Case Study: Safyre - Tribal Fusion Mix

def generate_fingerprint(audio_segment):
    # 1. Spectral Analysis
    stft = librosa.stft(audio_segment, n_fft=2048, hop_length=512)
    magnitude = np.abs(stft)
    
    # 2. Perceptual Weighting
    mel_basis = librosa.filters.mel(sr=44100, n_fft=2048, n_mels=128)
    mel_spec = np.dot(mel_basis, magnitude)
    
    # 3. Peak Detection
    peaks = find_spectral_peaks(mel_spec, min_distance=3)
    
    # 4. Constellation Generation
    landmarks = []
    for i, (time_idx, freq_idx) in enumerate(peaks):
        # Create pairs with nearby peaks
        for j in range(i+1, min(i+FAN_OUT, len(peaks))):
            target_time, target_freq = peaks[j]
            if target_time - time_idx <= MAX_TIME_DELTA:
                landmarks.append((
                    freq_idx, target_freq,
                    target_time - time_idx, time_idx
                ))
    
    # 5. Hash Generation
    fingerprints = []
    for freq1, freq2, delta_time, abs_time in landmarks:
        hash_val = hash((freq1, freq2, delta_time)) & 0xFFFFFFFF
        fingerprints.append((hash_val, abs_time))
    
    return fingerprints
                

-- Fingerprint storage optimized for fast lookup
CREATE TABLE fingerprints (
    hash_id BIGINT NOT NULL,
    track_id INT NOT NULL,
    time_offset FLOAT NOT NULL,
    INDEX hash_idx (hash_id),
    INDEX track_time_idx (track_id, time_offset)
);

-- Track metadata with full-text search
CREATE TABLE tracks (
    id INT PRIMARY KEY,
    artist VARCHAR(255) NOT NULL,
    title VARCHAR(255) NOT NULL,
    duration FLOAT,
    fingerprint_count INT,
    FULLTEXT(artist, title)
);

-- Matching algorithm uses hash-based lookup:
-- 1. Query: SELECT track_id, time_offset FROM fingerprints WHERE hash_id IN (...)
-- 2. Group by track_id, count matches
-- 3. Apply temporal alignment scoring
-- 4. Return top matches above confidence threshold
                

// Time Complexity Analysis for Core Operations

1. Audio Preprocessing: O(n) where n = audio sample count
   - FFT: O(n log n) for each window
   - Mel filtering: O(k * m) where k=bins, m=frequencies
   
2. Fingerprint Generation: O(p²) where p = peaks per segment  
   - Peak detection: O(n) per frequency bin
   - Constellation mapping: O(p²) for all peak pairs
   
3. Database Lookup: O(1) average case with hash indexing
   - Hash collision handling: O(k) where k = collisions
   - Result ranking: O(r log r) where r = results
   
4. Overall Processing: O(s * n log n) where s = segments

Space Complexity: O(f + h) where f = fingerprints, h = hash table
                

-- Academic-grade database design demonstrating normalization

-- Third Normal Form (3NF) schema
CREATE TABLE artists (
    id INT PRIMARY KEY AUTO_INCREMENT,
    name VARCHAR(255) NOT NULL UNIQUE,
    created_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP
);

CREATE TABLE tracks (
    id INT PRIMARY KEY AUTO_INCREMENT,
    title VARCHAR(255) NOT NULL,
    artist_id INT NOT NULL,
    duration INT,
    release_date DATE,
    FOREIGN KEY (artist_id) REFERENCES artists(id),
    INDEX idx_artist_title (artist_id, title)
);

CREATE TABLE fingerprints (
    hash_id BIGINT NOT NULL,
    track_id INT NOT NULL,
    time_offset DECIMAL(5,2) NOT NULL,
    confidence DECIMAL(3,2) DEFAULT 0.50,
    FOREIGN KEY (track_id) REFERENCES tracks(id),
    PRIMARY KEY (hash_id, track_id, time_offset),
    INDEX idx_hash_lookup (hash_id),
    INDEX idx_track_time (track_id, time_offset)
) ENGINE=InnoDB PARTITION BY HASH(hash_id) PARTITIONS 16;

-- Demonstrates: Normalization, Indexing, Partitioning, Referential Integrity