Digital Filter Design

Prince E. Adjei

Kwame Nkrumah University of Science and Technology

Topic: Digital Filters Module 2: Signal Processing

Biosignal Processes And Analysis (BME 366)

Digital Filter Design

Topics:

(1). FIR vs IIR Filtering in ECG Signal Processing

(2). Design and Specification of Digital Filters

(3). Filter Effects: Phase, Delay, and Stability Considerations

(4). Real-Time vs Offline ECG Filtering Approaches

(5). Introduction to ECG Signal Compression

Learning Objectives

•Differentiate between FIR and IIR filters and choose appropriate types

for ECG signal cleaning.

•Design ECG band-pass and notch filters using common tools and

interpret filter specifications.

•Analyze the impact of phase distortion and ensure filter stability in ECG

applications.

•Compare real-time and offline filtering implementations, including

hardware constraints.

•Explain the principles of ECG signal compression and evaluate quality

across different bit rates.

Review

•Filtering is the process of removing unwanted components

(e.g., noise) from a signal. Filters can be applied in both the

time and frequency domains. Some types of filters include:

•Low-pass filter

•High-pass filter

•Band-Pass filter

•Notch Filter

Analogue vs Digital Filters

•Analogue filters process continuous-time electrical signals before

digitization.

•They are built using electronic components like resistors,

capacitors, and op-amps forming circuits that define the filter

response.

•Typically placed in the front-end of ECG hardware to remove

baseline drift,high-frequency noise,and prevent aliasing.

•They are difficult to modify once implemented, since changes

require replacing physical components.

•Filter performance may vary due to component tolerances,

temperature changes, and aging, affecting long-term reliability.

Analogue vs Digital Filters

•Digital filters operate on sampled (discrete-time) signals after

analog-to-digital conversion.

•They are implemented in software or embedded hardware, like

DSPs or microcontrollers.

•Offer high flexibility and precision, allowing for exact control of

filter characteristics.

•Easy to modify or tune by changing software parameters.

•Their behavior is consistent and reproducible across devices.

•Can handle advanced processing, such as adaptive filtering.

Analogue vs Digital Filters

Aspect

Analog Filters

Digital Filters

Signal Type

Continuous

-time

Discrete

-time (sampled)

Implementation

Physical components (e.g., resistors,

-amps)

Software or embedded systems

(e.g., MCU)

Flexibility

Hard to modify once built

Easy to update and reconfigure

Accuracy

Affected by component tolerances

Precise and reproducible

FIR Filters

•Finite Impulse Response (FIR) filters are digital filters where the

output depends only on a finite number of past input values.

•They do not use feedback from past outputs.

Key Properties

•Always stable (no feedback loop)

•Linear phase possible, which means they preserve the shape of

waveforms (critical for things like QRS in ECG)

•Simple implementation using convolution.

•Require more taps than IIR for sharp transitions →higher

computational cost.

•Difference Equation

•Only uses past input samples

•Coefficients {bo,b1,...,bN} define filter behavior

•Implemented using a convolution sum

•The response to a single impulse input ends after a finite duration

•Hence the name: Finite Impulse Response

FIR Filters

Window Method:

•Simple approach using a truncated ideal filter (like sinc) multiplied

by a window function (e.g., Hamming, Blackman).

•Easy to implement, but may require a high filter order for sharp

transitions.

Parks–McClellan Algorithm:

•An optimal design method (equiripple) that minimizes the worst-

case error between the desired and actual response.

•More efficient than windowing for tight filter specs.

FIR Filter Design Methods

IIR Filters

•Infinite Impulse Response (IIR) filters are digital filters where the

output depends on both past inputs and past outputs, meaning they

use feedback.

Key Properties

•Can achieve sharp filtering with fewer coefficients than FIR

•Typically have a non-linear phase, which can distort time-sensitive

signals

•Risk of instability if not designed carefully

•Efficient for real-time or embedded applications due to lower order

IIR Filters

•Difference equation

•Uses both input and output history.

•Coefficients {ai},{bk} determine the filter’s response.

•Recursive: feedback makes it powerful, but more sensitive.

•The response to an impulse theoretically continues forever.

•Hence the name: Infinite Impulse Response

Filter Concepts Explained

1. Passband

•The range of frequencies a filter lets through with minimal attenuation

•For example: 5–45 Hz in an ECG filter →this is the desired signal range.

2. Stopband

•The frequency range where the filter strongly attenuates the signal.

•Example: Below 5 Hz (baseline wander), above 45 Hz (muscle noise)

3. Cut-off frequency

The point where the filter starts to transition between passing and

attenuating

•Defined at –3dB (about 70.7% of the original amplitude)

•A filter may have two cutoffs in a bandpass case (e.g., 5 Hz and 45 Hz)

Common Type of IIR Filters

Butterworth:

•Has a very smooth, flat response in the passband (no ripples).

•It’s a good general-purpose filter but requires more order than other

types for sharp transitions.

Chebyshev Type I:

•Allows ripples in the passband to achieve a sharper cutoff than

Butterworth.

•However, these ripples can distort signal amplitude, especially in

ECG.

Common Type of IIR Filters

Chebyshev Type II:

•Ripples are pushed to the stopband, keeping the passband flat.

•This makes it better for preserving waveform shape while still

improving sharpness.

Elliptic (Cauer):

•Has ripples in both passband and stopband, but gives the sharpest

transition with the lowest filter order.

•Best for strict specs, but may distort signal morphology more than

others.

Common Type of IIR Filters

Questions

1) What is the main difference

between analog and digital filters?

2) Why might we choose a linear-

phase filter when working with

ECG signals?

3) What are some types of IIR filters,

and what makes each one unique?

Passband & Stopband Specification –ECG Filtering

Passband:

•ECG signal content mainly lies between 0.5 Hz and 40 Hz.

•This range preserves P waves, QRS complexes, and T waves.

•Ideal for general clinical ECG, R-peak detection, and HRV analysis.

Stopband:

•Frequencies below 0.5 Hz (baseline wander) should be attenuated.

•Frequencies above 40 Hz (e.g., muscle noise, EMG) should also be

removed.

•Additional notch at 50 Hz (or 60 Hz) to suppress powerline

interference.

Design Demo: FIR vs IIR in Python

Goal: Design a band-pass filter (0.5–40 Hz) for ECG using both FIR and

IIR methods, and compare their filter order and performance.

Python Tools Used

•scipy.signal.firwin

⚬FIR design using the window method.

⚬Requires specifying the number of taps (order),cutoff

frequencies, and window type.

•scipy.signal.iirdesign

⚬IIR design based on specified passband,stopband,ripple, and

attenuation.

⚬Automatically chooses filter type and order

Design Demo: FIR vs IIR in Python

Phase and Group Delay

•Phase delay tells you how much a specific frequency component of a

signal is delayed in time by a filter.

Mathematically:

•If the filter’s phase response is ϕ(ω), then the phase delay is:

•where ωis the frequency in radians/sec.

•It describes how much a single frequency is shifted in time as it

passes through the system.

•Group delay measures how the phase of a filter changes with

frequency.

•It reflects the time delay of the overall signal envelope or a group of

nearby frequencies.

Mathematically:

•If group delay is constant across all frequencies, then all

components of the signal are delayed equally, and the waveform

shape is preserved.

•If it varies, then some frequencies lag more than others, and the

signal gets distorted.

Phase and Group Delay

Phase & Group Delay Demo: FIR vs IIR on QRS

•ECG QRS distortion with 4-pole Butterworth vs 200-tap FIR

Filter stability & overflow

•A filter is stable if its output remains bounded for any bounded input.

•FIR filters are always stable because they have no feedback (no poles

outside the origin).

•For IIR filters, stability depends on the location of poles (they must lie

inside the unit circle in the z-domain).

•Overflow occurs when intermediate values in a filter computation exceed

the maximum range that the hardware or data type can represent.

•This can lead to clipping of values,wraparound errors (e.g., 32768

becomes -32768), and unstable or distorted output.

•To avoid overflows, IIR filters are implemented using cascade (biquad)

structures.

Direct-form vs Cascade (Biquads)

Direct Form implements the full IIR filter in one equation (using the full

numerator and denominator).

Common forms: Direct Form I and II.

•Sensitive to numerical errors, especially in high-order filters.

Can become unstable on fixed-point systems due to:

•Coefficient rounding

•Overflow

•Feedback accumulation

Direct-form vs Cascade (Biquads)

Cascade Form (Biquads)

•Breaks a high-order filter into a series of second-order sections (SOS).

•Each biquad handles a small portion of the response:

Improves:

•Numerical stability

•Resistance to overflow

•Precision in embedded (fixed-point) implementations

IIR Filtering using Cascade (Biquads)

Questions

1) Why do we filter ECG signals

between 0.5 and 40 Hz?

2) What is phase delay, and how can

it affect the shape of ECG signals like

the QRS complex?

3) What does "filter overflow" mean,

and how can using SOS (second-order

sections) improve filter stability?

Real-time vs Offline Filtering

Offline Filtering

•The entire signal is available in memory before filtering.

•Ideal for: Research and analysis, ECG post-processing, HRV feature

extraction.

•Allows use of floating-point, high-order filters with no concern for

real-time constraints.

Real-Time Filtering

•Signal is processed sample-by-sample or in small blocks as it arrives.

•Must be fast, memory-efficient, and stable.

•Used in: Wearables Monitoring systems (e.g., ICU, ambulatory ECG),

Embedded medical devices

Real-Time FIR

•FIR filters, especially those with a large number of taps (e.g., 200+),

can be computationally expensive in real-time.

To solve this, FFT-based block processing is used:

•The input signal is split into overlapping segments.

•Each block is zero-padded, transformed to the frequency domain

using the Fast Fourier Transform (FFT).

•The filter is also FFT-transformed, and frequency-domain

multiplication is applied.

•The result is transformed back (IFFT) to the time domain and

overlapped with previous blocks.

Real-Time IIR

•In embedded devices like smartwatches, ECG patches, or

microcontrollers (MCUs), memory and speed are limited.

•These systems use fixed-point arithmetic instead of floating-point.

To implement stable IIR filtering in this context:

•Avoid overflow: Use proper scaling of coefficients and intermediate

values.

•Preserve precision: Adopt a fixed-point format such as Q15 or Q31,

which allows fractions to be stored in integers.

•Use biquad sections: Breaking the filter into Second-Order Sections

(SOS) improves numerical robustness.

Compression Primer

•Long-term recordings of signals like ECG, EEG, EMG, and PPG can

generate huge data volumes, especially in high-resolution or multi-

channel setups.

Compression helps by enabling:

•Efficient storage (e.g., hospital servers, wearables, implantables)

•Low-bandwidth transmission (e.g., wireless body-area networks,

telehealth)

•Reduced power usage in mobile/edge devices

•Faster access for clinical review, machine learning pipelines, or

patient alerts

Bitrate

•Bitrate is the amount of data used per second to represent a signal,

usually measured in kilobits per second (kbps).

•Higher bitrate = more detail (diagnostic quality)

•Lower bitrate = smaller file, but less detail

Bitrate (bps)=Sampling rate×Bits per sample ×Number of channels

Compression lowers the bitrate by:

•Removing redundancy (e.g., repeated patterns in the signal)

•Quantizing more aggressively (e.g., reducing precision)

•Exploiting signal properties (e.g., using wavelets or predictive models)

“Quality-on-Demand” Idea

•Quality on demand involves adapting signal quality based on need:

Application

Required quality

Bitrate Target

Trend tracking (e.g., HR, RR)

Low to moderate

–8 kbps

Real

-time monitoring (e.g., ICU)

Moderate to high

–16 kbps

Diagnostic storage/telecardiology

High (diagnostic

-grade)

–24+ kbps

Effect of Bitrate on ECG Compression Quality (4, 8, 16 kbps)

Summary

•FIR filters offer linear phase (good for preserving QRS timing) but need

a high order.

•IIR filters are computationally efficient (low order) but may distort

timing due to nonlinear phase.

•FIR design methods include the window method and Parks–

McClellan for linear-phase filters.

•Butterworth (flat), Chebyshev I/II (ripple control), and Elliptic (sharpest

cutoff) are common IIR designs.

•IIR filters can be implemented using cascade biquads for stability.