## 1 Introduction  
Timing recovery estimates and corrects the sampling phase in a receiver. As transmitters and receivers usually operate using different clock sources, sampling points at the receiver will not be aligned to the incoming data symbols. This corresponds to small sampling frequency offsets and drifting sampling phase relations. A timing recovery then estimates the sampling phase and resamples the signal to align the symbols and samples. The synchronization of the receiver clock can be achieved in the analog or the digital domain. * Most analog receivers rely on a phase locked loop (PLL). Here, the received signal is multiplied with a reference clock and the low pass filtered product is used to drive a voltage-controlled oscillator (VCO). This way, the reference clock, which is the output of the VCO, is converging to the transmitter clock. This synchronized clock is used to process the signal. The concept of the PLL can be extended to a Costas loop, which has increased sensitivity and therefore reduced jitter in the estimate. * Next generation receivers mainly operate in the digital domain. A number of digital processing techniques have been developed. These techniques can be classified into three categories: pure time domain, combined time and frequency domain, and pure frequency domain. Pure time domain techniques typically observe the shape of the received waveform. These techniques process the time domain signal and shift the sampling time towards the maximum eye opening. The most common candidate of this group is the Gardner method [1]. Here, two samples per symbol are acquired, and the samples are shifted in such a way that the zero crossings occur right in between the samples that correspond to the symbols. Another common technique is the early-late gate synchronization (also called the Alexander phase detector) [2]. Three samples are acquired and compared. The correct sampling phase is reached when the early and the late samples have a similar amplitude and the optimum sample in between is located at the maximum of the pulse. In addition, techniques that use symbol decisions in a decision directed approach are proposed in the literature. One example of such a structure is the Mueller and Muller algorithm [3]. Combined time and frequency domain techniques process a time signal and calculate a frequency domain coefficient corresponding to the clock tone of the signal. This clock tone then contains the sampling phase information. Two commonly known examples are the Order and Meyer technique [4] and the Lee technique [5]. Both are flexible with respect to oversampling (the Order and Meyer technique requires more than two samples per symbol), but are rather computationally heavy. In the pure frequency domain technique, the domain coefficients of the signal can be used to calculate the clock tone directly with the [PERSON] [6] algorithm. Here, a twofold oversampled signal is processed in the frequency domain. These techniques are designed to operate with a single carrier modulation format, such as pulse amplitude modulation (PAM) or quadrature amplitude modulation (QAM) with different pulse shapes. It is interesting to note that most of the techniques mentioned above are approximately equivalent, and can be converted into each other [7]. Therefore, the main question is which implementation is most versatile for a variety of signals, symbol rates, and oversampling factors, while still allowing for a low complexity implementation. The ideal timing recovery technique would fulfill two conditions. First, it should operate with less than two samples per symbol to reduce the total amount of samples that have to be processed. Second, it should operate in the frequency domain to benefit from the already existing Fourier transform blocks for chromatic dispersion compensation and filtering. However, none of the shown state-of-the-art techniques meets both conditions. In this paper, we present our real-time capable modified Godard timing recovery [8].