Filter Creator • iPhone App

Welcome to Filter Creator App!

This website is designed to show you what you can do with the iPhone app Filter Creator! Filter Creator helps you to better understand the mathematics of discrete and continuous audio filters and is particularly aimed at students of signal processing classes. However, some previous signal processing knowledge is required for the use of this App since this is a large field and we cannot explain everything on this one website...

How to use Filter Creator

Defining a filter

Filter Creator lets you define a filter and test its effect. You can define your filter in the discrete or the continuous domain. Let's first have a look on how to do this in the discrete mode. Any real filter can be described by the following formula:

For real-valued filter, the poles and zeros aare either real-valued or come in complex conjugate pairs.

In order to define your filter in Filter Creator, all you need to do is set the poles (p_i) and zeros (q_i). You can either drag the poles and zeros to where you want them or tap on the coordinates on top of the display and enter the values directly. Remember that the poles need to be inside of the unit circle for the filter to be stable.

If you are working in the continuous mode, Filter Creator needs to transform the continuous filter into a discrete one before it can use it since the iPhone is a digital device. This transformation is done by mapping the poles and zeros you define in the continuous domain into the discrete domain in the following way.

If a continuous point (pole or zero) is written like this

then it is written like this in the discrete domain:

where f_s is the sampling frequency of the microphone. In Filter Creator, the sampling frequency is fixed 32'000 Hz. Remember that the poles of a continuous filter have to be to the left of the imaginary axis for the filter to be stable.

In order to do the actual filtering, the formula of the the discrete filter is transformed into recursive formulas which are then applied consecutively to the signal.

Zero on real axis
Pole on real axis
Pair of zeros
Pair of poles

Properties of the filter

You can see some properties of your filter in the second view of the App. In the case of a discrete filter, the following two formulas are used to calculate the amplitude response and the phase response (T is the sampling period).

Amplitude response
Phase response

For continuous filters, the amplitude and phase response are calculated as follows.

Amplitude response
Phase response		where and ai and bi are the real respectively imaginary parts of the i pole or zero

Filtering sound

In the third view of Filter Creator you can record up to four minutes of sound and play it back while activating or deactivating the filter. You can also play the recorded sound in the first view while you are modifying the filter. There, you can also apply the filter to a white noise signal or you can play a beep that corresponds to the frequency of the currently selected pair of points.

Settings

In settings you can choose if you want to work in the discrete or the continuous domain. You can also choose how you want to display and define the coordinates of the poles and zeros by selecting one of the three display modes.