Response of singlerate, fixedpoint IIR filter
report = limitcycle(hd)
report = limitcycle(hd,ntrials,inputlengthfactor,stopcriterion)
report = limitcycle(hd)
returns
the structure report
that contains information
about how filter hd
responds to a zerovalued input
vector. By default, the input vector has length equal to twice the
impulse response length of the filter.
limitcycle
returns a structure whose elements
contain the details about the limit cycle testing. As shown in this
table, the report includes the following details.
Output Object Property  Description 

 Contains one of the following results:

 Contains the initial condition value(s) that caused the detected limit cycle to occur. 
 Contains the output of the filter in the steady state. 
 Returns the number of the Monte Carlo trial on which
the limit cycle testing stopped. For example, 
Using an input vector longer than the filter impulse response
ensures that the filter is in steadystate operation during the limit
cycle testing. limitcycle
ignores output that occurs
before the filter reaches the steady state. For example, if the filter
impulse length is 500 samples, limitcycle
ignores
the filter output from the first 500 input samples.
To perform limit cycle testing on your IIR filter, you must
set the filter Arithmetic
property to fixed
and hd
must
be a fixedpoint IIR filter of one of the following forms:
df1
— directform I
df1t
— directform I transposed
df1sos
— directform I with
secondorder sections
df1tsos
— directform I
transposed with secondorder sections
df2
— directform II
df2t
— directform II transposed
df2sos
— directform II
with secondorder sections
df2tsos
— directform II
transposed with secondorder sections
When you use limitcycle
without optional
input arguments, the default settings are
Run 20 Monte Carlo trials
Use an input vector twice the length of the filter impulse response
Stop testing if the simulation process encounters either a granular or overflow limit cycle
To determine the length of the filter impulse response, use impzlength
:
impzlength(hd)
During limit cycle testing, if the simulation runs reveal both overflow and granular limit cycles, the overflow limit cycle takes precedence and is the limit cycle that appears in the report.
Each time you run limitcycle
, it uses a different
sequence of random initial conditions, so the results can differ from
run to run.
Each Monte Carlo trial uses a new set of randomly determined
initial states for the filter. Test processing stops when limitcycle
detects
a zeroinput limit cycle in filter hd
.
report = limitcycle(hd,ntrials,inputlengthfactor,stopcriterion)
returns
a report of how filter hd
responds to a zerovalued
input vector, using the following optional input arguments:
ntrials
— Number of Monte
Carlo trials (default is 20).
inputlengthfactor
— integer
factor used to calculate the length of the input vector. The length
of the input vector comes from (impzlength(hd)
* inputlengthfactor
), where inputlengthfactor
=
2 is the default value.
stopcriterion
— the criterion
for stopping the Monte Carlo trial processing. stopcriterion
can
be set to either
(the default), granular
, overflow
.
This table describes the results of each stop criterion.
stopcriterion Setting  Description 

 Stop the Monte Carlo trials when 
 Stop the Monte Carlo trials when 
 Stop the Monte Carlo trials when 
Note
An important feature is that if you specify a specific limit
cycle stop criterion, such as 
In this example, there is a region of initial conditions in which no limit cycles occur and a region where they do. If no limit cycles are detected before the Monte Carlo trials are over, the state sequence converges to zero. When a limit cycle is found, the states do not end at zero. Each time you run this example, it uses a different sequence of random initial conditions, so the plot you get can differ from the one displayed in the following figure.
s = [1 0 0 1 0.9606 0.9849]; hd = dfilt.df2sos(s); hd.arithmetic = 'fixed'; greport = limitcycle(hd,20,2,'granular') oreport = limitcycle(hd,20,2,'overflow') figure, subplot(211),plot(greport.Output(1:20)), title('Granular Limit Cycle'); subplot(212),plot(oreport.Output(1:20)), title('Overflow Limit Cycle'); greport = LimitCycle: 'granular' Zi: [2x1 double] Output: [1303x1 embedded.fi] Trial: 1 oreport = LimitCycle: 'overflow' Zi: [2x1 double] Output: [1303x1 embedded.fi] Trial: 2
The plots shown in this figure present both limit cycle types — the first displays the small amplitude granular limit cycle, the second the larger amplitude overflow limit cycle.
As you see from the plots, and as is generally true, overflow
limit cycles are much greater magnitude than granular limit cycles.
This is why limitcycle
favors overflow limit
cycle detection and reporting.