Matlab Design Digital Filter

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From the author

Design and validate digital filters in MATLAB. Use when cleaning up noisy signals, removing interference, filtering signals, designing FIR/IIR filters (lowpass/highpass/bandpass/bandstop/notch), or comparing filters in Filter Analyzer.

— the description by MathWorks

AutoGineer summary

Written by AutoGineer from the skill’s own files, not by the author

This skill provides a structured workflow for designing and validating digital filters within MATLAB. It guides users through signal analysis, architecture selection, and verification, ensuring that filter designs meet specific frequency and magnitude requirements. The skill emphasizes the use of standard MATLAB functions like designfilt and filterAnalyzer, while enforcing best practices for numerical stability and frequency-aware design.

What it does

Designs FIR and IIR filters including lowpass, highpass, bandpass, bandstop, and notch types.
Provides a systematic workflow for signal analysis and architecture selection.
Facilitates visual comparison of filter designs using Filter Analyzer.
Enforces best practices for numerical stability, such as using SOS forms for IIR filters.
Includes validation steps to verify filter performance against specifications.
Supports both streaming and offline filtering implementation strategies.

When to use it

When you need to clean up noisy signals or remove specific interference.
When designing digital filters with specific frequency and ripple requirements.
When comparing different filter architectures like FIR versus IIR.
When working on streaming or batch signal processing pipelines.

Advantages

Ensures consistent design methodology through a preflight and verification checklist.
Promotes numerical stability by recommending specific filter forms.
Integrates directly with MATLAB's signal processing and DSP toolboxes.
Provides clear guidance on handling narrow transition bands.

Usage examples

“Design a lowpass filter for a 1000 Hz signal with a 200 Hz cutoff.”: The agent will ask for the sample rate (Fs), filter mode (streaming vs offline), and phase requirements before generating the design code.
“How do I compare two different filter designs in MATLAB?”: The agent will guide you to use the filterAnalyzer function and provide the necessary steps to visualize and compare their magnitude and group delay responses.

Install

Download the skill as a ZIP:
https://mp-staging.autogineer.com/agent-skills/matlab/matlab-design-digital-filter/download

Unzip it into the cross-client skills folder of your project:

mkdir -p .agents/skills && unzip matlab-design-digital-filter.zip -d .agents/skills

Documentation by MathWorks

Design Digital Filters in MATLAB

Design, implement, and validate digital filters using Signal Processing Toolbox and DSP System Toolbox. Choose the right architecture (single-stage vs efficient alternatives), generate correct code, and verify the result with plots and numbers.

When to Use

Designing lowpass, highpass, bandpass, bandstop, or notch filters
Cleaning up noisy signals or removing interference
Choosing between FIR and IIR filter architectures
Comparing filter designs in Filter Analyzer
Building streaming (real-time) or offline (batch) filtering pipelines
Handling narrow transition bands with multirate or IFIR approaches

When NOT to Use

Adaptive filtering (LMS, RLS) -- use Signal Processing Toolbox docs directly
Audio-specific processing (equalization, room correction) -- use Audio Toolbox
Image filtering (2D convolution, morphological ops) -- use Image Processing Toolbox
General spectral analysis without filtering intent -- FFT/periodogram docs suffice

Key Rules

Read references/INDEX.md before writing any filter design code.
Always write to .m files. Never put multi-line MATLAB code directly in evaluate_matlab_code. Write to a .m file, run with run_matlab_file, edit on error.
Preflight before ANY MATLAB call. Before calling any function listed in INDEX.md, read the required quick-ref first. State Preflight: [files] at the top of the response.
Do not guess key requirements. If Mode (streaming vs offline) or Phase requirement is not stated, ask.
No Hz designs without Fs. If Fs is unknown, stop and ask (unless the user explicitly wants normalized frequency).
Always pin the sample rate. Use designfilt(..., SampleRate=Fs) and freqz(d, [], Fs).
IIR stability: Prefer SOS/CTF forms (avoid high-order [b,a] polynomials).

Preflight Procedure

List MATLAB functions to call
Check references/INDEX.md for each (function-level + task-level tables)
Read required quick-ref files
State at response top: Preflight: quick-ref/filter-analyzer.md, quick-ref/designfilt.md (or Preflight: none required)

Workflow

Phase 1: Signal Analysis

Analyze input data via MCP (spectrum, signal length, interference location)
Compute trans_pct and identify interference characteristics

Phase 2: Clarify Intent

After signal analysis, ask Mode + Phase if not stated:

Mode: streaming (causal) | offline (batch)
Phase: zero-phase | linear-phase | don't-care

Wait for answer before showing any approach comparison or overview.

Phase 3: Architecture Selection

Open references/efficient-filtering.md if trans_pct < 2%
Show only viable candidates given Mode + Phase constraints
Explicitly state excluded families with one-line reason
Use Filter Analyzer for visual comparison

Design Intake Checklist

Required signal + frequency spec (cannot proceed without)

Fs (Hz)
Response type: lowpass / highpass / bandpass / bandstop / notch
Edge frequencies in Hz

If any item is missing, ask.

Required intent for architecture choice (ask if unknown)

Mode: streaming (causal) | offline (batch)
Phase: zero-phase | linear-phase | don't-care
Magnitude constraints: Rp_dB passband ripple (default 1 dB), Rs_dB stopband attenuation (default 60 dB)

If Mode or Phase is unknown, ask 1-2 clarifying questions and stop.

Architecture Checkpoint

Compute and state before finalizing an approach:

trans_bw = Fstop - Fpass
trans_pct = 100 * trans_bw / Fs
M_max = floor(Fs/(2*Fstop)) (only meaningful for lowpass-based multirate)

Decision rule:

trans_pct > 5% -- single-stage FIR or IIR is usually fine
2% <= trans_pct <= 5% -- single-stage possible; mention efficient alternatives if cost/latency matters
trans_pct < 2% -- stop and do a narrow-transition comparison (see references/quick-ref/efficient-filtering.md)

Design + Verify

Feasibility check -- Let designfilt choose minimum order, then query filtord(d). Optionally use kaiserord/firpmord for FIR length estimates.
Design candidates -- Prefer designfilt() with explicit Rp/Rs and SampleRate=Fs. Streaming IIR: use SystemObject=true. Offline zero-phase: filtfilt() is allowed but state that it squares the magnitude response.
Compare visually -- Use filterAnalyzer() for comparing 2+ designs. Read references/quick-ref/filter-analyzer.md first. Minimum displays: magnitude + group delay.
Verify with numbers -- Worst-case passband ripple and stopband attenuation vs spec. For filtfilt(), verify the effective response (magnitude squared).
Deliver the output -- Specs recap, derived metrics, chosen architecture + why, MATLAB code, verification snippet + results, implementation form.

Key Functions

Function	Purpose
`designfilt()`	Primary filter design (FIR and IIR, all response types)
`filterAnalyzer()`	Visual comparison of 2+ filter designs
`freqz()`, `grpdelay()`	Frequency response and group delay analysis
`filtfilt()`	Zero-phase offline filtering
`dsp.SOSFilter`	Streaming IIR via `SystemObject=true`
`designMultirateFIR()`	Multirate decimator/interpolator design
`ifir()`	Interpolated FIR for narrow transitions at constant rate
`cost()`	MPIS (MultiplicationsPerInputSample) on DSP System objects
`kaiserord()`, `firpmord()`	FIR order estimation

Conventions

Always specify SampleRate=Fs in designfilt() and plot in Hz with freqz(d, [], Fs)
Use filterAnalyzer() for multi-filter comparison, not custom freqz/grpdelay plots
Use SOS form for IIR (avoid [b,a] for order > 8)
Use tiledlayout/nexttile for multi-panel figures (not subplot)

Files

ATTRIBUTION.mdAdded by AutoGineer1.0 KiB
LICENSELicence file added by AutoGineer1.4 KiB
SKILL.md6.1 KiB
manifest.yaml473 B
references/INDEX.md2.9 KiB
references/best-practices.md7.8 KiB
references/efficient-filtering.md14.4 KiB
references/filter-analyzer.md18.1 KiB
references/multirate.md13.2 KiB
references/multistage-ifir.md8.5 KiB
references/patterns.md16.2 KiB
references/quick-ref/designfilt.md6.0 KiB
references/quick-ref/efficient-filtering.md6.1 KiB
references/quick-ref/filter-analyzer.md3.0 KiB
references/quick-ref/general-iir-fir.md3.0 KiB
references/quick-ref/multirate-offline.md2.3 KiB
references/quick-ref/multirate-streaming.md3.6 KiB
references/quick-ref/multistage-ifir.md2.8 KiB

references/best-practices.md

Filter Design Best Practices

Guidelines for robust filter design, validation workflows, and professional interactions. Consult this file when you need guidance on methodology and approach.

Core Principles
Provide Complete Solutions
Validation Workflow
Architecture Decision Workflow
Streaming vs Offline
Performance Optimization
Quick Lookup

Core Principles

Always Consider

Sample Rate Implications
- Frequency specifications are relative to Fs/2 (Nyquist)
- Narrow transition bands (< 2% of Fs) require special handling
- Plot in Hz for clarity: freqz(d, [], Fs)
Filter Order vs Performance Trade-offs
- Higher order = sharper cutoff but more computation
- IIR = fewer coefficients but non-linear phase
- FIR = linear phase but longer filters
Computational Efficiency for Real-Time
- Prefer IIR for streaming with sharp cutoff
- Use multistage for narrow transition bands
- Consider fftfilt() for long FIR (> 100 taps)
Numerical Stability for IIR
- Always use SOS or CTF form (not [b,a])
- Use designfilt() which handles stability internally
- For high-order IIR (> 8), verify pole locations

Provide Complete Solutions

Every filter design response should include:

1. Design Code

d = designfilt("lowpassfir", ...
    PassbandFrequency=Fpass, StopbandFrequency=Fstop, ...
    PassbandRipple=Rp, StopbandAttenuation=Rs, ...
    SampleRate=Fs, DesignMethod="equiripple");

2. Visualization Code

figure;
freqz(d, [], Fs);
grid on;
title('Filter Response');

3. Parameter Explanation

Why this filter type was chosen
Trade-offs considered
Key specifications achieved

4. Validation Steps

How to verify the design meets specs
Test signal suggestions
Performance metrics to check

Validation Workflow

Pre-Application Checks

% 1) Order (MATLAB's actual order)
fprintf("Filter order: %d\n", filtord(d));

% 2) Frequency response (Hz-aware)
Nfft = 8192;
[h, f] = freqz(d, Nfft, Fs);
mag_dB = 20*log10(abs(h) + eps);

% 3) If the final application is filtfilt(d,x), verify the *effective* response
use_filtfilt = false;  % set true if you will apply filtfilt()
if use_filtfilt
    mag_dB = 2*mag_dB;  % |H|^2 -> dB doubles
end

% 4) Build pass/stop masks by RESPONSE TYPE
responseType = "lowpass";  % "highpass" | "bandpass" | "bandstop"

switch responseType
    case "lowpass"
        pass = f <= Fpass;
        stop = f >= Fstop;
    case "highpass"
        pass = f >= Fpass;
        stop = f <= Fstop;
    case "bandpass"
        pass = (f >= Fpass1) & (f <= Fpass2);
        stop = (f <= Fstop1) | (f >= Fstop2);
    case "bandstop"
        pass = (f <= Fpass1) | (f >= Fpass2);
        stop = (f >= Fstop1) & (f <= Fstop2);
end

% 5) Measured specs (worst-case)
Rp_meas_dB = max(mag_dB(pass)) - min(mag_dB(pass));
Rs_meas_dB = -max(mag_dB(stop));

fprintf("Measured ripple: %.3f dB (spec %.3f dB)\n", Rp_meas_dB, Rp);
fprintf("Measured stopband attenuation: %.1f dB (spec %.1f dB)\n", Rs_meas_dB, Rs);

% 6) Plot (optional but recommended)
figure; plot(f, mag_dB); grid on;
xlabel("Frequency (Hz)"); ylabel("Magnitude (dB)");
title("Magnitude Response (verified in Hz)");

Post-Filtering Checks

% 1. Visual comparison
figure;
plot(t, x, 'b', t, y, 'r');
legend('Original', 'Filtered');

% 2. Spectrum comparison
figure;
pwelch(x, [], [], [], Fs); hold on;
pwelch(y, [], [], [], Fs);
legend('Original', 'Filtered');

% 3. SNR improvement (if ground truth available)
snr_before = 10*log10(sum(clean.^2) / sum((noisy - clean).^2));
snr_after = 10*log10(sum(clean.^2) / sum((filtered - clean).^2));
fprintf('SNR Improvement: %.1f dB\n', snr_after - snr_before);

Architecture Decision Workflow

Pre-Design Check (MANDATORY)

For EVERY filter design, calculate:

% Template
% Transition width (Δf) should match the RESPONSE TYPE.
% Use the *constraining* transition (smallest transition band) in Hz.
%
% lowpass:   Δf = Fstop - Fpass
% highpass:  Δf = Fpass - Fstop
% bandpass:  Δf = min(Fpass1 - Fstop1, Fstop2 - Fpass2)
% bandstop:  Δf = min(Fstop1 - Fpass1, Fpass2 - Fstop2)

delta_f = ...;                         % fill based on response type (Hz)
trans_pct = 100 * (delta_f / Fs);      % Transition width as % of sample rate

% FIR length heuristic (sanity check only; not a guarantee)
N_est = (Rs * Fs) / (22 * delta_f);

% Max decimation factor is straightforward for LOWPASS cases:
% M_max ≈ floor(Fs / (2 * Fstop))
% For highpass/band* cases, safe decimation depends on spectral placement and is not a single formula.
M_max = floor(Fs / (2 * Fstop));

    ### Prefer MATLAB-Native FIR Order Estimators (recommended)

    The heuristic `N_est = (Rs * Fs)/(22 * Δf)` is **sanity-check only**. For a more standard, MATLAB-native estimate:

    - **Kaiser window estimate**: `kaiserord` (good quick order estimate for windowed FIR)
    - **Equiripple estimate**: `firpmord` (order estimate for Parks–McClellan FIR)

    ```matlab
    % Convert dB specs to linear deviations
    dev_p = (10^(Rp/20)-1) / (10^(Rp/20)+1);
    dev_s = 10^(-Rs/20);

    % LOWPASS example (adapt f/a for other responses):
    f = [Fpass Fstop];     % Hz
    a = [1 0];             % desired amplitudes in each band
    dev = [dev_p dev_s];   % linear deviations

    [N_kaiser, Wn, beta, ftype] = kaiserord(f, a, dev, Fs);
    [N_pm, fo, ao, w] = firpmord(f, a, dev, Fs);

    fprintf("Order estimates: Kaiser=%d, Equiripple=%d\n", N_kaiser, N_pm);
    ```

    **Workflow recommendation**:
    1) Use `kaiserord`/`firpmord` to estimate if a single-stage FIR is plausible.
    2) Design the real filter (e.g., `designfilt(..., DesignMethod="equiripple")`).
    3) Verify with `freqz` + measured `Rp_meas_dB` / `Rs_meas_dB`.

Decision Matrix

trans_pct	Action
> 5%	Single-stage OK
2-5%	Mention multistage option
< 2%	Present tradeoff to user (see `quick-ref/efficient-filtering.md`)

Response Template

"Architecture check: Transition BW = X% of Fs, estimated ~Y taps. [Single-stage recommended / Multistage recommended - asking user preference]."

Streaming vs Offline

Offline Processing

Use filtfilt() for zero-phase
Use resample() for multirate
Process entire signal at once
No state management needed

Streaming/Real-Time

Use dsp.SOSFilter with SystemObject=true
Or use ctffilt() (R2024b+) with state management
Process frame-by-frame
Reset state when needed

Key Rule

Offline zero-phase → resample() + filtfilt() Streaming causal → System objects + filter()

Never mix: System objects with filtfilt() = catastrophic failure

Performance Optimization

Long FIR Filters

if length(b) > 100
    y = fftfilt(b, x);  % FFT-based, faster
else
    y = filter(b, 1, x);  % Direct form OK
end

Narrow Transition Bands

Consider multistage approach
Calculate efficiency gain: (N_single) / (N_dec + N_sharp/M + N_interp)
For trans_pct < 2%, multistage often 5-10x more efficient (see quick-ref/efficient-filtering.md)

IIR Numerical Stability

Always use SOS form via designfilt() or zp2sos()
Avoid [b,a] form for order > 8
Check pole locations if stability concerns arise

Quick Lookup

Topic	Consult
Code templates	`patterns.md`
API details	references/INDEX.md
Architecture decision	Pre-Design Check above
Offline vs streaming	Streaming vs Offline section
Validation	Validation Workflow section

Requirements and compatibility

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Attribution and licence

Created by

MathWorks

Publisher

MathWorks (Official)

Source

matlab/matlab-agentic-toolkit · skills-catalog/signal-processing/matlab-design-digital-filter · commit 2a7f215

Licence

BSD 2-Clause License (redistribution allowed)

LICENSE (added by AutoGineer from LICENSE.md)
ATTRIBUTION.md (written by AutoGineer)

Synced

2026-11-08

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