Abstract of Analysis

This gave us a deeper insight to the world of trigonometry in music:
Harmonic detection is the basis of harmonic issues and harmonic detection method is the key of harmonic measurement. Based on Fourier Transform and Wavelet Transform, ways and means of detecting and analyzing are developed, but both of them have the problem of spectrum leakage. In this paper, a novel power harmonic algorithm based on the family of trigonometric functions is developed for the characterization of harmonics. The algorithm has designed a set of discrete reference signals and only estimated the amplitudes and the phases which are needed. Besides it hasn't been involved in the influence of the leakage, this algorithm is also easy to carry out and has much high resolution precision than the traditional Fourier algorithm and Wavelet algorithm. The algorithm also has the characteristic of being more sensitive to sampling frequency and less sensitive to sampling points. Using this characteristic, the algorithm can adjust sampling parameters in order to give consideration to both precision and real-time performance. The simulation results have proved that the outstanding advantage of the algorithm is that when chosen a proper sampling frequency the algorithm can pick out harmonics components with high precision in very few fundamental periods. Comparing with Fast Fourier Transform (FFT), Windowed-FFT and Wavelet Package Transform, the algorithm has its certain advantage.