=+7. For 0 ≤ r < n/2, define the rectangular and triangular smoothing sequences cj = 1 2r + 1 1{−r≤j≤r}

dj = 1 r

1{−r≤j≤r}



1 − |j|

r

and extend them to have period n. Show that cˆk = 1 n(2r + 1)

sin (2r+1)kπ

n sin kπ

n 13.8 Problems 351

ˆ

dk = 1 nr2

sin rkπ

n sin kπ

n 2

.