## Documentation |

Bandstop filter specification object

`D = fdesign.bandstopD = fdesign.bandstop( SPEC)D = fdesign.bandstop(SPEC,specvalue1,specvalue2,...)D = fdesign.bandstop(specvalue1,specvalue2,specvalue3,specvalue4,...specvalue5,specvalue6,specvalue7)D = fdesign.bandstop(...,Fs)D = fdesign.bandstop(...,MAGUNITS)`

`D = fdesign.bandstop` constructs
a bandstop filter specification object `D`, applying
default values for the properties `Fpass1`, `Fstop1`, `Fstop2`, `Fpass2`, `Apass1`, `Astop1` and `Apass2`.

`D = fdesign.bandstop( SPEC)` constructs
object

`'Fp1,Fst1,Fst2,Fp2,Ap1,Ast,Ap2'`(default spec)`'N,F3dB1,F3dB2'``'N,F3dB1,F3dB2,Ap'`*`'N,F3dB1,F3dB2,Ap,Ast'`*`'N,F3dB1,F3dB2,Ast'`*`'N,F3dB1,F3dB2,BWp'`*`'N,F3dB1,F3dB2,BWst'`*`'N,Fc1,Fc2'``'N,Fc1,Fc2,Ap1,Ast,Ap2'``'N,Fp1,Fp2,Ap'``'N,Fp1,Fp2,Ap,Ast'``'N,Fp1,Fst1,Fst2,Fp2'``'N,Fp1,Fst1,Fst2,Fp2,C'`*`'N,Fp1,Fst1,Fst2,Fp2,Ap'`*`'N,Fst1,Fst2,Ast'``'Nb,Na,Fp1,Fst1,Fst2,Fp2'`*

The string entries are defined as follows:

`Ap`— amount of ripple allowed in the passband in decibels (the default units). Also called Apass.`Ap1`— amount of ripple allowed in the pass band in decibels (the default units). Also called Apass1.`Ap2`— amount of ripple allowed in the pass band in decibels (the default units). Also called Apass2.`Ast`— attenuation in the first stopband in decibels (the default units). Also called Astop1.`BWp`— bandwidth of the filter passband. Specified in normalized frequency units.`BWst`— bandwidth of the filter stopband. Specified in normalized frequency units.`C`— Constrained band flag. This enables you to specify passband ripple or stopband attenuation for fixed-order designs in one or two of the three bands.In the specification string

`'N,Fp1,Fst1,Fst2,Fp2,C'`, you cannot specify constraints simultaneously in both passbands and the stopband. You can specify constraints in any one or two bands.`F3dB1`— cutoff frequency for the point 3 dB point below the passband value for the first cutoff.`F3dB2`— cutoff frequency for the point 3 dB point below the passband value for the second cutoff.`Fc1`— cutoff frequency for the point 6 dB point below the passband value for the first cutoff. (FIR filters)`Fc2`— cutoff frequency for the point 6 dB point below the passband value for the second cutoff. (FIR filters)`Fp1`— frequency at the start of the pass band. Also called Fpass1.`Fp2`— frequency at the end of the pass band. Also called Fpass2.`Fst1`— frequency at the end of the first stop band. Also called Fstop1.`Fst2`— frequency at the start of the second stop band. Also called Fstop2.`N`— filter order.`Na`— denominator order for IIR filters.`Nb`— numerator order for IIR filters.

Graphically, the filter specifications look similar to those shown in the following figure.

Regions between specification values like `Fp1` and `Fst1` are
transition regions where the filter response is not explicitly defined.

The filter design methods that apply to a bandstop filter specification
object change depending on the `Specification` string.
Use `designmethods` to determine
which design methods apply to an object and the `Specification` property
value.

Use `designopts` to determine
the design options for a given design method. Enter `help(D,METHOD)` at
the MATLAB^{®} command line to obtain detailed help on the design
options for a given design method, `METHOD`.

`D = fdesign.bandstop(SPEC,specvalue1,specvalue2,...)` constructs
an object `D` and sets its specifications at construction
time.

`D = fdesign.bandstop(specvalue1,specvalue2,specvalue3,specvalue4,...specvalue5,specvalue6,specvalue7)` constructs
an object

`D = fdesign.bandstop(...,Fs)` adds
the argument `Fs`, specified in Hz to define the
sampling frequency. If you specify the sampling frequency as a trailing
scalar, all frequencies in the specifications are in Hz as well.

`D = fdesign.bandstop(...,MAGUNITS)` specifies
the units for any magnitude specification you provide in the input
arguments. `MAGUNITS` can be one of

`'linear'`— specify the magnitude in linear units`'dB'`— specify the magnitude in dB (decibels)`'squared'`— specify the magnitude in power units

When you omit the `MAGUNITS` argument, `fdesign` assumes
that all magnitudes are in decibels. Note that `fdesign` stores
all magnitude specifications in decibels (converting to decibels when
necessary) regardless of how you specify the magnitudes.

Construct a bandstop filter to reject the discrete frequency band between 3π/8 and 5π/8 radians/sample. Apply the filter to a discrete-time signal consisting of the superposition of three discrete-time sinusoids.

Design an FIR equiripple filter and view the magnitude response.

d = fdesign.bandstop('Fp1,Fst1,Fst2,Fp2,Ap1,Ast,Ap2',2/8,3/8,5/8,6/8,1,60,1); Hd = design(d,'equiripple'); fvtool(Hd)

Construct the discrete-time signal to filter.

n = 0:99; x = cos(pi/5*n)+sin(pi/2*n)+cos(4*pi/5*n); y = filter(Hd,x); xdft = fft(x); ydft = fft(y); freq = 0:(2*pi)/length(x):pi; plot(freq,abs(xdft(1:length(x)/2+1))); hold on; plot(freq,abs(ydft(1:length(y)/2+1)),'r','linewidth',2); xlabel('Radians/Sample'); ylabel('Magnitude'); legend('Original Signal','Bandstop Signal');

Create a Butterworth bandstop filter for data sampled at 10 kHz. The stopband is [1,1.5] kHz. The order of the filter is 20.

d = fdesign.bandstop('N,F3dB1,F3dB2',20,1e3,1.5e3,1e4); Hd = design(d,'butter'); fvtool(Hd);

Zoom in on the magnitude response plot to verify that the 3-dB down points are located at 1 and 1.5 kHz.

The following example requires the DSP System Toolbox license.

Design a constrained-band FIR equiripple filter of order 100 for data sampled at 10 kHz. You can specify constraints on at most two of the three bands: two passbands and one stopband. In this example, you choose to constrain the passband ripple to be 0.5 dB in each passband. Design the filter, visualize the magnitude response and measure the filter's design.

d = fdesign.bandstop('N,Fp1,Fst1,Fst2,Fp2,C',100,800,1e3,1.5e3,1.7e3,1e4); d.Passband1Constrained = true; d.Apass1 = 0.5; d.Passband2Constrained = true; d.Apass2 = 0.5; Hd = design(d,'equiripple'); fvtool(Hd); measure(Hd)

With this order filter and passband ripple constraints, you achieve approximately 50 dB of stopband attentuation.

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