User`s guide

Convolution
5-100
5Convolution
Purpose Compute the convolution of two inputs.
Library Signal Operations
Description The Convolution block convolves corresponding columns (channels) of M
u
-by-N
input matrix u and M
v
-by-N input matrix v.
Frame-Based Inputs
Matrix inputs must be frame-based. The output, y, is a frame-based
(M
u
+M
v
-1)-by-N matrix whose jth column has elements
where
∗ denotes the complex conjugate. Inputs u and v are zero when indexed
outside of their valid ranges. When both inputs are real, the output is real;
when one or both inputs are complex, the output is complex.
When one input is a column vector (single channel) and the other is a matrix
(multiple channels), the single-channel input is independently convolved with
each channel of the multichannel input. For example, if u is a M
u
-by-1 column
vector and v is an M
v
-by-N matrix, the output is an (M
u
+M
v
-1)-by-N matrix
whose jth column has elements
Sample-Based Inputs
If u and v are sample-based vectors with lengths M
u
and M
v
, the Convolution
block performs the vector convolution
y
ij,
u
kj,
v
ik– 1+()j,
*
1 iM
u
M
v
1–+()≤≤
k 1=
max M
u
M
v
,()
∑
=
y
ij,
u
k
v
ik– 1+()j,
*
1 iM
u
M
v
1–+()≤≤
k 1=
max M
u
M
v
,()
∑
=
y
i
u
k
v
ik– 1+()
*
1 iM
u
M
v
1–+()≤≤
k 1=
max M
u
M
v
,()
∑
=