The main objective in lab this week is to practice computing the convolution sum for discrete-time systems and the convolution integral for continuous-time systems. We will also learn about the impulse function and impulse response of continuous-time systems. Please work in groups of two or three students.
Important point: Linear, time-invariant (LTI) systems are very nice. The impulse response h(t) of the system can be measured fairly easily. Then, the system response to any other input signal x(t) is obtained by convolving the input signal with h(t), i.e. the output is y(t) = x(t) * h(t) . This is why convolution is important!
These signals and filters are commonly used in digital communication systems that transmit bits (0s and 1s) from one place to another.
The MATLAB script mus.m passes digitized music through discrete-time systems with various impulse responses and then plays the resulting music. Simulations of this type are used to understand how an audio speaker or a listening room with a certain impulse response will affect the music that is heard in the room. The impulse response can be measured easily in practice in order to obtain a model for a listening room.
Run the Matlab script mus.m on a Sun computer. The original music will be played, followed by the music convolved with g(t) = (2 pi 300) exp(-2 pi 300 t), and then the music convolved with a different function h(t). The impulse responses g(t) and h(t) will be plotted on your screen. The program takes a while to run, so be patient!
You can listen to the results here, without running the MATLAB program:
Please write brief answers to the following questions. You don't have to submit any plots.
All reports are due on Friday, October 9 at 9 AM.
Thank you, and have fun!