stepz

Step response of discrete-time filter System object

Syntax

[stepResp,t] = stepz(sysobj)

[stepResp,t] = stepz(sysobj,n)

[stepResp,t] = stepz(sysobj,n,fs)

[stepResp,t] = stepz(sysobj,[],fs)

[___] = stepz(___,'Arithmetic',arithType)

stepz(sysobj)

Description

[stepResp,t] = stepz(sysobj) computes the step response of the filter System object™ and returns the response in the column vector stepResp, and a vector of times (or sample intervals) in t, where t = [0 1 2 ...k-1]'. k is the number of filter coefficients.

[stepResp,t] = stepz(sysobj,n) computes the step response at floor(n) 1-second intervals. The time vector t equals (0:floor(n)-1)'.

[stepResp,t] = stepz(sysobj,n,fs) computes the step response at floor(n) 1/fs-second intervals. The time vector t equals (0:floor(n)-1)'/fs.

[stepResp,t] = stepz(sysobj,[],fs) computes the step response at k 1/fs-second intervals, where k is the number of filter coefficients. The time vector t equals (0:k-1)'/fs.

[___] = stepz(___,'Arithmetic',arithType) analyzes the filter System object based on the arithmetic specified in arithType using any one of the previous syntaxes.

stepz(sysobj) launches fvtool and plots the step response of the filter System object.

For more input options, see stepz in Signal Processing Toolbox™.

stepz works for both real and complex filters. When you omit the output arguments, the stepz function plots only the real part of the step response.

Examples

Step Response of Equiripple Lowpass FIR Filter

Design an equiripple lowpass FIR filter and compute the step response of the filter.

Use the fdesign.lowpass specification object to define the filter specifications. Run the design function on the specification object to create a dsp.FIRFilter object. Specify the passband frequency to be 20 kHz, stopband frequency to be 22.05 kHz, passband ripple to be 1 dB, and the stopband attenuation to be 80 dB. Specify the sampling frequency to be 96 kHz.

Fs = 96e3; filtSpecs = fdesign.lowpass(20e3,22.05e3,1,80,Fs);
firlp2 = design(filtSpecs,'equiripple','SystemObject',true)

firlp2 = 
  dsp.FIRFilter with properties:

            Structure: 'Direct form'
      NumeratorSource: 'Property'
            Numerator: [1x123 double]
    InitialConditions: 0

  Show all properties

Compute the step response of the filter using the stepz function.

stepz(firlp2)

Input Arguments

sysobj — Input filter

filter System object

Input filter, specified as one of the following filter System objects:

• dsp.AllpassFilter

• dsp.AllpoleFilter

• dsp.BiquadFilter

• dsp.Channelizer

• dsp.CICCompensationDecimator

• dsp.CICCompensationInterpolator

• dsp.CICDecimator

• dsp.CICInterpolator

• dsp.CoupledAllpassFilter

• dsp.Differentiator

• dsp.FarrowRateConverter

• dsp.FilterCascade

• dsp.FIRDecimator

• dsp.FIRFilter

• dsp.FIRHalfbandDecimator

• dsp.FIRHalfbandInterpolator

• dsp.FIRInterpolator

• dsp.FIRRateConverter

• dsp.FourthOrderSectionFilter

• dsp.HighpassFilter

• dsp.IIRFilter

• dsp.IIRHalfbandDecimator

• dsp.IIRHalfbandInterpolator

• dsp.LowpassFilter

• dsp.NotchPeakFilter

• dsp.SOSFilter

• dsp.VariableBandwidthFIRFilter

• dsp.VariableBandwidthIIRFilter

n — Length of step response vector

positive integer

Length of the step response vector, specified as a positive integer.

Data Types: single | double

fs — Sampling frequency

1 (default) | positive scalar

Sampling frequency used in computing the step response, specified as a positive scalar.

Data Types: single | double

arithType — Arithmetic type

'double' (default) | 'single' | 'Fixed'

Arithmetic used in the filter analysis, specified as 'double', 'single', or '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.

The 'Fixed' value applies to filter System objects with fixed-point properties only.

When the '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 'double' or '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 isLocked function.

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.

Output Arguments

stepResp — Step response

vector

Step response, returned as an n-element vector. If n is not specified, the length of the step response vector equals the number of coefficients, k in the filter.

Data Types: double

t — Time vector

vector

Time vector of length n in seconds. The vector t consists of n equally spaced points in the range (0:floor(n)-1)'/fs. If n is not specified, the function uses the number of coefficients k in the filter.

Data Types: double