Digital Filter Design & Speech Vocoding (MATLAB)

This repository contains an Advanced Digital Signal Processing project with two deliverables:

1. Speech vocoder implementation (channel vocoder using analysis/synthesis filter banks and noise carrier)
2. Digital filter design & analysis using MATLAB: FIR equiripple (Parks–McClellan) and IIR elliptic filters

The work focuses on interpreting magnitude, phase, and group delay responses, and on practical implementation trade-offs such as filter order, latency, and numerical stability.

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Key technical highlights

Part 1 — Vocoder (channel vocoder)

• Input audio: bkbe2114.wav
• Sampling: Fs = 22 kHz, bandwidth analysed: 0–11 kHz
• 12 channels (analysis + synthesis band-pass filter banks)
• Frequency cutoffs derived from the mapping: [ f = 165.4(100.06^{x}-1) ] giving approximate cutoffs: [0, 69.53, 168.28, 308.55, 507.79, 790.77, 1192.71, 1763.61, 2574.51, 3726.27, 5362.19, 7685.79, 11000] Hz
• Envelope extraction per band:
  • Half-wave rectification
  • 3rd-order Butterworth LPF, fc = 160 Hz
• Carrier: white noise
• Modulation: envelope × noise, then synthesis filtering and summation into final vocoded speech

Part 2 — Digital filter design (Fs = 48 kHz)

• FIR equiripple designs (firpmord + firpm):
  • Order effects: sharper transitions + deeper stopband at higher order, but constant delay ≈ N/2
  • Density factor effects: plot/grid resolution, not the true response
• IIR elliptic designs (ellipord + ellip; also Filter Designer App with SOS):
  • Very efficient at low order (e.g., N≈4–5 meets stringent specs)
  • Nonlinear phase + frequency-dependent group delay
  • High forced orders (e.g., N=50 or N=100) show numerical/conditioning issues in code and pathological delay behaviour in the app

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Results snapshot

Speech vocoder (MATLAB)

Original (spectrum)	Envelope extraction (LPF @ 160 Hz)
Baseline speech spectrum with clear low-frequency concentration and formant/harmonic structure.	Rectification + 160 Hz LPF yields the smooth amplitude envelope used to control the carrier.

Noise carrier modulation (spectrum)	Vocoder output (spectrum)
Envelope-shaped noise shows broadband energy whose amplitude follows speech dynamics.	Output becomes noise-like (harmonics removed) while retaining overall spectral shaping for intelligibility.

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Digital filter design (FIR vs IIR)

FIR: density factor comparison (df=20 vs df=50)	FIR: min order vs N=100 (magnitude/phase/group delay)
df=20 and df=50 overlap → density mainly affects grid/plot resolution, not the true response.	Higher FIR order improves selectivity/attenuation but increases constant group delay (≈ N/2).

FIR: order sweep (N=100 vs N=130)	IIR elliptic: min-order bandpass (nonlinear phase & delay peaks)
N=130 gives slightly sharper skirts/deeper stopband than N=100, with higher constant delay.	Low-order elliptic IIR is magnitude-efficient but shows frequency-dependent delay (nonlinear phase).

Takeaway: FIR ⇒ linear phase + predictable constant delay; IIR elliptic ⇒ lower order for sharp magnitude specs but nonlinear phase/delay variation; vocoding preserves intelligibility via envelope extraction and noise-carrier modulation.

Repository layout

• src/ — MATLAB source code (vocoder + filter design)
• docs/ — detailed write-ups per part + full report PDF
• (Optional) results/figures/ — exported plots used in docs
• (Optional) data/audio_in/ and data/audio_out/ — short audio samples

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How to run

Requirements

• MATLAB (R20xx or later recommended)
• Signal Processing Toolbox (for firpm, firpmord, ellip, ellipord, freqz, grpdelay, etc.)

Run the vocoder

1. Place bkbe2114.wav in the same folder as src/vocoder/vocoder_main.m or update the path inside the script.
2. In MATLAB, set the repo root as Current Folder.
3. Run:
   • src/vocoder/vocoder_main.m
4. The script:
   • plays the original and vocoded audio (soundsc)
   • generates time + spectrum plots at key pipeline stages

Run the filter design tasks

1. In MATLAB, set the repo root as Current Folder.
2. Run:
   • src/filter_design/run_all_filter_tasks.m
3. The script should generate responses (magnitude/phase/group delay) for the FIR and IIR tasks.

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Documentation

• Vocoder pipeline & results: docs/vocoder.md
• FIR/IIR design tasks & conclusions: docs/filter-design.md
• Methodology and assumptions: docs/methodology.md
• Limitations & improvements: docs/limitations.md
• References: docs/references.md
• Full academic report: docs/report.pdf

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Notes to reviewers

This project emphasizes engineering interpretation:

• Why FIR order increases stopband rejection but adds latency
• Why density factor changes visual smoothness rather than filter behaviour (FIR equiripple)
• Why high-order elliptic IIR designs become ill-conditioned in direct coefficient form, and why SOS helps (but can still be impractical)