Simple, effective estimation of frequency based on Prony's method

Frequency Estimation of Single-Tone Sinusoids Under Additive and Phase Noise

“…It is shown in [21] that the frequency ambiguity could be resolved using two correlations with relatively prime correlation lags; this is further explained in [22], [23]. www.ijacsa.thesai.org…”

Low-complexity frequency synchronization for GSM systems: Algorithms and implementation

“…By re-using the results of the LRP detection, Q can be reduced to Q = N EST − L 2 , which results in about half the computational complexity compared to standard T&F with conventional parameters [5]. For comparison, the periodogram estimator which takes the peak of the spectra requires as many as 6N log 2 N real-valued multiplications for the radix-2 FFT [9].…”

“…The T&F estimator [5] resolves this ambiguity without being computationally intensive by computing two correlations r L1 and r L2 with different correlation lags L 1 and L 2 . If L 1 and L 2 are relatively prime, unambiguous FOE up to f max o = 67.7 kHz.…”

“…Choosing L 2 = L 1 + 1 has been proposed in [5] as a common setting. Our analyses have shown that ambiguity resolution benefits from a small correlation lag, whereas high frequency accuracy can only be achieved with a larger lag.…”

“…The corresponding FOE is presented in Section IV where we analyze algorithms that can be combined with FBD to minimize implementation complexity. We propose a frequency estimator based on Prony's method [5] that re-uses results of the FB detector to achieve high FOE accuracy at low computational cost.…”