I: Non-linear systems
In this module you will explore the limits of linear systems, and start to explore non-linear systems models.
Required readings
- Lee and Varaiya, Section 6.1, Mixed models
- Lee and Varaiya, Section 6.2, Modal models
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- Sketch a system that generates a sine wave, but switches between a frequency of 1kHz and 1111 Hz at intervals of 100 ms. Characterize the output signal in the frequency domain.
- Suppose the Plucked String Instrument program (from the labs) was modified to play a different note whenever a key is pressed. (Or, alternately, to play a pre-programmed sequence of notes.) What problem do you foresee for audio output quality, and how would you address it?
- A simple method of "noise reduction" for magnetic audio tapes is to use the following perceptual trick. When the music is playing, you don't notice the tape hiss as much as when there is no music. So, reduce the system gain when the signal levels falls below a certain threshold. Sketch an outline of such as system, and analyze possible issues with it. (Note: this same system is still used in sound reinforcement and recording, to reduce extraneous noise and feedback from microphones.)
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