A signal flow graph is a representation of the signal processing in a system through a directed , weighted graph . The nodes of this graph are small processing units that process the incoming signals in a certain form and then send the result to all outgoing edges.
The multiplication by a constant is used, inter alia, a differential equation for the processing of the coefficients.
The convolution is a general link.
The integrator only exists in systems that are continuous over time.
The delay element is only available in time-discrete systems.
The same rules apply to signal flow graphs as to signal flow diagrams. The only difference is the graphical representation. The relationships in the time domain were not shown here, as they are too confusing. The relationships are much simpler in the image area. With the basic circuits, complex signal flow graphs can be transformed and thus simplified.
Creation of signal flow graphs
From the differential equation
4th order differential equation
The usual, linear, inhomogeneous differential equation with constant coefficients of the 4th order is given
We carry the 4 state variables
a. The 4th order differential equation can thus be converted into a system of 4 1st order differential equations
with the initial equation
be convicted. So we need a series connection of 4 integrators in the forward path of the signal flow graph. The multiplication with the coefficients takes place in the backward paths leading to the summation node.
From the transfer function
4th order transfer function
The transfer function is given
After multiplying the numerator and denominator by , the transfer function has a form from which the required integrators can be seen immediately.
The numerator contains the factors of the forward path and the denominator those of the reverse path. This allows the signal flow graph to be drawn directly.
From the signal flow plan
Signal flow diagram of a 4th order transfer function
By interchanging nodes and edges, the signal flow diagram is obtained from the signal flow graph and vice versa.
Modifications of signal flow graphs
In the same way as linear systems of equations can be transformed, the associated signal flow graph can also be transformed. Some rules are explained below.
Combine parallel edges
Different edges with the same source and the same sink can be combined into one edge. So the distributive law is applied:
To do this, the vectors of the combined edges must be added in the signal flow graph.
Edges with the same source and target point can be combined.
Combine sequential edges
If three points , and connected only by two edges in such a way so that is valid , then the central node can be removed from the display. So the associative law is applied: