Signal Lead and Lag Explanation

What Does "Signal Leads" or "Signal Lags" Mean?

It describes the relative time shift between two signals. Think of two identical waveforms placed on a time axis.

Figure 1: Illustration of Signal Lag (The second signal is delayed relative to the first signal). Conversely, the first signal leads the second signal.

Signal A Leads Signal B

Signal A happens earlier in time. It is shifted to the left.

Time →
A:  ****
B:      ****
                

• A leads B
• B lags A

Signal A Lags Signal B

Signal A happens later in time. It is shifted to the right.

Time →
B:  ****
A:      ****
                

• A lags B
• B leads A

Mathematical Representation

If you have a signal:

x(t)
                

Delay (lag) by τ:

x(t − τ)
                

Advance (lead) by τ:

x(t + τ)
                

In Correlation

If the correlation peak occurs at index k > 0, then the received signal lags the reference by k samples.

If the peak occurs at k = 0, the signals are perfectly aligned.

Summary

• Lead → arrives first → left shift
• Lag → arrives later → right shift