What is the effect of data gaps in obtaining power spectral density using periodogram?? please help

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Chris Martin
Chris Martin 2014-10-24
评论： Chris Martin 2014-11-12
Dear all I have computed power spectral density using periodogram of my time series data. But there is data gaps in the time series, how periodogram takes account of the data gaps...pleas help me

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Image Analyst
Image Analyst 2014-10-24
As you know, multiplication in the time domain is convolution in the spectral domain. Gaps in the data is like having a bunch of rects multiplied by continuous data. And the Fourier Transform of a rect is a sinc function. But you have a bunch of rects if you have a bunch of gaps. Because the Fourier Transform is a linear system F(A+B) = F(A) + F(B). So a bunch of rects is a bunch of sincs summed together in the Fourier (spectral) domain. So it would be like you have a pattern of sincs convolved with your spectrum. Now depending on the spacing and location of these gaps, the spectrum might look not much different, or it may have some ripples on it due to the convolution with the ripply sinc function. Does all that make sense or does it sound like gibberish? If gibberish, here are some tutorials to increase your knowledge and understanding:
http://www.cv.nrao.edu/course/astr534/FourierTransforms.html
http://blogs.mathworks.com/steve/category/fourier-transforms/
http://www.mathworks.com/matlabcentral/fileexchange/28810-fourier-transform-demonstration/content/fourier_demo/html/fourier_demo.html
http://cns-alumni.bu.edu/~slehar/fourier/fourier.html
Also look up MATLAB demos and webinars where they talk about spectral analysis and the pwelch() function (in the Signal Processing Toolbox) - they just held one a couple of weeks ago. http://www.mathworks.com/searchresults/?q=spectral&q1=spectral&q2=&q3=&notq=&c[]=webinars

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