Analysis and Simulation of Filters: Low Pass Filter

Description| How it works| Low Pass Filter| Tuning a Radio

Low pass filters are very commonly used in signal processing. We have seen an example of a second order low pass filter on the Description page. We will look at first order low pass filters here. Examples of low pass filters are air recievers for reciprocating compressors and capacitors across signals. Incidentally, the exponential filter in Excel's Analysis Toolpak is a low pass filtering app.

Removing Noise from Signals

Data is often corrupted by high frequency noise and low pass filters are used to remove the high frequency components from such signals.

To see how this works, lets use a first order (or exponential) filter on a signal that contains a low frequency signal corrupted by high frequency sinusoidal noise. Such a signal can be modelled by SIN(x) + 0.5* sin(5*x). The entries for such a filter and its response to the input signal are shown below.

Low pass filter

Low pass filter

The filteration can be made better by using a larger filter time constant (τ), however, there is a tradeoff between the amount of filtering and attenuation of the desired signal. An exponential filter also helps in filtering out random noise from a signal, see the effect below on the input signal modelled by SIN(0.5*x) + 0.5 * (RAND()-0.5)

Noise Filtering