# 3.14. Jitter and shimmer#

The speech production system is not a rigid, mechanical machine, but composed of an assortment of soft-tissue components. Therefore, although parts of a speech signal might seem stationary, there are always small fluctuations in it, as vocal fold oscillation is not exactly periodic. Variations in signal frequency and amplitude are called jitter and shimmer, respectively. Jitter and shimmer are acoustic characteristics of voice signals, and they are caused by irregular vocal fold vibration. They are perceived as roughness, breathiness, or hoarseness in a speaker’s voice. All natural speech contains some level of jitter and shimmer, but measuring them is a common way to detect voice pathologies. Personal habits such as smoking or alcohol consumption might increase the level of jitter and shimmer in voice. However, many other factors can have an effect as well, such as loudness of voice, language, or gender. As jitter and shimmer represent individual voice characteristics that humans might use to recognize familiar voices, these measures could even be useful for speaker recognition systems.

There are several different ways to measure jitter and shimmer. For instance, when detecting voice disorders, they are measured as percentages of the average period, where values above certain thresholds are potentially related to pathological voices. Jitter and shimmer are most clearly detected from long, sustained vowels.

A commonly used jitter value is the absolute jitter. This measure expresses the average absolute difference between consecutive periods.

$Jitter(absolute) = \frac{1}{N-1}\sum_{i=1}^{N-1}\|T_i-T_{i+1}\|$

where Ti are the extracted F0 period lengths and N is the number of extracted F0 periods.

When this is divided by the average period, another common measure, relative jitter, is obtained.

$Jitter(relative) = \frac{\frac{1}{N-1}\sum_{i=1}^{N-1}\|T_i-T_{i+1}\|}{\frac{1}{N}\sum_{i=1}^{N}T_i}$

where Ti are the extracted F0 period lengths and N is the number of extracted F0 periods.

A commonly used shimmer value, here Shimmer(dB), expresses the average absolute base-10 logarithm of the difference between the amplitudes of consecutive periods multiplied by 20.

$Shimmer(dB) = \frac{1}{N-1}\sum_{i=1}^{N-1}\|20\log(A_{i+1}/A_i)\|$

where Ai are the extracted peak-to-peak amplitude data and N is the number of extracted fundamental frequency periods.

Relative shimmer expresses the average absolute difference between the amplitudes of consecutive periods divided by the average amplitude.

$Shimmer(relative) = \frac{\frac{1}{N-1}\sum_{i=1}^{N-1}\|A_i-A_{i+1}\|}{\frac{1}{N}\sum_{i=1}^{N}A_i}$

where Ai are the extracted peak-to-peak amplitude data and N is the number of extracted fundamental frequency periods.