Time-domain Features
Not all useful features come from the frequency domain. Some of the most practical descriptors are computed directly from the raw signal, without any Fourier transform. These time-domain features are computationally cheap, easy to interpret, and often complement the spectral features we have already covered.
Time-domain features are particularly useful in applications where speed is critical — embedded systems, real-time monitoring, or low-power devices. They are also a good first step in analysing a signal before deciding whether more expensive frequency-domain processing is needed.
Zero-Crossing Rate (ZCR)
The zero-crossing rate counts how many times the signal changes sign within a frame. For a discrete signal, this is the number of times the sample values go from positive to negative or from negative to positive.
The intuition is simple: a signal that crosses zero often has high-frequency content. A pure sine wave, for example, crosses zero twice per period — at higher frequencies, it crosses more often per unit time. A noisy signal, on the other hand, tends to have many zero crossings because the values jump around randomly.
In practice, ZCR is widely used in speech processing to distinguish between voiced sounds (like vowels, which have a low ZCR) and unvoiced sounds (like /s/ or /f/, which have a high ZCR). It is also used in music analysis to separate percussive instruments (high ZCR) from sustained ones (low ZCR).
ZCR is extremely cheap to compute — it requires no multiplications, only comparisons. This makes it a popular choice for real-time applications.
RMS Energy
RMS (Root Mean Square) energy is a measure of the signal's overall power within a frame. It is defined as:
This is simply the square root of the average of the squared sample values. It gives a sense of how "loud" the signal is at a given moment. Unlike the peak amplitude, which can be misleading for short transients, RMS energy reflects the effective power of the signal.
RMS energy is used in many applications: detecting silent or noisy segments, adjusting gain in audio systems, measuring the dynamic range of a recording, or even in speech activity detection (VAD) to determine whether someone is speaking.
One common trick is to compute RMS energy on a sliding window and use it as a rough envelope of the signal — this reveals the overall shape of the amplitude over time, which is useful for detecting onsets and offsets.
Short-Time Energy (STE)
The Short-Time Energy is a measure of the total energy of the signal within a short frame. Unlike RMS energy, which represents the average power, STE gives the accumulated energy over the frame. It is defined as:
This is simply the sum of the squared sample values in the frame. The name "Short-Time" refers to the fact that the energy is computed over a short segment, rather than over the entire signal. This makes it sensitive to changes in the signal's amplitude over time.
STE is particularly useful in applications where the absolute energy level matters — for example, detecting the presence or absence of a signal, measuring the intensity of a transient event, or comparing the loudness of different frames. In speech processing, STE is often used to distinguish between voiced and unvoiced segments, as well as to detect silence or background noise.
Unlike RMS, which normalises by the frame length, STE grows with the frame size. This makes it less suitable for comparing frames of different lengths, but more intuitive when the frame size is fixed. In many real-time systems, STE is computed using a sliding window, providing a running measure of the signal's energy.
Because STE only requires squaring and summing, it is computationally efficient. It is often used as a first-pass detector before applying more expensive operations like spectral analysis.
Crest Factor
The crest factor is the ratio of the peak amplitude to the RMS energy of a signal:
This simple ratio tells us how "peaky" the signal is. A pure sine wave has a crest factor of approximately √2 ≈ 1.414, because the peak is 1.414 times the RMS value. A square wave has a crest factor of 1, because the peak and the RMS are equal. An impulsive signal — like a drum hit or a click — has a very high crest factor, because the peak is much larger than the average power.
The crest factor is widely used in vibration analysis and machine diagnostics. A sudden change in the crest factor can indicate a developing fault, such as a bearing defect or an impact in a rotating machine. In audio, it is used to assess the dynamic range of a recording — a high crest factor means a wide dynamic range, while a low crest factor suggests heavy compression.
Because the crest factor is based only on the peak and the RMS, it is extremely fast to compute and does not require any frequency analysis.
Practical Considerations
All three time-domain features share some common characteristics:
- Low computational cost — they require only basic arithmetic and comparisons.
- No windowing or FFT needed — they work directly on the raw samples.
- Frame-based — like spectral features, they are typically computed on short overlapping frames.
- Complementary to spectral features — they capture different aspects of the signal and can be combined for better analysis.
These features are not a replacement for frequency-domain analysis — rather, they are a simple and effective first layer of description. In many practical systems, a few time-domain features are used as a fast filter to decide whether more expensive frequency-domain processing is worth performing.