# Capturing pulse periods by sampling accurately

Regarding the following statement:

In order to preserve the integrity of the pulse through a system, it is mandatory that the group delay of the system be constant up to the maximum frequency component of the pulse.

What is meant by "maximum frequency of the pulse"?

If I sample a f Hz D% duty cycle pulse train coming from a rotating device for instance where each incoming individual pulse period is randomly distributed around f and if I also want to capture each pulse's length(period) with a good accuracy what should be the sampling rate fs? I will capture each rising edges and find the period for each individual pulse by an ADC/DAQ.

If I can quantify the rising time of the pulses of the pulse train by a scope. How can I proceed to decide the sampling rate to have an accurate period of each pulse? Let's say we have a roughly 30 Hz 50% duty cycle pulse train(with each pulse period might be 10% different) but if we measure the rising edge rise time as 1ms. What determines the sampling rate here?

• Do you know what the Fourier Transform of a square wave looks like? – Kevin Kruse Mar 21 at 13:42
• Yes I know. But I will not use FFT. That will not give me the period of each individual pulse. – cm64 Mar 21 at 13:44
• no, but understanding the frequency content of such a signal should answer your question What is meant by "maximum frequency [component] of the pulse"? – Kevin Kruse Mar 21 at 13:51
• Always use engineering units. Your "good accuracy" may be my "terrible accuracy" and visa-versa. – TimWescott Mar 21 at 14:42
• See also this answer where group delay issues in a digital communication system can have impacts on ISI. electronics.stackexchange.com/questions/135475/… – Peter Smith Mar 21 at 15:02

The maximum frequency of a pulse may be defined by any criteria in time domain pulse width, jitter or spectral density cutoff point like -3dB or -20dB depending on your requirements and the negative effects.

1) f-3dB= 0.35/tr for rise time 10 to 90% where -3dB

2) Below on a Log scale are the time and frequency display of a pulse with a 1/16 ratio and showing that at 16x f repetition rate of approx. 1kHz there is a null.

Imagine if the duty cycle of the pulse changes from 10% to 90% PWM then the null spectrum occurs from 2f for 50% duty ( square waves have a null at 2nd harmonic and all higher even harmonics , then at 10% and 90% the null only occurs at 9x f , 18x f etc so criteria 1) above based on rise time is the effective BW defined by -3dB

The problem in most filters that attenuate sharply is the phase shifts rapidly and causes group delay distortion near the breakpoint, except for Bessel aka Cauer Filters which use the lowest Q for smooth elliptical filtering.

For Data pulses ( e.g. NRZ, RZ, Bi-Phase etc) there is another class of filters called called Raised Cosine filters with resonance that rings exactly at the pulse zero crossings which is important for analog comparators to restore pulse width or data transitions to reduce jitter from Intersymbol interference (ISI) and thus preserve error rate.

If your sampling with an ADC or a DAC, then the max frequency is determined by the nyquist sampling frequency. This states that the sampling frequency must be two times higher than the bandwidth of the signal you want to observe.

If your using a hardware timer on a microprocessor or FPGA the interval of sampling is set by the hardware timer clock, this determines how accurate time is measured by the timer. Hardware timers are a good choice for measuring digital signals or generating/measuring signals with duty cycles or pulses.

• Does that mean if the rising edge is 1ms the sampling period should be at least 0.5ms? – cm64 Mar 21 at 15:10