# Help on understanding Gardner's original paper for QPSK symbol timing recovery?

I am fairly new to DSP and RF receivers in general, and I was recommended to read Gardner's original paper for symbol timing error recovery for QPSK signals.

I have a question regarding an equation for early-late gates; in the following picture, why is L(r-1) equal to x^2((r-5/4)*T)? It seems to me that it should be x^2((r-3/4)*T). Am I missing something?

Also, intuitively, if the spacing for the Early and Late is 1/4 each, then the spacing between Early and Late should be 2 * 1/4 T = 1/2 T, not 1 * T.

• You are right. It should have been 3/4. Otherwise I am missing to understand something obvious. May be a typo. – jithin Apr 11 at 7:44
• I agree looks like a typo. I have more info on how the Gardner TED works at this post that may further help you in your study: dsp.stackexchange.com/questions/62453/… – Dan Boschen Apr 11 at 13:37