HP MLIB User's Guide Vol. 2 7th Ed.

Chapter 6 Correlation and Convolution Subprograms 599
Tapered correlation and convolution STCONV/DTCONV
Name STCONV/DTCONV
Tapered correlation and convolution
Purpose These subprograms compute the discrete tapered correlation or discrete
tapered convolution of two real data sequences.
If x
i
and w
i
, i = 1, 2, ..., n are two data sequences, their discrete correlation y
k
is defined by
for k = −n+2, −n+3, ..., n, where the sum is taken over all indices i for which
both x
k+i−1
and w
i
are defined.
Again, if x
i
and w
i
, i = 1, 2, ..., n are two data sequences, their discrete
convolution z
k
is defined by
for k = 1, 2, ..., 2n−1, where the sum is taken over all indices i for which both
x
k−i+1
and w
i
are defined.
These subprograms compute only m elements on one side of the correlation or
convolution, specifically the part where . Hence, they compute
for . If for . This is the tapered
correlation operation if w is stored or indexed in the same direction as x, and is
the tapered convolution operation if x and w are stored or indexed in opposite
directions.
Usage VECLIB:
INTEGER*4 incx, incw, incy, m, n
REAL*4 x(lenx), w(lenw), y(leny)
CALL STCONV(x, incx, w, incw, y, incy, m, n)
INTEGER*4 incx, incw, incy, m, n
REAL*8 x(lenx), w(lenw), y(leny)
CALL DTCONV(x, incx, w, incw, y, incy, m, n)
y
k
x
ki1–+
w
i
,
i
∑
=
z
k
i
∑
x
k−i+1
w
i
,=
lkm≤≤
y
˜
k
x
ki1–+
i 1=
nk–1+
∑
w
i
,=
k 12… m,, ,= mn> y
˜
k
0=, kn1+ n 2+ … m,,,=