Discrete Convolution Doesn’t Work for Simple Example

aa[y_, a0_, b0_, a1_, b1_, a2_, b2_] :=  Piecewise[{{1 - a0, y == 0}, {a0 - a1, y == 1}, {a1 - a2,     y == 2}, {a2, y == 3}}, 0]
a[y_,a0_,b0_,a1_,b1_,a2_,b2_]:=Piecewise[{{1-a0,y==0},{a0-a1,y==1},{a1-a2,y==2},{a2,y==3},{a3,y==4},{a4,y==5}},0]

DiscreteConvolve[aa[y, a0, b0, a1, b1, a2, b2], aa[y, a0, b0, a1, b1, a2, b2], y, x]

 

DiscreteConvolve[a[y, a0, b0, a1, b1, a2, b2], a[y, a0, b0, a1, b1, a2, b2], y, x]

The first convolution works but not the second.. I don’t understand why..