Lesson plan
Sinusoidal model
In statistics, signal processing, and time series analysis, a sinusoidal model is used to approximate a sequence y_i to a sine function: : y_i = c + \alpha\sin(\omega t_i + \varphi) + \varepsilon_i where c is constant defining a mean level, \alpha is an amplitude for the sine, \omega is the angular frequency, t_i is a time variable, \varphi is the phase-shift, and \varepsilon_i is the error sequence. This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, routines may require good starting values for the unknown parameters. Fitting a model with a single sinusoid is a special case of spectral density estimation and least-squares spectral analysis.
Article summary
In statistics, signal processing, and time series analysis, a sinusoidal model is used to approximate a sequence y_i to a sine function: : y_i = c + \alpha\sin(\omega t_i + \varphi) + \varepsilon_i where c is constant defining a mean level, \alpha is an amplitude for the sine, \omega is the angular frequency, t_i is a time variable, \varphi is the phase-shift, and \varepsilon_i is the error sequence. This sinusoidal model can be fit using nonlinear least squares; to obtain a good fit, routines may require good starting values for the unknown parameters. Fitting a model with a single sinusoid is a special case of spectral density estimation and least-squares spectral analysis.
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.