# describing a block diagram // How do I describe multiplying a signal through multiple branches formally?

Let's say I made this block diagram and I want to explain it: FYI: $x$ is a signal and each $y$ box is a matrix

I want to say that:

The signal $x$ is multiplied by each matrix $y$ in the different branches independently to produce $f_0=xy_0$

$f_1=xy_1$

...

$f_m=xy_m$

I want to ask the experts in the signal processing world if this is formal enough? or am I sounding weird?

Edit 1:

What if I said:

The signal $x$ is multiplied by a set of matrices $y_k$ where $k = 0,1,..., m$

does it sound better? or would it imply that $x$ is multiplied like: $x*y_0*y_1*...*y_k$

which is NOT what I intend to say

• If the $y_m$ are matrices already, why are you splitting them into separate paths? Your first statement seems clear enough. – Peter K. Apr 23 '16 at 12:09
• $x$ is a $1 \times N$ vector and each $y$ is an $N \times N$ matrix @PeterK. – HappyBee Apr 23 '16 at 12:19
• So why not just have $Y$ as a $N\times N(m+1)$ matrix? – Peter K. Apr 23 '16 at 12:22
• @PeterK. my head froze while imagining it this way. – HappyBee Apr 23 '16 at 12:25
• I find anti-freeze works wonders on neurons. 😜 – Peter K. Apr 23 '16 at 12:41

• Add $m$ multiplier blocks, using a circle with a $\times$ inside
• Each multiplier would have inputs $X$ and $Y_k$
• Each multiplier would have output $f_k$
Then I would say something like "The system has input $X$ and outputs $f_k=XY_k$, for $k = 0,\ldots,m$. In the diagram, $\times$ stands for signal-matrix multiplication, which is defined as follows...".