Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and here for more.

Types of Filters

Filtering 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:

Low-pass filters cut off all high frequency parts of a signal, lower frequencies can pass the filter. Low-pass filters are closely related to smoothing procedures, such as moving averages.

High-pass filters cut off the low parts of the spectrum and let the high frequencies pass. High-pass filters are related to the first derivative of a function.

Band-pass filters are formed by a combination of low-pass and high-pass 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 high-pass 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 state-space filter.