Harmonic

About: Harmonic is a research topic. Over the lifetime, 44833 publications have been published within this topic receiving 495922 citations. The topic is also known as: overtone & partial.

On frequency estimation

Abstract: SUMMARY t This paper discusses a least-squares procedure and the use of the periodogram for isolating a discrete harmonic of a time series. It is shown that the usual asymptotics on estimation of frequency, amplitude and phase of such a harmonic have to be used with great caution from a moderate sample perspective. Computational issues are discussed and some illustrations are provided. Bolt & Brillinger (1979) make use of these asymptotic results. We consider a time series model of the form X, = a cos {wt + (f>) + e,, where e, is a stationary noise sequence, and one is interested in estimating the amplitude, frequency and phase of the harmonic component. The asymptotic theory of the least-squares estimates of these parameters has a long history. Whittle (1951,1953) obtained some of the earliest results. More recent results are by Hasan (1982), Hannan (1973) and Walker (1971), who formalize and extend Whittle's results. In these works it is shown that the asymptotic variance of the frequency estimate is of order n~3 and that the asymptotic variances of the other two components are of the more usual order n~\ These results extend when there are several harmonic components. The rate for the estimate of w seems almost unbelievably good, and our work was motivated by a desire to see how reliable the asymptotic theory is. In brief, we find that the product of the amplitude and the sample size, n, must be quite large in order for the asymptotic theory to be meaningful. If this product is not large, the frequency estimate is much more variable than indicated by the asymptotic theory and the amplitude estimate is severely biased. In applications in which the amplitude is small, giving rise to a small peak in the periodogram, these results suggest that naive application of the asymptotic theory to gauge resolution can be quite misleading. Section 2 of this paper is devoted to a review and examination of the asymptotic theory. We are also concerned with computational issues arising from the least-squares problem. This problem is nonlinear in the parameters, so that some sort of iterative search must be employed. Typically, search methods start from an initial guess and then proceed by a sequence of modified Newton-Raphson steps. For this nonlinear least-squares problem, it turns out that there are many local minima with a separation in frequency about n~l which makes the stationary point to which the iterative scheme converges extremely sensitive to the starting values, and this problem gets worse as the sample size increases. Furthermore, it follows from the results of § 2 that the estimate of the amplitude is very biased unless the frequency is resolved with order o(n~') so that failure to converge to the global minimum may give a very poor estimate of amplitude. The problem becomes

Multifrequency cross‐correlation phase fluorometer using synchrotron radiation

Abstract: The construction and operation of a cross‐correlation phase and modulation fluorometer using the synchrotron radiation facility at the ADONE–Frascati electron storage ring is described. In the frequency domain the high repetition rate pulsed source gives a large series of equally spaced harmonic frequencies. Use of cross‐correlation techniques in conjunction with such a light source permits one to isolate one harmonic frequency from the adjacent frequencies with high precision. The cross‐correlation frequency required for the analysis of the phase delay and modulation ratio is obtained using two coupled frequency synthesizers, one of which drives the radio‐frequency cavity of the storage ring and the other which modulates the response of the photomultipliers used for the signal detection. The accuracy, reproducibility, and sensitivity of the instrumentation have been determined on a number of systems and are reported.

Digital Filters for Fast Harmonic Sequence Component Separation of Unbalanced and Distorted Three-Phase Signals

Abstract: In this paper, two methods for determining the fundamental frequency and harmonic positive- and negative-sequence components of three-phase signals are investigated. Many aspects of the space-vector discrete Fourier transform and generalized delayed signal cancellation (GDSC) such as response time for different possible implementations, frequency adaptation schemes, stability of recursive implementation, and rounding error effects are discussed. A new design procedure for GDSC transformations is presented. New indices for characterizing three-phase unbalanced and distorted signals are proposed. Simulations and experiments are included in order to verify the performances and illustrate the theoretical conclusions.

A software-defined radio receiver architecture robust to out-of-band interference

Abstract: In a software-defined radio (SDR) receiver it is desirable to minimize RF band-filtering for flexibility, size and cost reasons, but this leads to increased out-of-band interference (OBI). Besides harmonic and intermodulation distortion (HD/IMD), OBI can also lead to blocking and harmonic mixing. A wideband LNA [1, 2] amplifies signal and interference with equal gain. Even a low gain of 6dB can clip 0dBm OBI to a 1.2V supply, blocking the receiver. Hard-switching mixers not only translate the wanted signal to baseband but also the interference around LO harmonics. Harmonic rejection (HR) mixers have been used [3, 1, 4], but are sensitive to phase and gain mismatch. Indeed the HR in [4] shows a large spread, whereas other work only shows results from one chip [3, 1]. This paper describes techniques to relax blocking and HD/IMD, and make HR robust to mismatch.

70GHz CMOS Harmonic Injection-Locked Divider

Abstract: A 70GHz CMOS harmonic injection-locked divider (HILD) is presented, where a third-harmonic mixer is realized by a differential-voltage-driven MOSFET. The chip is fabricated in a 6M 90nm CMOS process. A maximum operating frequency of 71.6GHz with a locking range of 12% at a supply voltage of 0.5V is measured. The chip consumes 2.75mW