Bird Chirp Signal Analysis using Handcrafted Signal Processing Features

The BirdCLEF competition, hosted on Kaggle, is a large-scale bioacoustic benchmark designed for automatic bird species identification using audio recordings. The dataset consists of field recordings collected from diverse ecological regions, containing bird vocalizations along with environmental noise such as wind, insects, and human activity.

These challenges—background noise, overlapping calls, class imbalance, and environmental variability—make it the perfect testbed for evaluating both classical signal processing and modern machine learning approaches. Below, we explore the time-frequency representations of these signals, extract critical handcrafted features, and compare results between two distinct species (Bird 1 and Bird 5).

1. Signal in the Time Domain

A bird chirp is a non-stationary signal characterized by time-varying frequency. In continuous-time representation, it is described as: $$x(t) = A(t)\cos\left(2\pi \int_0^t f(\tau) \, d\tau + \phi \right)$$ where $ A(t) $ is the amplitude envelope, $ f(t) $ is the instantaneous frequency, and $ \phi $ is the phase.

The raw waveform provides an initial understanding of chirp structure, amplitude variation, and temporal sparsity.

Figure 1: Amplitude vs Time representation of a bird chirp signal

Observations from the Time Domain:

Uniform spacing between chirp frquencies over time

2. Frequency Sweep Features

Instantaneous Frequency captures how frequency content evolves, derived using the Hilbert transform: $$f_i(t) = \frac{1}{2\pi} \frac{d}{dt} \theta(t)$$ Chirp Slope measures the rate of change: $ \text{Slope} = \frac{df(t)}{dt} $. For a linear chirp, this simplifies to $ k $.

Bird 1 Frequency Sweep — Bird 1: Frequency Sweep

Bird 5 Frequency Sweep — Bird 5: Frequency Sweep

Observations:

Both birds exhibit different signal characteristics: a) Bird 1 signal is continuous which represents territorial display, b) Bird 5 signal is discrete which represents alerting/communicating behaviour.
Bird1: Stable frequency Band, Bird5: High Variational Frequency band - More information encoded by bird5.
Bird1: Complex sweep rate, Bird5: Narrow sweep rate - Bird1: Richer Acoustic structure.

3. Harmonic Features

Harmonics are integer multiples of the fundamental frequency $ f_0 $: $$f_n = n f_0, \quad n = 1, 2, 3, \dots$$ The Harmonic-to-Noise Ratio (HNR) measures the proportion of periodic energy to noise energy: $$\text{HNR} = 10 \log_{10} \left( \frac{P_{\text{harmonic}}}{P_{\text{noise}}} \right)$$

Bird 5 Harmonics — Bird 5: Harmonic Structure

Observations:

Tonal species show clear, stacked harmonic structures.
Noisy calls exhibit blurred or entirely absent harmonic periodicity.

4. Temporal Features

Chirp Duration ($ T_{\text{chirp}} = t_e - t_s $) and Inter-Chirp Interval ($ \Delta T = t_s^{(i+1)} - t_s^{(i)} $) capture rhythm. Chirp Rate quantifies vocal activity levels: $ R = \frac{N}{T} $.

Bird 1 Temporal Patterns — Bird 1: Temporal Patterns

Bird 5 Temporal Patterns — Bird 5: Temporal Patterns

Observations:

Bird 1 shows highly regular chirp intervals (steady rhythm).
Bird 5 exhibits irregular, burst-like temporal calling patterns.

5. Spectral Features

The Spectral Centroid acts as the "center of mass" for the spectrum, indicating brightness: $$C = \frac{\sum_{k} f_k |X(k)|}{\sum_{k} |X(k)|}$$ Spectral Entropy measures randomness: $ H = -\sum_{k} p_k \log p_k $, distinguishing tonal vs. noise-like signals.

Bird 1 Spectral Features — Bird 1: Spectral Features

Bird 5 Spectral Features — Bird 5: Spectral Profile

Observations:

A higher centroid indicates high-frequency dominant chirps.
Bandwidth successfully differentiates narrowband whistling from broadband complex calls.

6. Modulation Features

Modulation captures changes over time/frequency axes via 2D Fourier transforms applied to the spectrogram: $$M(\omega_t, f) = \mathcal{F}_t \{ S(t, f) \}$$

Bird 5 Modulation — Bird 5: Modulation Features

Observations:

Fast temporal modulation corresponds to rapid trills.
Slow temporal modulation aligns with isolated, spaced chirps.

7. Wavelet Features

The Discrete Wavelet Transform (DWT) captures localized time-frequency patterns: $$W(a, b) = \int x(t) \psi_{a,b}(t) \, dt$$ where $ \psi_{a,b}(t) $ is the wavelet basis at scale $ a $ and shift $ b $.

Bird 5 Wavelets — Bird 5: Wavelet Coefficients

Observations:

Chirps appear strongly at highly specific wavelet scales.
Different species show fundamentally distinct scale-energy distributions, separating high and low-frequency calls.

8. Cepstral Features (MFCCs)

Mel-Frequency Cepstral Coefficients (MFCCs) represent the spectral envelope: $$c_n = \sum_{k} \log(S_k)\cos\left[\frac{\pi n}{K}(k - 0.5)\right]$$ Temporal dynamics are captured using Delta ($ \Delta $) and Delta-Delta ($ \Delta^2 $) coefficients.

Bird 5 MFCC — Bird 5: MFCC Representation

Observations:

MFCC patterns differ drastically across species, providing a compact envelope representation.
Tracking the temporal evolution of these coefficients heavily improves species discrimination.

9. Energy Distribution & Handcrafted Filters

Ridge-based features find local maxima in the spectrogram $ f_r(t) = \arg\max_f S(t, f) $, while handcrafted filters isolate directional structural components (vertical for onsets, horizontal for harmonics, diagonal for sweeps).

Energy Distribution Across Frequency Bands

Bird 1 Energy Bands — Bird 1: Energy Bands

Bird 5 Energy Bands — Bird 5: Energy Frequencies

Handcrafted Filter Responses

Bird 5 Filters — Bird 5: Filter Responses

Observations:

Bird 1 shows concentrated energy within a narrow band (highly tonal).
Bird 5 exhibits a wider spread of energy (complex/noisy call).
Vertical filters highlight chirp onsets and abrupt changes.
Horizontal filters emphasize harmonic structures.
Diagonal filters capture the frequency sweeps unique to chirps.

Conclusion

In this study, we explored bird chirp signals using classical signal processing techniques. Starting from raw waveform analysis, we developed a representation based on time-frequency analysis and extracted a comprehensive set of handcrafted features. The exploratory analysis demonstrates that chirp structure, frequency evolution, modulation, and harmonic features provide strong separability. Classical signal processing features remain highly effective for bioacoustic classification and lay the groundwork for machine learning models.

Reference / Bibliography:
Schuller, B. W. (2013). Intelligent Audio Analysis. Signals and Communication Technology. Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36806-6