Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Bivariate Data Time Series Filtering Signals  
See also: time and frequency, filtering in the frequency domain  
Types of FiltersFiltering in its most general sense means removing parts of the spectrum of a signal. Depending on the part which is removed from the signal, there are several basic types of filters: Lowpass filters cut off all high frequency parts of a signal, lower frequencies can pass the filter. Lowpass filters are closely related to smoothing procedures, such as moving averages. Highpass filters cut off the low parts of the spectrum and let the high frequencies pass. Highpass filters are related to the first derivative of a function. Bandpass filters are formed by a combination of lowpass and highpass filters so that only frequencies within a certain range (band) can pass the filter. Notch filters remove a certain band from the frequency spectrum and are also formed by a combination of low and highpass filters. Please note that the characteristic frequency responses shown above are only theoretical curves  in reality the filter response functions do not show infinite steepness at the cutoff frequencies, nor do they exhibit a smooth transfer characteristic. Filter can be implemented both in analog and digital electronics. A few important digital filters are: The first two filter types are commonly known as statespace filter. 

Home Bivariate Data Time Series Filtering Signals 