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# fdesign.notch

Notch filter specification

## Description

The fdesign.notch function returns a notch filter design specification object that contains the specifications for a filter, such as passband ripple, stopband attenuation, and filter order. Then, use the design function to design the filter from the filter design specifications object.

For more control options, see Filter Design Procedure. For a complete workflow, see Design a Filter in Fdesign — Process Overview.

notchSpecs = fdesign.notch constructs a notch filter specification object with the filter order set to 10, center frequency set to 0.5, and quality factor set to 2.5.

notchSpecs = fdesign.notch(n,f0,q) constructs a notch filter specification object with the filter order, center frequency, and quality factor specified by n,f0, and q, respectively.

example

notchSpecs = fdesign.notch(spec,value1,...,valueN) constructs a notch filter specification object with a particular filter order, center frequency, and other specification options. Indicate the options you want to specify in the expression spec. After the expression, specify a value for each option.

notchSpecs = fdesign.notch(___,Fs) provides the sample rate of the signal to be filtered.

notchSpecs = fdesign.notch(___,magunits) provides the units for any magnitude specification given. magunits can be one of the following: 'linear', 'dB', or 'squared'. If this argument is omitted, 'dB' is assumed. The magnitude specifications are always converted and stored in decibels regardless of how they were specified. If Fs is provided, magunits must follow Fs in the input argument list.

## Examples

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Design a direct-form I notching filter that has a filter order of 6, center frequency of 0.5, quality factor of 10, and a passband ripple of 1 dB.

Create a notch filter design specification object using the fdesign.notch function and specify these design parameters.

notchSpecs  = fdesign.notch('N,F0,Q,Ap',6,0.5,10,1);

Design the notch filter using the design function. The resulting filter is a dsp.BiquadFilter System object™. For details on how to apply this filter on streaming data, refer to dsp.BiquadFilter.

notchFilt = design(notchSpecs,'SystemObject',true)
notchFilt =
dsp.BiquadFilter with properties:

Structure: 'Direct form II'
SOSMatrixSource: 'Property'
SOSMatrix: [3x6 double]
ScaleValues: [4x1 double]
InitialConditions: 0
OptimizeUnityScaleValues: true

Show all properties

Visualize the frequency response of the designed filter using fvtool.

fvtool(notchFilt)

## Input Arguments

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Specification expression, specified as one of these character vectors:

• 'N,F0,Q' (default)

• 'N,F0,Q,Ap'

• 'N,F0,Q,Ast'

• 'N,F0,Q,Ap,Ast'

• 'N,F0,BW'

• 'N,F0,BW,Ap'

• 'N,F0,BW,Ast'

• 'N,F0,BW,Ap,Ast'

This table describes each option that can appear in the expression.

Specification optionDescription
NFilter order (must be even)
F0Center frequency
QQuality factor
BW3 dB bandwidth
ApPassband ripple (dB)
AstStopband attenuation (dB)

The design methods available for designing the filter depend on the specification expression. You can obtain these methods using the designmethods function. The table lists each specification expression supported by fdesign.notch and the corresponding design methods available.

Specification expressionSupported design methodFilter description
'N,F0,Q'butter

Butterworth digital filter

'N,F0,Q,Ap'cheby1

Chebyshev Type I digital filter

'N,F0,Q,Ast'cheby2

Chebyshev Type II digital filter

'N,F0,Q,Ap,Ast'ellip

Elliptical digital filter

'N,F0,BW'butter

Butterworth digital filter

'N,F0,BW,Ap'cheby1

Chebyshev Type I digital filter

'N,F0,BW,Ast'cheby2

Chebyshev Type II digital filter

'N,F0,BW,Ap,Ast'ellip

Elliptical digital filter

To design the filter, call the design function with one of these design methods as an input. You can choose the type of filter response by passing 'FIR' or 'IIR' to the design function. For more details, see design.

For more details on the procedure, see Filter Design Procedure. For an example, see Design Notch Filter.

Specification values, specified as a comma-separated list of values. Specify a value for each option in spec in the same order that the options appear in the expression.

Example: d = fdesign.notch('N,F0,BW,Ast',n,f0,bw,ast)

The arguments below describe more details for each option in the expression.

Filter order, specified as an even positive integer.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Center frequency of the filter, specified as a scalar. When the input sampling frequency Fs is specified, the center frequency is in Hz. When the input sample rate is not specified, the center frequency is in normalized units between 0 and 1.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Quality factor of the filter, specified as a real positive scalar.

Quality factor of the filter is defined as the ratio of the center frequency to the 3 dB bandwidth.

$q={f}_{0}/bw$

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

3 dB bandwidth of the filter, specified as a real scalar.

Specify the 3 dB bandwidth value in normalized frequency units between 0 and 1. If you specify the sample rate Fs, then specify the bandwidth value in Hz instead.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Passband ripple, specified as a positive scalar in dB. If magunits is 'linear' or 'squared', the passband ripple is converted and stored in dB by the function regardless of how it has been specified.

Data Types: double

Stopband attenuation of the filter, specified as a positive scalar in dB. If magunits is 'linear' or 'squared', the stopband attenuation is converted and stored in dB by the function regardless of how it has been specified.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Sample rate of the signal to be filtered, specified as a scalar in Hz. Specify the sample rate as a scalar trailing the other numerical values provided. When Fs is provided, Fs is assumed to be in Hz, as are all other frequency values provided. Note that you do not have to change the specification string.

Consider a design specification where N is set to 4, F0 is set to 1200 Hz, and Q is set to 6.5. Specify the sample rate of the input signal as 8000 Hz. Here is how the design looks:

d = fdesign.notch('N,F0,Q',4,1200,6.5,8e3); filt = design(d,'Systemobject',true);

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Magnitude specification units, specified as 'dB', 'linear', or 'squared'. If this argument is omitted, 'dB' is assumed. Note that the magnitude specifications are always converted and stored in dB regardless of how they were specified. If Fs is one of the input arguments, magunits must be specified after Fs in the input argument list.

## Output Arguments

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Notch filter design specification object, returned as a notch object. The fields of the object depend on the spec input character vector.

Consider an example where the spec argument is set to 'N,F0,Q,Ap,Ast', and the corresponding values are set to 6, 0.5, 10, 1, 80, respectively. The notch filter design specification object is populated with the following fields:

## See Also

### Objects

Introduced in R2011a

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