Spectral Analysis and Key Features of Sound Signals

Understanding Spectral Features

Every sound wave contains a combination of different frequencies. Mathematically, any periodic signal can be decomposed into a sum of constant frequency waves, each contributing a specific weight to the overall signal. This weight distribution forms the spectrum of the sound, providing a "signature" that describes the composition of the signal.

For instance, if a sound is close to a pure frequency wave, that frequency will have a strong presence in the spectrum, while others remain low. In contrast, complex sounds consist of multiple high-value frequency components, sometimes spanning continuous regions in the spectrum.

Applying the Fourier Transform

To compute the spectrum , we apply the Fourier Transform, which converts our digital time-domain signal into a frequency-domain representation without information loss. Data reduction then occurs by selecting relevant frequencies or grouping the spectrum into bands.

To group the spectrum, we divide the full range of frequencies into smaller segments called bins or bands. Each bin groups together the sound energy within a specific frequency range. While these bins can be evenly spaced, it’s sometimes  more useful to adapt them to how humans perceive sound. For example, the mel scale adjusts bin sizes so that frequencies we hear more easily are represented with finer detail, while those we perceive less distinctly are grouped into larger bins.

Apart from grouping the spectrum, we can also extract features that describe certain aspects of the weight distribution. Some common spectral features include:

• Spectral Mean and Standard Deviation (and higher statistical moments) – Provide insight into the overall shape of the spectrum.

• Spectral Flatness – Measures whether the spectrum is flat or spiky.

• Spectral Rolloff – Identifies the frequency below which a specified percentage of total power is concentrated.

• Harmonic Distortions – Quantifies the relative power of harmonics.

Spectrogram, male voice with background noise

By leveraging spectral analysis, we can extract highly informative sound descriptors useful for condition monitoring and anomaly detection.

The Role of Spectrograms

When applying the Fourier transform to a sound that changes over time, the resulting spectrum captures all the frequencies present in the signal but does not indicate when they occur. To address this limitation, one can use spectrograms.

Spectrograms are visual representations of sound, mapping intensity across frequency bands over time. By computing short-time Fourier transforms in small overlapping windows, we create spectrograms that balance temporal and spectral detail. Typical spectrogram resolutions include 64, 128, or even 256 frequency bands, with time steps as small as 10 milliseconds.

Spectrograms provide a valuable compromise between keeping temporal and spectral information while reducing data complexity. They are particularly useful for detecting non-constant patterns in sound or pinpointing the precise start and end of sound events. Many of our analysis models are based on spectrogram representations.