Verify that discrete-time filter System object is minimum phase
Design a Chebyshev Type I IIR filter and determine if the filter has minimum phase and is stable.
Fs = 48000; % Sampling frequency of input signal d = fdesign.lowpass('N,F3dB,Ap', 10, 9600, .5, Fs); filt = design(d,'cheby1','Systemobject',true)
filt = dsp.BiquadFilter with properties: Structure: 'Direct form II' SOSMatrixSource: 'Property' SOSMatrix: [5x6 double] ScaleValues: [6x1 double] InitialConditions: 0 OptimizeUnityScaleValues: true Show all properties
isminphase function, determine if the filter has minimum phase.
ans = logical 1
Verify the location of poles and zeros of the filter transfer function on the z-plane. By definition, the poles and zeros of the minimum phase filter must be on or inside the unit circle.
All minimum phase filters are stable. To verify if the designed filter is stable, use the
ans = logical 1
sysobj— Filter System object
Input filter, specified as one of the following filter System objects:
tol— Tolerance value
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
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
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 minimum phase
Flag to determine if the filter has minimum phase, returned as a logical:
1 –– Filter has minimum phase.
0 –– Filter has non minimum phase.
A causal and stable discrete-time system is said to be strictly minimum-phase when all its zeros are inside the unit circle. A causal and stable LTI system is a minimum-phase system if its inverse is causal and stable as well.
Such a system is called a minimum-phase
system because it has the minimum group delay (
grpdelay) of the set of systems that have the same magnitude response.