Calculation method of instantaneous frequency of am-fm signal based on differential

Abstract

Based on differential AM-FM signal instantaneous frequency calculation method, the steps are: (1) input AM-FM signal x(t)=a(t)cos[θ(t)], and carry out denoising and discrete sampling processing; ( 2) Obtain the local maximum, minimum and occurrence time of the signal x(t)=a(t)cos[θ(t)], denoted as (t _j , a(t _j )); (3) According to the obtained a(t _j ) value, using spline interpolation function to fit a(t _j ) to obtain the envelope function a(t) of the input signal; (4) obtain the first order derivative x'(t) of the input signal x(t)=a(t)cos[θ(t)]; (5) Calculate the local maximum and minimum values ​​of x′(t) and the occurrence time, denoted as (t _i , x′(t _i )); (6) Calculate t according to the formula _i The instantaneous frequency of the input signal f(t _i ); (7) carry out phase-shift processing to x(t)=a(t)cos[θ(t)], obtain x respectively ₁ (t),x ₂ (t),...x _n-1 (t), where n≥1; (8) for the obtained x ₁ (t),x ₂ (t),...x _n-1 (t), repeat steps (2) ~ (6), get (t _i , f(t _i )) point sequence; (9) according to the obtained (t _i , f(t _i )) point sequence, using spline interpolation function to fit f(t _i ), get the instantaneous frequency function f(t) of x(t)=a(t)cos[θ(t)].

Description

technical field [0001] The invention relates to a method for calculating instantaneous frequency, in particular to a method for calculating instantaneous frequency of AM-FM signal based on differentiation. Background technique [0002] Non-stationary signals are signals whose statistics (correlation function, power spectrum, etc.) change with time. In the early days, there were almost no formal analysis methods for non-stationary signals. The earliest and most mature signal analysis method is Fourier transform. In the Fourier transform theory, the basic quantity that characterizes signal alternation is the frequency that has nothing to do with time, and the basic time-domain signal is a stationary simple harmonic signal. Stationary signals are prone to contradictory phenomena such as false signals and aliasing frequencies, and lack physical meaning when used to analyze non-stationary signals. Therefore, the time-frequency analysis method is an effective means to analyze non...

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Problems solved by technology

The main disadvantage of this method is that the construction and analysis signal has a large amount of calculation, and the error of the instantaneous frequency result is large.

This method also calculates the instantaneous frequency of the IMF structural analysis signal, but the disadvantage is that the calculation of the structural analysis signal is large, and the error of the instantaneous frequency result is large.

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