# FFT based symbol synchronization for digital demodulation

Where can I read more about "slow search" methods for symbol synchronization based on FFT for extracting a clock signal from the modulated signal?

I have read here (8.7 Symbol synchronization)

One method of synchronization is to extract a harmonic of the symbol frequency from the received signal. Then a local symbol clock can be synchronized by methods that are very similar to the phase-locked loops used to recover the carrier phase. If necessary, a start-up procedure, such as one that uses a slow search, can be used for initialization. Synchronization is then maintained by locking a feedback loop to a clock signal that is extracted from the modulated waveform.

Then here I found a diagram which seems to be the kind of algorithm I am looking for:

The timing tone can be extracted by ... computing DFT at the symbol frequency (i.e., a single point of the DFT output is needed for each data block)

There must be more literature about this technique? I am not interested in high-performance methods for synchronization, but rather recovering the clock signal by any means without conserving memory or processing time.

I figure the basic technique is to

• Pass the signal through a matched filter
• "Condition" the signal (and make it purely real) by computing the magnitude (as in the diagram)
• Passing the signal through a DFT computation
• Searching the DFT bins for the highest power frequency
• Use the discovered frequency of the DFT bin to generate a local timing signal
• Use the discovered phase of the DFT bin (as in the diagram) to adjust the local timing signal offset

Symbol timing synchronization seems to be a complex topic although once you get some basic principles right, it all makes simple sense. The method you have referred to is known as Digital Filter and Square Timing Recovery$\ ^{[1]}$, also referred to as Oerder and Meyr algorithm.