Length of impulse response of discrete-time filter System object
Impulse Response Length of Filter System object
This example requires DSP System Toolbox™ software.
Design a 4th-order lowpass elliptic filter with a cutoff frequency of 0.4 rad/sample. Specify 1 dB of passband ripple and 60 dB of stopband attenuation. Design the filter in pole-zero-gain form and obtain the second order section matrix using the
zp2sos function. Create an SOS filter object and input the object to
[z,p,k] = ellip(4,1,60,.4); [sos,g] = zp2sos(z,p,k); hSosFilt = dsp.SOSFilter(Structure='Direct form I',... Numerator=sos(:,1:3),Denominator=sos(:,4:6),... HasScaleValues=true,ScaleValues=g); len = impzlength(hSosFilt)
len = 80
Impulse Response Length for Filter System Objects
Design an IIR Butterworth and an FIR equiripple filter for data sampled at 1 kHz. Set the passband frequency to 100 Hz and the stopband frequency to 150 Hz. Set the passband ripple to 0.5 dB and the stopband attenuation to 60 dB. Create System objects for the filters and compare the filter impulse response sequence lengths.
d = fdesign.lowpass('Fp,Fst,Ap,Ast',100,150,0.5,60,1000); Hd1 = design(d,'butter',SystemObject=true)
Hd1 = dsp.SOSFilter with properties: Structure: 'Direct form II' CoefficientSource: 'Property' Numerator: [9x3 double] Denominator: [9x3 double] HasScaleValues: true ScaleValues: [0.1020 0.0927 0.0852 0.0793 0.0748 0.0713 0.0689 ... ] Show all properties
Hd2 = design(d,'equiripple',SystemObject=true)
Hd2 = dsp.FIRFilter with properties: Structure: 'Direct form' NumeratorSource: 'Property' Numerator: [-7.9808e-04 -2.8559e-04 0.0011 0.0036 0.0064 ... ] InitialConditions: 0 Show all properties
len = [impzlength(Hd1) impzlength(Hd2)]
len = 1×2 183 49
sysobj — Filter System object
filter System object
Input filter, specified as one of the following filter System objects:
tol — Tolerance for IIR filter effective impulse response length
5e-5 (default) | positive scalar
Tolerance for IIR filter effective impulse response length, specified as a positive number. The tolerance determines the term in the absolutely summable sequence after which subsequent terms are considered to be 0. Increasing the tolerance returns a shorter effective impulse response sequence length. Decreasing the tolerance returns a longer effective impulse response sequence length.
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.
len — Length of impulse response
Length of the impulse response, specified as a positive integer. For stable IIR
filters with absolutely summable impulse responses,
returns an effective length for the impulse response beyond which the coefficients are
essentially zero. You can control this cutoff point by specifying the optional
tol input argument.
Introduced in R2013a