Book contents
- Time Series Data Analysis in Oceanography
- Time Series Data Analysis in Oceanography
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to MATLAB
- 3 Time and MATLAB Functions for Time
- 4 Deterministic and Random Functions
- 5 Error and Variability Propagation
- 6 Taylor Series Expansion and Application in Error Estimate
- 7 Spherical Trigonometry and Distance Computation
- 8 A System of Linear Equations and Least Squares Method
- 9 Base Functions and Linear Independence
- 10 Generic Least Squares Method and Orthogonal Functions
- 11 Harmonic Analysis of Tide
- 12 Fourier Series
- 13 Fourier Transform
- 14 Discrete Fourier Transform and Fast Fourier Transform
- 15 Properties of Fourier Transform
- 16 More Discussion on the Harmonic Analysis and Fourier Analysis
- 17 Effect of Finite Sampling
- 18 Power Spectrum, Cospectrum, and Coherence
- 19 Window Functions for Reducing Side Lobes
- 20 Convolution, Filtering with the Window Method
- 21 Digital Filters
- 22 Rotary Spectrum Analysis
- 23 Short-Time Fourier Transform and Introduction to Wavelet Analysis
- 24 Empirical Orthogonal Function Analysis
- References
- Index
20 - Convolution, Filtering with the Window Method
Published online by Cambridge University Press: 21 April 2022
- Time Series Data Analysis in Oceanography
- Time Series Data Analysis in Oceanography
- Copyright page
- Contents
- Preface
- Acknowledgments
- 1 Introduction
- 2 Introduction to MATLAB
- 3 Time and MATLAB Functions for Time
- 4 Deterministic and Random Functions
- 5 Error and Variability Propagation
- 6 Taylor Series Expansion and Application in Error Estimate
- 7 Spherical Trigonometry and Distance Computation
- 8 A System of Linear Equations and Least Squares Method
- 9 Base Functions and Linear Independence
- 10 Generic Least Squares Method and Orthogonal Functions
- 11 Harmonic Analysis of Tide
- 12 Fourier Series
- 13 Fourier Transform
- 14 Discrete Fourier Transform and Fast Fourier Transform
- 15 Properties of Fourier Transform
- 16 More Discussion on the Harmonic Analysis and Fourier Analysis
- 17 Effect of Finite Sampling
- 18 Power Spectrum, Cospectrum, and Coherence
- 19 Window Functions for Reducing Side Lobes
- 20 Convolution, Filtering with the Window Method
- 21 Digital Filters
- 22 Rotary Spectrum Analysis
- 23 Short-Time Fourier Transform and Introduction to Wavelet Analysis
- 24 Empirical Orthogonal Function Analysis
- References
- Index
Summary
The objective of this chapter is to demonstrate the linkage between convolution and filtering and to discuss preliminary filtering with examples. The simplest low-pass filtering that allows low frequency to pass to the output is a “moving average,” which is essentially through a computation involving a rectangular window function (in this case, it is a filter), with a length determined by the cutoff frequency. The filtering action is accomplished by a convolution between the filter and the time series. However, moving average has its drawbacks because of the rectangular window effect or the side lobe effect. It is considered as a “poor man’s filter” because of the lack of sophistication in getting rid of the leakage from side lobes. One improvement over the moving average is using a non-rectangular window function in the convolution to reduce the sharp change at the edges. The basic ideas and examples presented here are useful in demonstrating how to do filtering with several MATLAB functions. When a low-pass filter is designed, a high-pass filter can be defined. With two or more low-pass filters, one can also design band-pass and band-stop filters. There are also other filters that can have various controls on the results.
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- Time Series Data Analysis in OceanographyApplications using MATLAB, pp. 357 - 373Publisher: Cambridge University PressPrint publication year: 2022