Software for Teaching and Learning

Filtering an Audio Signal

This demonstration package addresses fundamental concepts in signal and systems, including poles and zeros, frequency response, impulse response, and difference equations. Relationships between time and frequency domain signals are fundamental to all aspects of this demonstration.

This demo runs a digital notch filter in real-time, processing signals from a microphone input. A slide whistle is quite useful for generating inputs, as it can be easily adjusted towards the notched center frequency.The tabbed windows in the lower left of the display are updated in response to changes in the slider positions. A variety of "What If..." may be posed to students, asking them to predict one filter representation, given another.

The design of this digital filter is straight forward, accomplished via the method of 'pole/zero placement'. Zeros are placed on the unit circle to eliminate a given center frequency, and poles are located at the same orientation - with a given radius. The center frequency and pole radius are specified using sliders.

Download Audio Notch Filter Demonstration

 

Learning Objectives

The following learning objectives are associated with the above demonstration, with supporting lecture and possible programming assignment.

Area / Learning Objective
Filtering
Find magnitude of output spectrum, given input spectrum and given frequency response
Find output amplitude in time domain, given input and given frequency response
Predict output spectrum changes, given real-time input with time-varying/mixed content
 
Frequency Response
Estimate Q of filter given poles and zeros
Predict changes to magnitude of frequency response, given movement of poles/zeros
 
Poles and Zeros
Predict movement of poles and zeros, given changes to center frequency.
Determine stability given pole and zero locations
 
Impulse Response
Estimate duration of impulse response, given poles (envelope).
Find frequency of oscillation of response, given poles
 
Difference Equation
Find difference equation coefficients, given poles and zeros
Predict changes to difference equation, given changes in pole/zero locations
 
Time and Frequency Domain Relationships
Predict spectrum in frequency domain, given time domain signal
Predict time domain signal, given spectrum
Predict changes in spectrum associated with real-time signal (such as a slide whistle)