Verify that discrete-time filter System object is maximum phase
Determine if Filter has Maximum Phase
Design an allpass filter and determine if the filter has maximum phase.
dsp.AllpassFilter System object™, design an allpass filter that uses the minimum multiplier structure.
a = dsp.AllpassFilter
a = dsp.AllpassFilter with properties: Structure: 'Minimum multiplier' AllpassCoefficients: [-0.7071 0.5000] TrailingFirstOrderSection: false
ismaxphase function, determine if the filter has maximum phase.
ans = logical 1
Verify the location of poles and zeros of the filter transfer function on the z-plane. By definition, the zeros of the maximum phase filter must be outside the unit circle.
sysobj — Filter System object
filter System object
Input filter, specified as one of the following filter System objects:
tol — Tolerance
eps^(2/3) (default) | positive scalar
Tolerance value to determine when two numbers are close enough to be considered
equal, specified as a positive scalar. If not specified,
arithType — Arithmetic type
'double' (default) |
Arithmetic used in the filter analysis, specified as
'Fixed'. When the arithmetic
input is not specified and the filter System object is unlocked, the analysis tool assumes a double-precision filter. When the
arithmetic input is not specified and the System object is locked, the function performs the analysis based on the data type of
the locked input.
'Fixed' value applies to filter System objects with fixed-point
'Arithmetic' input argument is specified as
'Fixed' and the filter object has the data type of the
coefficients set to
'Same word length as input', the arithmetic
analysis depends on whether the System object is unlocked or locked.
unlocked –– The analysis object function cannot determine the coefficients data type. The function assumes that the coefficients data type is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.
locked –– When the input data type is
'single', the analysis object function cannot determine the coefficients data type. The function assumes that the data type of the coefficients is signed, has a 16-bit word length, and is auto scaled. The function performs fixed-point analysis based on this assumption.
To check if the System object is locked or unlocked, use the
When the arithmetic input is specified as
'Fixed' and the filter
object has the data type of the coefficients set to a custom numeric type, the object
function performs fixed-point analysis based on the custom numeric data type.
flag — Flag to determine if filter has maximum phase
Flag to determine if the filter has maximum phase, returned as a logical:
1–– Filter has maximum phase.
0–– Filter has non maximum phase.
Maximum Phase Filters
A causal and stable discrete-time system is said to be strictly maximum-phase when all its zeros are outside the unit circle. A causal and stable LTI system is a maximum-phase system if its inverse is causal and unstable.
Such a system is called a maximum-phase system
because it has the maximum group delay (
grpdelay) of the set of systems that have the same magnitude response.