Digital singnal system processing(help school homework)?

[lolala1020]

A digital filter is described by
Y[n]-1/2y[n-1]=x[n]-1/4x[n-1]
Assume all zero initial conditions
1.
Generate the input signal x[n], which is a sinusold of frequency500 HZ sampled at 6 HZ
2.
compute the first four cycles of the output by directly implementing the above difference equation.Plot the input and output on the same graph
3.
Implement the above filter by using the MATLAB “filter” function .Compare your result with (2).Comment on your result
4.
Plot the impulse response of the filter
5.
The above filter is obviously an IIR filter ;That is,the lengh of its impulse is infinite.If we truncate this impulse response up 32 points, then this impulse response can represent an FIR filter that approximate
The given IIR filter. Let this FIR filter impulse response be represented by h1[n]. Find the output signal of the FIR filter by using Matlab conv function . Compare your result with (2) and (3)
6.
Generate a new input signal x[n] , which is a summation of two sinusolds with frequentcy 500HZ and 1500HZ sampled at 6KHZ Repeat (3)