Measuring Timing Relationships

What kinds of circuits would you want to measure the Timing Relationships?

Is measuring a circuits input to output a timing relationship? to verify if the input and output are in sync?

What kinds of circuits would you want to measure the Timing Relationships?
e.g. SONAR, RADAR, ultrasonic anemometer etc. These are some applications where the output and input time difference is measured i.e. after input is given to system how long does it take for system to produce output. In embedded application like aerospace applications, biomedical etc., the response time of command input is extremely important. So, in a way, circuits in these application do take care of timing relationship.

Is measuring a circuits input to output a timing relationship? to verify if the input and output are in sync?
I did not fully understand the question i guess, but here is based on what I understood. It depends on application, whether timing is important factor. For e.g. in amplifiers and filters, usually output is measured with respect to input in terms of phase angle i.e. output in phase to input and output out of phase by 90 degree etc. But, how much time it takes to produce output is little less important. But, filters do have time constants which determines, phase relation of output to input and also time it takes to change the output from 10% to 90% of full output.

Hope that helps.

In video circuits there is a parametre called "group delay". This is to ensure that all components of the video waveform (25 HZ to 5 MHZ) pass through a circuit with the minimum distortion. At the higher frequency end it becomes harder too do as the effects of spurious capacitance become evident.
In digital circuits some times data would be saved when a clock pulse goes positive.If the data is too slow at arriving, the clock pulse edge happens but no data is saved because it has not arrived yet, so timing is crucial.
Frank