To quantify the amplitude of fluctuations in a continuous signal or time series, you can use various techniques from signal analysis. Here are a few common methods:
Peak-to-Peak Amplitude: Measure the difference between the highest peak and the lowest valley in the signal. This method provides a simple and intuitive measure of the signal's amplitude. However, it does not capture the overall fluctuations within the signal.
Root Mean Square (RMS) Amplitude: Compute the square root of the mean of the squared values of the signal. The RMS amplitude provides a measure of the average magnitude of the fluctuations in the signal. It considers both positive and negative fluctuations and is commonly used in the analysis of oscillatory signals.
Standard Deviation: Calculate the standard deviation of the signal values. This measure quantifies the dispersion or spread of the signal around its mean value. It provides an estimate of the typical amplitude of the fluctuations in the signal.
Fourier Transform: Apply the Fourier transform to convert the signal from the time domain to the frequency domain. The magnitude of the Fourier coefficients represents the amplitude of different frequency components in the signal. By analyzing the spectrum, you can identify the amplitudes of specific frequency ranges or dominant frequencies in the signal.
Wavelet Transform: Perform a wavelet transform to analyze the signal in both time and frequency domains simultaneously. The wavelet transform decomposes the signal into different frequency components, each associated with a different scale. By examining the wavelet coefficients, you can determine the amplitude of fluctuations at different scales.
These methods provide different perspectives on quantifying the amplitude of fluctuations in a continuous signal or time series. The choice of technique depends on the characteristics of the signal and the specific information you seek to extract.