1. create the echo signal load the 'matlab' speech signal with the command > > load mtlb then type who to see your variables. you can listen to the signal mtlb with the command soundsc(mtlb, fs), provided your computer has a sound card. you should hear the phrase 'matlab'. for convenience, lets redefine this to be x by typing x = mtlb; . make a plot of the signal x versus time (in seconds). you will need the sampling frequency fs which is loaded when you typed load mtlb. you should find that the speech signal is about 0.55 seconds in duration.

2. how do you find the exact duration of this signal in seconds?
3. we can create an echo by filtering this signal with the following difference equation: y(n) = x(n) +a x(n - n) where x(n) is the echo-free speech signal, which has been delayed by n samples and added back in with its amplitude scaled by a. this is a reasonable model for an echo resulting from the signal reflecting off an absorbing surface like a wall. the delay parameter to in seconds is n/f, where f, is the sampling frequency. (can you explain why? ) what is the impulse response of this system?

4. lets add an echo to the signal with a delay of to = 0.12 seconds and an amplitude of a=0.8. what is the delay n in samples? based on the difference equation, create an echo version of the signal x using the command y = conv(h, x); . what is h? listen to the output of the difference equation. do you hear the echo?