数字信号处理卷积问题R4(n)卷积(n+1)R5(n)

Question

数字信号处理卷积问题
R4(n)卷积(n+1)R5(n)

Answer 1

R4(n)={1,1,1,1},0≤n≤3,(n+1)R5(n)={1,2,3,4,5},0≤n≤4
y(n)=sum(R4(k)*(n-k+1)*R5(n-k)),0≤k≤3,n≥k,n-k≤4
y(0)=R4(0)*(0-0+1)*R5(0-0)=1*1=1
y(1)=R4(0)*(1-0+1)*R5(1-0)+R4(1)*(1-1+1)*R5(1-1)=1*2+1*1=3
y(2)=R4(0)*(2-0+1)*R5(2-0)+R4(1)*(2-1+1)*R5(2-1)+R4(2)*(2-2+1)*R5(2-2)=1*3+1*2+1*1=6
y(3)=R4(0)*(3-0+1)*R5(3-0)+R4(1)*(3-1+1)*R5(3-1)+R4(2)*(3-2+1)*R5(3-2)+R4(3)*(3-3+1)*R5(3-3)=1*4+1*3+1*2+1*1=10
y(4)=R4(0)*(4-0+1)*R5(4-0)+R4(1)*(4-1+1)*R5(4-1)+R4(2)*(4-2+1)*R5(4-2)+R4(3)*(4-3+1)*R5(4-3)=1*5+1*4+1*3+1*3=14
y(5)= R4(1)*(5-1+1)*R5(5-1)+R4(2)*(5-2+1)*R5(5-2)+R4(3)*(5-3+1)*R5(5-3)= 1*5+1*4+1*3=12
y(6)= R4(2)*(6-2+1)*R5(6-2)+R4(3)*(6-3+1)*R5(6-3)= 1*5+1*4=9
y(7)= R4(3)*(7-3+1)*R5(7-3)= 1*5=5