3 Hz ────────────── 35 Hz ]             |
|   EMG (Chin/Leg):                           [==== 10 Hz ───────── 100 Hz ]  |
|   ECG:                   [======= 0.3 Hz ──────────────────── 70 Hz ]       |
|   Airflow / RIP:     [=== 0.1 Hz ──────── 15 Hz ]                           |
|   Nasal Pressure: [= 0.03 Hz ──────────── 15 Hz ]                           |
+-----------------------------------------------------------------------------+

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2. Filter Physics, Cutoff Frequencies & Time Constants

Low-Frequency Filters (LFF) / High-Pass Filters:

• Mechanism: Permits frequencies higher than the cutoff frequency ($f_c$) to pass while attenuating frequencies lower than $f_c$.
• Cutoff Definition: The frequency at which the signal amplitude is reduced by $30%$ ($-3\text{ dB}$), allowing $70.7%$ of the original voltage to pass.
• Time Constant (TC): The time required for a calibration square wave signal to decay to $37%$ of its peak amplitude. Mathematically linked to the LFF:

$TC = \frac{1}{2\pi \times LFF} \approx \frac{0.16}{LFF} \quad \Longleftrightarrow \quad LFF = \frac{1}{2\pi \times TC} \approx \frac{0.16}{TC}$

+-----------------------------------------------------------------------------+
|                   TIME CONSTANT & LFF INTERACTION TABLE                     |
|                                                                             |
|   LFF Setting     Time Constant (TC)     Clinical Effect on EEG Signal      |
|   0.1 Hz          1.60 seconds           Long TC: Passes slow sweat sway    |
|   0.3 Hz (Std)    0.53 seconds           Standard AASM: Ideal delta capture |
|   1.0 Hz          0.16 seconds           Short TC: Attenuates delta waves;  |
|                                          produces forward phase lead        |
+-----------------------------------------------------------------------------+

High-Frequency Filters (HFF) / Low-Pass Filters:

• Mechanism: Permits frequencies lower than the cutoff frequency to pass while attenuating frequencies higher than $f_c$.
• Effects of Altering HFF:
  • Lowering HFF (e.g., from 35 Hz to 15 Hz on EEG) reduces high-frequency muscle noise, but blunts and rounds sharp wave peaks (sleep spindles, vertex waves, K-complexes) and causes a backward phase shift (phase lag).
  • Raising HFF (e.g., from 35 Hz to 70 Hz on EEG) allows high-frequency muscle interference to obscure cerebral rhythms.

+-----------------------------------------------------------------------------+
|                        PHASE SHIFTS INDUCED BY FILTERS                      |
|                                                                             |
|   - Low-Frequency Filter (LFF) Increase  ---> PHASE LEAD (Shifts peak LEFT) |
|   - High-Frequency Filter (HFF) Decrease ---> PHASE LAG  (Shifts peak RIGHT)|
+-----------------------------------------------------------------------------+

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3. The 60 Hz Notch Filter: Clinical Precautions

The 60 Hz notch filter (50 Hz in Europe) is a specialized narrow band-stop filter designed to eliminate alternating current (AC) line frequency interference.

+-----------------------------------------------------------------------------+
|                    60 Hz NOTCH FILTER CLINICAL RULES                        |
|                                                                             |
|   [RULE 1] NEVER turn on the notch filter routinely at study start.         |
|   [RULE 2] The notch filter does NOT eliminate the cause of artifact; it    |
|            only cosmetically masks high impedance (>5 kOhm) or bad grounds. |
|   [RULE 3] First-line intervention: Re-prep skin, re-apply electrode paste, |
|            lower impedances (<5 kOhm, balanced <2 kOhm), check ground lead. |
|   [RULE 4] Engaging the notch filter can distort rapid transients and       |
|            attenuate legitimate cerebral waveforms near 60 Hz.              |
+-----------------------------------------------------------------------------+

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4. Digital Sampling Rates & The Nyquist Theorem

To digitize continuous analog electrical potentials without introducing distortion or phantom frequencies, polysomnographic acquisition systems must satisfy the Nyquist-Shannon Sampling Theorem.

$\text{Sampling Rate } (f_s) \ge 2 \times f_{\max} \quad (\text{Nyquist Rate})$

• Aliasing: If a signal is sampled at less than twice its highest frequency component, high-frequency signals appear falsely as artificial, lower-frequency waveforms (aliasing).

AASM Sampling Rate Standards:

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5. Display Sensitivity & Epoch Time Base

Mathematical Sensitivity Formula:

Sensitivity defines the ratio of input voltage to physical screen/pen trace deflection:

$\text{Sensitivity } (S) = \frac{\text{Voltage } (V)}{\text{Deflection } (D)} \quad \Longleftrightarrow \quad \text{Deflection } (D) = \frac{\text{Voltage } (V)}{\text{Sensitivity } (S)}$

• Inverse Relationship Rule:
  • A HIGHER numerical sensitivity (e.g., $14\text{ }\mu\text{V/mm}$) produces a SMALLER visual deflection (reduces trace height).
  • A LOWER numerical sensitivity (e.g., $3.5\text{ }\mu\text{V/mm}$) produces a LARGER visual deflection (increases trace height).

CONCRETE SENSITIVITY CALCULATION EXAMPLES:
1. A Stage N3 slow delta wave measures 70 µV.
   - At standard EEG sensitivity (7 µV/mm): Deflection = 70 µV / 7 µV/mm = 10.0 mm
   - If sensitivity is changed to 14 µV/mm:  Deflection = 70 µV / 14 µV/mm = 5.0 mm
   - If sensitivity is changed to 3.5 µV/mm: Deflection = 70 µV / 3.5 µV/mm = 20.0 mm

2. A Stage N2 sleep spindle measures 35 µV.
   - At 7 µV/mm: Deflection = 35 µV / 7 µV/mm = 5.0 mm

AASM Standard Display Sensitivities:

• EEG Channels: $7\text{ }\mu\text{V/mm}$ (standard baseline for sleep staging and scoring $75\text{ }\mu\text{V}$ delta waves).
• EOG Channels: $7\text{ }\mu\text{V/mm}$ (adjustable to $5\text{--}7.5\text{ }\mu\text{V/mm}$).
• Chin EMG: $2\text{ to } 5\text{ }\mu\text{V/mm}$ (adjusted to render baseline muscle tone at $2\text{--}3\text{ mm}$ height).
• Leg EMG: $5\text{ to } 10\text{ }\mu\text{V/mm}$ (calibrated so $\ge 8\text{ }\mu\text{V}$ PLMS threshold is readily identifiable).
• ECG: $20\text{ to } 50\text{ }\mu\text{V/mm}$ (or $0.5\text{ to } 1.0\text{ mV/cm}$) to prevent tall R-waves from overlapping adjacent channels.

Standard Time Base Display:

• Standard 30-Second Epoch: The universal time window for staging sleep and scoring physiological events (equivalent to $10\text{ mm/sec}$ paper speed).
• Extended Time Windows (2 to 5 minutes): Utilized during live acquisition to evaluate periodic breathing patterns, Cheyne-Stokes respiration, and oxygen desaturation trends.