# Filters

Written by Travis M. Moore
Last edited 2-Oct-2019

### Frequency Response

If a transfer function attenuates (makes softer) certain frequencies, we can say that the function is filtering out those frequencies. In fact, a system with a transfer function that passes some frequencies and attenuates others is called a filter. Just like any other system, we can characterize a filter by measuring the output for a range of inputs. A common way to refer to the transfer function of a filter is as its frequency response.

Specifically, we can measure the output amplitude (y axis) for a number of input frequencies (x axis). As long as we keep the input level of each frequency we put through the system constant, the shape of the transfer function will reveal what the system does. Figure 1 shows the brute force method of measuring the transfer function: input one frequency at a time, and record the output.

You can image how tedious this can get if you're measuring a filter's frequency response in real life. Luckily, there is a shortcut. As long as the filter is linear, we can simply put all the frequencies through the filter at once. What type of signal contains a wide range of frequencies that all have the same amplitude? White noise.

Let's look at a Fourier Transform to confirm the spectrum of white noise is flat (the same amplitude across all frequencies).