1. Consider the audio system in a car. Some people like to hear a lot of bass. Give an equation, in your preference of time or frequency domain, for a bass boost.
2. Write a MATLAB or Octave program that, given a sequence, f[k], of samples in the time domain, calculates a filtered output y[k], given by the formula y[k]=-a_2[k-1]-a_1y[k-2]-a_0y[k-3]+b_3f[k]+b_2f[k-1]+b_1f[k-2]+b_0f[k-3]. The values y are outputs, k is an index into a sequence, (so if "now"=k, one sample in the past is k-1), there are coefficient vectors a and b, which can be input parameters to the function. Make up a sequence f. Plot the input f and that output, y.
3. Run your program with all of the a coefficients set to 0. Plot the input and output.