Introduction to Filtering
What is Filtering?
The sampled signal values can contain the noise and unwanted frequencies of the original signal. Filtering is about cleaning signals to remove unwanted components like noise or drift. This is useful for revealing the underlying health-related pattern in messy sensor data. Think of it like a sieve: useful data passes through, unwanted parts are blocked.
Filtered signal
Sampled signal
Interpolation Effect
Filters (especially low-pass) inherently act like interpolators. This means that a filter will reconstruct a smooth curve from discrete points. So, filtering doesn’t just remove noise — it also “connects the dots” between samples. In the diagram below, notice how the sampled signal consisting of discrete points smooth outs after the application of a filter.
Filtered signal
Sampled signal
Types of Filters
Views of Filters - Time Domain Filtering
Filtering in the time domain means reshaping a signal directly by convolving it with the filter’s impulse response, which often looks like smoothing, averaging, or reshaping the waveform. For example, a smart ring accelerometer might pick up the waveform shown below while detecting user's steps. Click the diagram to see how this waveform would transform when filtered in the time domain.
Essentially, a moving average filter has taken each point and replaced it with the average of itself + neighbors → noise has smoothed out.
Views of Filters - Frequency Domain Filtering
On the previous slide, the signal was represented as values (magnitudes) over time domain axis. However, a signal can also be represented as its frequency components (using the Fourier Transform). This simplifies filtering as we now have to remove frequencies that we do not want. For example, a smartwatch ECG signal can both the heartbeat (1–40 Hz) and unwanted 60 Hz mains noise. Click the graph below to see what will happen after applying the notch filter to the signal.
Essentially, a frequency filtering would modify the signal's spectrum, keeping the useful frequencies and suppressing the unwanted ones.
Benefits of Filtering
Click to learn more
SYSTEM DESIGN
FEATURE EXTRACTION
PREVENT ALIASING
NOISE REDUCTION
Sometimes only a certain frequency band carries the information you want.
Real-world signals are never clean — they carry motion artifacts, electrical interference, or environmental noise.
Filters prepare signals for specific applications — making them stable, efficient, and interpretable.
If high frequencies remain before digitizing, they “fold” into the lower frequencies (aliasing), creating false signals.
Key Takeaways
Filter Types
Interpretability
Different filters serve different purposes depending on the health signal.
Filtering makes raw signals interpretable and reliable for AI models.
Congratulations, you have completed this activity.
Example
A smartwatch measuring heart rate with PPG needs to filter out motion-induced noise above the Nyquist limit before storing or transmitting the signal.
Otherwise, those high-frequency wrist-motion artifacts could appear in the digital data as false heartbeat spikes. A smart ring tracking sleep stages filters raw accelerometer data before digitizing, preventing finger tremors (high-frequency) from being misread as movement during sleep.
Band-Stop (Notch) Filter
Blocks a narrow frequency band. Use Case: Removing power line interference (50/60 Hz) from biosignals. Example: A wearable EEG connected via Bluetooth might pick up a faint 50/60 Hz hum due to line interference— notch filters remove that interference without affecting brainwave signals.
Band-Pass Filter
Passes only a specific band of frequencies (keeps only a middle frequency range of interest). Use case: Accelerometers in smartphones and smart rings can capture user's step information. Walking produces vibrations (noise) mostly in the 0.5–3 Hz band. A band-pass filter isolates this range to improve accuracy of step counts.
Low-Pass Filter
Passes low frequencies (keeps slow changes). Blocks high frequencies (removes fast fluctuations). Use case: Human motion (movement, walking, etc.) can add noise to heart rate data captured by PPG. A low-pass filter removes high-frequency noise to yield a clean heart rate trend.
High-Pass Filter
Passes high frequencies (keeps fast changes) Blocks low frequencies (removes slow drifts) Use case: For smartwatch ECG (like Apple Watch), the contact between skin and electrodes can shift as the wrist moves, causing the ECG baseline to wander up and down. A high-pass filter removes this low-frequency drift, leaving a clean ECG trace with sharp waves representing heartbeat.
Example
Accelerometer data has many components, but walking is mainly in the 0.5–3 Hz range. Band-pass filtering isolates this range to accurately count steps. But walking is mainly in the 0.5–3 Hz range. Filtering helps us separate the meaningful part (e.g., steps at 0.5–3 Hz) from the unwanted parts (drift, vibration).
Example
A mobile telehealth app may filter and compress biosignals before sending them to the cloud, ensuring smooth transmission and accurate downstream AI analysis.
Example
A smartwatch PPG sensor while jogging produces spiky noise due to wrist motion. Filtering reduces these spikes so the heart-rate trend is reliable.
Introduction to Filtering
Beenish Chaudhry
Created on September 27, 2025
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Transcript
Introduction to Filtering
What is Filtering?
The sampled signal values can contain the noise and unwanted frequencies of the original signal. Filtering is about cleaning signals to remove unwanted components like noise or drift. This is useful for revealing the underlying health-related pattern in messy sensor data. Think of it like a sieve: useful data passes through, unwanted parts are blocked.
Filtered signal
Sampled signal
Interpolation Effect
Filters (especially low-pass) inherently act like interpolators. This means that a filter will reconstruct a smooth curve from discrete points. So, filtering doesn’t just remove noise — it also “connects the dots” between samples. In the diagram below, notice how the sampled signal consisting of discrete points smooth outs after the application of a filter.
Filtered signal
Sampled signal
Types of Filters
Views of Filters - Time Domain Filtering
Filtering in the time domain means reshaping a signal directly by convolving it with the filter’s impulse response, which often looks like smoothing, averaging, or reshaping the waveform. For example, a smart ring accelerometer might pick up the waveform shown below while detecting user's steps. Click the diagram to see how this waveform would transform when filtered in the time domain.
Essentially, a moving average filter has taken each point and replaced it with the average of itself + neighbors → noise has smoothed out.
Views of Filters - Frequency Domain Filtering
On the previous slide, the signal was represented as values (magnitudes) over time domain axis. However, a signal can also be represented as its frequency components (using the Fourier Transform). This simplifies filtering as we now have to remove frequencies that we do not want. For example, a smartwatch ECG signal can both the heartbeat (1–40 Hz) and unwanted 60 Hz mains noise. Click the graph below to see what will happen after applying the notch filter to the signal.
Essentially, a frequency filtering would modify the signal's spectrum, keeping the useful frequencies and suppressing the unwanted ones.
Benefits of Filtering
Click to learn more
SYSTEM DESIGN
FEATURE EXTRACTION
PREVENT ALIASING
NOISE REDUCTION
Sometimes only a certain frequency band carries the information you want.
Real-world signals are never clean — they carry motion artifacts, electrical interference, or environmental noise.
Filters prepare signals for specific applications — making them stable, efficient, and interpretable.
If high frequencies remain before digitizing, they “fold” into the lower frequencies (aliasing), creating false signals.
Key Takeaways
Filter Types
Interpretability
Different filters serve different purposes depending on the health signal.
Filtering makes raw signals interpretable and reliable for AI models.
Congratulations, you have completed this activity.
Example
A smartwatch measuring heart rate with PPG needs to filter out motion-induced noise above the Nyquist limit before storing or transmitting the signal. Otherwise, those high-frequency wrist-motion artifacts could appear in the digital data as false heartbeat spikes. A smart ring tracking sleep stages filters raw accelerometer data before digitizing, preventing finger tremors (high-frequency) from being misread as movement during sleep.
Band-Stop (Notch) Filter
Blocks a narrow frequency band. Use Case: Removing power line interference (50/60 Hz) from biosignals. Example: A wearable EEG connected via Bluetooth might pick up a faint 50/60 Hz hum due to line interference— notch filters remove that interference without affecting brainwave signals.
Band-Pass Filter
Passes only a specific band of frequencies (keeps only a middle frequency range of interest). Use case: Accelerometers in smartphones and smart rings can capture user's step information. Walking produces vibrations (noise) mostly in the 0.5–3 Hz band. A band-pass filter isolates this range to improve accuracy of step counts.
Low-Pass Filter
Passes low frequencies (keeps slow changes). Blocks high frequencies (removes fast fluctuations). Use case: Human motion (movement, walking, etc.) can add noise to heart rate data captured by PPG. A low-pass filter removes high-frequency noise to yield a clean heart rate trend.
High-Pass Filter
Passes high frequencies (keeps fast changes) Blocks low frequencies (removes slow drifts) Use case: For smartwatch ECG (like Apple Watch), the contact between skin and electrodes can shift as the wrist moves, causing the ECG baseline to wander up and down. A high-pass filter removes this low-frequency drift, leaving a clean ECG trace with sharp waves representing heartbeat.
Example
Accelerometer data has many components, but walking is mainly in the 0.5–3 Hz range. Band-pass filtering isolates this range to accurately count steps. But walking is mainly in the 0.5–3 Hz range. Filtering helps us separate the meaningful part (e.g., steps at 0.5–3 Hz) from the unwanted parts (drift, vibration).
Example
A mobile telehealth app may filter and compress biosignals before sending them to the cloud, ensuring smooth transmission and accurate downstream AI analysis.
Example
A smartwatch PPG sensor while jogging produces spiky noise due to wrist motion. Filtering reduces these spikes so the heart-rate trend is reliable.