The main goal of this talk is to get people acquainted with frequency domain analysis of existing data processing methods, such as polynomial fitting also known as a Savitzky-Golay filter. I will give examples on how to implement these signal processing techniques by using the functionality of the Numpy and Scipy packages.
In the field of data processing and analysis we typically have to deal with noisy signals. One possible approach to attenuate the noise is by fitting a polynomial to a subset of samples where the smoothed value is obtained by evaluating the polynomial at the desired time location. In 1964, Abraham Savitzky and Marcel Golay found out that this approach can be interpreted as a convolution between the noisy input signal and a second signal which depends on the settings of the polynomial. Since convolution is a well-known process from the field of signal processing this facilitates frequency domain analysis of such a polynomial smoother. This gives better insights on how to choose free parameters such as the degree of the polynomial and the number of samples used in the fit. The main goal of this talk is to get people acquainted with frequency domain analysis of existing data processing methods, such as polynomial fitting. I will give examples on how to implement these techniques by using the functionality of the Numpy and Scipy packages.