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

1. List MATLAB functions to call
2. Check references/INDEX.md for each (function-level + task-level tables)
3. Read required quick-ref files
4. 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

1. Feasibility check -- Let designfilt choose minimum order, then query filtord(d). Optionally use kaiserord/firpmord for FIR length estimates.
2. 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.
3. Compare visually -- Use filterAnalyzer() for comparing 2+ designs. Read references/quick-ref/filter-analyzer.md first. Minimum displays: magnitude + group delay.
4. Verify with numbers -- Worst-case passband ripple and stopband attenuation vs spec. For filtfilt(), verify the effective response (magnitude squared).
5. 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)

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