In signal processing, the zero-crossing rate is the rate at which a signal changes sign, i.e. crosses the horizontal axis or zero level. The zero-crossing rate can be calculated by counting the number of times a signal crosses zero within a given time interval and dividing it by the length of that interval. $ \text{ZCR} = \frac{1}{N} \sum_{n=0}^{N-1} | \text{sign}(x(n)) - \text{sign}(x(n-1))| $ The zero-crossing rate is a very simple way of measuring the smoothness of a signal. For example, a sinusoidal signal of 100 Hz will cross zero 100 times per second, while an unvoiced fricative can have 3000 zero crossings per second. A [[short-time processing]] of the zero-crossing rate of a signal provides the change of this feature over time. ![[Zero-crossing_rate_1_0.png]] [[Backstrom 2022]]: zero-crossing rate counts crossings with both positive and negative derivatives. ![[Zero-crossing_rate_4_0-2.png]] [[Backstrom 2022]]: zero-crossing rate is almost the opposite of the graph of the evolution in time of the lag-1 autocorrelation ($R_{x x}(1)$).