# Sampling Frequencies Ratio Estimation and Symbol Timing Recovery for Baseband Binary Pulse Amplitude Modulation

Abstract (Summary)

The original intent of this pro ject was to perform real time digital communications between a personal computer (PC) as the transmitter and a digital signal processor (DSP) as the receiver using the audio band analog channel. Although transmitter and receiver were both designed with baseband binary Pulse Amplitude Modulation (PAM), a low data rate and a sampling rate of 8 kilohertz, it was not possible to achieve communication between the two with traditional synchronization algorithms because of large di?erences in sampling clock frequencies. This thesis explores the theory and results of implementing digital communications between systems with di?erent sampling frequencies. The receiver structure has no a priori knowledge of the transmitter's sampling rate, although it is assumed to be approximately equal to that of the receiver. Therefore, a receiver structure that can correct this clock frequency o?set is developed. Similar sampling frequencies at the transmitter and receiver are assumed in most derivations in the literature. A search of the literature found no cases of a large di?erence in the sampling frequencies. In general, if the receiver knows the transmitter's sampling rate, a resampling ?lter at the receiver converts the signal to one compatible with the transmitters sampling rate. However, here it is assumed that the receiver does not know the transmitter's exact sampling frequency and must be estimated. The mathematical expressions for the signals in the system are derived. The sampling frequency o?set introduces errors in the correct detection of the signal when it is done through traditional synchronization algorithms. Therefore, a receiver structure that corrects the sampling frequency o?set based on the interpolation concept is proposed. This structure will be shown to work when the correct sampling frequency ratio is known. Later, an approach to estimate the sampling frequency ratio is explored. A feedback estimator structure is derived from the Maximum Likelihood optimum criteria. A feed forward estimator that assumes the clock frequency of the transmitter and uses a synchronization sequence is explored as well.
Bibliographical Information:

Advisor:

School:Utah State University

School Location:USA - Utah

Source Type:Master's Thesis

Keywords:baseband binary frequencies

ISBN:

Date of Publication:05/01/2008