To form the frequency spectrum from time series wave data, various methods can be used. Here are some commonly employed techniques:
Fourier Transform: The Fourier Transform is a widely used method for analyzing the frequency content of a time series. It converts a time-domain signal into its frequency-domain representation. The Fast Fourier Transform (FFT) algorithm is commonly employed for efficient computation. The resulting spectrum provides information about the amplitudes and phases of different frequency components present in the signal.
Short-Time Fourier Transform (STFT): The STFT is an extension of the Fourier Transform that allows the frequency content of a signal to be analyzed over shorter time intervals. It involves dividing the signal into segments and computing the Fourier Transform for each segment. This approach provides information about how the frequency content changes over time and is particularly useful for non-stationary signals.
Wavelet Transform: The Wavelet Transform is a versatile technique that analyzes signals in both the time and frequency domains simultaneously. It decomposes a signal into a set of wavelet functions at different scales. This approach is effective for capturing localized frequency information and can provide insights into both high and low-frequency components of a signal.
Spectrogram: A spectrogram is a visual representation of the frequency spectrum of a signal as it varies over time. It is obtained using techniques like Short-Time Fourier Transform (STFT) or Wavelet Transform. A spectrogram displays how the frequency content changes with time and can reveal patterns, trends, and time-varying characteristics of a signal.
Power Spectral Density (PSD) Estimation: The PSD provides information about the distribution of signal power across different frequencies. It can be estimated using methods such as the periodogram, Welch's method, or autoregressive (AR) modeling. PSD estimation allows quantifying the relative strength or contribution of different frequency components in a signal.
These are just a few common methods used to form the frequency spectrum from time series wave data. The choice of method depends on the specific characteristics of the signal, the desired level of time-frequency resolution, and the particular analysis objectives.