What is the difference between time-domain and frequency-domain features?

Time-domain and frequency-domain features are two approaches to analyzing signals, each offering distinct insights based on how data is represented. Time-domain features are derived directly from the signal as it varies over time, making them intuitive to interpret since they align with raw measurements like sensor readings or audio samples. Examples include statistical metrics such as mean, variance, or peak amplitude, as well as temporal characteristics like signal duration or zero-crossing rate. For instance, in an ECG signal, time-domain analysis might detect the amplitude of heartbeats or the time between peaks. These features are computationally efficient and useful for detecting transient events, such as sudden spikes in sensor data or abrupt changes in system behavior.

Frequency-domain features, on the other hand, are extracted after transforming the signal into a representation of its frequency components, typically using methods like the Fast Fourier Transform (FFT). This reveals how much of the signal exists within specific frequency bands, which is valuable for identifying periodic patterns or oscillations. For example, in vibration analysis of machinery, frequency-domain features like spectral centroid or dominant frequency can pinpoint imbalances or misalignments by highlighting abnormal resonances. Similarly, in audio processing, frequency features like Mel-frequency cepstral coefficients (MFCCs) are used to characterize speech or music. While frequency analysis requires additional computational steps, it uncovers information that may be invisible in the time domain, such as harmonics or noise in specific frequency ranges.

The choice between domains depends on the problem context. Time-domain features are preferable when dealing with transient events, real-time processing, or when computational resources are limited. Frequency-domain features excel in scenarios involving periodic behavior, filtering, or noise separation. In practice, combining both can provide a more comprehensive view. For example, in fault detection for industrial equipment, time-domain metrics might capture sudden torque changes, while frequency analysis identifies worn bearings via high-frequency vibrations. Developers should consider the nature of the signal, the target phenomena, and the application’s computational constraints when selecting features, as both domains offer complementary strengths.