Signal and Systems Assignment-
Use MATLAB to:
Design an echo filter. The output should be the original signal followed by three echoes with attenuations of 10%, 25 % and 30% respectively and the delays should be 0.5 secs, 1 sec, and 1.5 secs respectively for each echo. Hint: Based on this information the original signal appears at the output with the same amplitude, the first echo has amplitude 0.9 of the original signal (10% attenuation), the second echo has amplitude 0.75 (25% attenuation) and the third echo has amplitude of 0.7 (30% attenuation).
a) Use a sampling frequency of Fs=8192. Load the signal Splat (see class MATLAB demo video)
b) Provide an expression for the unit sample response h[n] in terms of delayed unit samples.
c) Provide an expression of the system function H(z) for your echo filter.
d) Provide the filter difference equation.
e) Provide time domain and frequency domain plots of your signal before and after filtering.
f) Use the sound command to hear the signal before and after the indicated audio effect.
g) Turn in a formal report including, this paper as the first page of your report, introduction, conclusion, MATLAB code, plots and all expressions required in part b, c, d and e.
h) Check the MATLAB demo lecture in Bb for further technical discussion of this topic (echo filters).
If you can include an explanation will be perfect.