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# fdesign.highpass

Highpass filter specification object

## Syntax

D = fdesign.highpass D = fdesign.highpass(SPEC) D = fdesign.highpass(SPEC,specvalue1,specvalue2,...) D = fdesign.highpass(specvalue1,specvalue2,specvalue3, specvalue4) D = fdesign.highpass(...,Fs) D = fdesign.highpass(...,MAGUNITS) 

## Description

D = fdesign.highpass constructs a highpass filter specification object D, applying default values for the specification, 'Fst,Fp,Ast,Ap'.

D = fdesign.highpass(SPEC) constructs object D and sets the Specification property to SPEC. Entries in the SPEC represent various filter response features, such as the filter order, that govern the filter design. Valid entries for SPEC are shown below. These entries are not case sensitive.

### Note

Specification entries marked with an asterisk require the DSP System Toolbox™ software.

• 'Fst,Fp,Ast,Ap' (default spec)

• 'N,F3db'

• 'N,F3db,Ap' *

• 'N,F3db,Ast' *

• 'N,F3db,Ast,Ap' *

• 'N,F3db,Fp *

• 'N,Fc'

• 'N,Fc,Ast,Ap'

• 'N,Fp,Ap'

• 'N,Fp,Ast,Ap'

• 'N,Fst,Ast'

• 'N,Fst,Ast,Ap'

• 'N,Fst,F3db' *

• 'N,Fst,Fp'

• 'N,Fst,Fp,Ap' *

• 'N,Fst,Fp,Ast' *

• 'Nb,Na,Fst,Fp' *

The filter specifications are defined as follows:

• Ap — amount of ripple allowed in the pass band in decibels (the default units). Also called Apass.

• Ast — attenuation in the stop band in decibels (the default units). Also called Astop.

• F3db — cutoff frequency for the point 3 dB point below the passband value. Specified in normalized frequency units.

• Fc — cutoff frequency for the point 6 dB point below the passband value. Specified in normalized frequency units.

• Fp — frequency at the start of the pass band. Specified in normalized frequency units. Also called Fpass.

• Fst — frequency at the end of the stop band. Specified in normalized frequency units. Also called Fstop.

• N — filter order.

• Na and Nb are the order of the denominator and numerator.

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

Regions between specification values like Fst and Fp are transition regions where the filter response is not explicitly defined.

The filter design methods that apply to a highpass filter specification object change depending on the Specification. Use designmethods to determine which design method applies to an object and its specification.

Use designopts to determine which design options are valid for a given design method. For detailed information on design options for a given design method, METHOD, enter help(D,METHOD) at the MATLAB® command line.

D = fdesign.highpass(SPEC,specvalue1,specvalue2,...) constructs an object d and sets its specification values at construction time.

D = fdesign.highpass(specvalue1,specvalue2,specvalue3, specvalue4) constructs an object D with the default Specification property and the values you enter for specvalue1,specvalue2,....

D = fdesign.highpass(...,Fs) provides the sampling frequency for the filter specification object. Fs is in Hz and must be specified as a scalar trailing the other numerical values provided. If you specify a sampling frequency, all other frequency specifications are in Hz.

D = fdesign.highpass(...,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.

## Examples

collapse all

Highpass filter a discrete-time signal consisting of two sine waves.

Create a highpass filter specification object. Specify the passband frequency to be 0.25π rad/sample and the stopband frequency to be 0.15π rad/sample. Specify 1 dB of allowable passband ripple and a stopband attenuation of 60 dB.

d = fdesign.highpass('Fst,Fp,Ast,Ap',0.15,0.25,60,1);

Query the valid design methods for your filter specification object.

designmethods(d)
Design Methods for class fdesign.highpass (Fst,Fp,Ast,Ap): butter cheby1 cheby2 ellip equiripple ifir kaiserwin 

Create an FIR equiripple filter and view the filter magnitude response with FVTool.

Hd = design(d,'equiripple'); fvtool(Hd)

Create a signal consisting of the sum of two discrete-time sinusoids with frequencies of π/8 and π/4 rad/sample and amplitudes of 1 and 0.25 respectively. Filter the discrete-time signal with the FIR equiripple filter object.

n = 0:159; x = cos(pi/8*n)+0.25*sin(pi/4*n); y = filter(Hd,x);

Plot the original and filtered signals in the frequency domain.

freq = 0:(2*pi)/160:pi; xdft = fft(x); ydft = fft(y); plot(freq/pi,abs(xdft(1:length(x)/2+1))) hold on plot(freq/pi,abs(ydft(1:length(y)/2+1)),'r','linewidth',2) hold off legend('Original Signal','Lowpass Signal','Location','NorthEast') ylabel('Magnitude') xlabel('Normalized Frequency (\times\pi rad/sample)')

Create a filter of order 10 with a 6-dB frequency of 9.6 kHz and a sample rate of 48 kHz. Look at the available design methods.

d=fdesign.highpass('N,Fc',10,9600,48000); designmethods(d)
Design Methods for class fdesign.highpass (N,Fc): window 

The only available method is the FIR window method. Design the filter and display its magnitude response.

Hd = design(d); fvtool(Hd)

You can specify the shape of the stopband and the rate at which the stopband decays.

Create two FIR equiripple filters with different linear stopband slopes. Specify the passband frequency to be 0.3π rad/sample and the stopband frequency to be 0.35π rad/sample. Specify 1 dB of allowable passband ripple and a stopband attenuation of 60 dB. Design one filter with a 20 dB/(rad/sample) stopband slope and another filter with a slope of 40 dB/(rad/sample).

D = fdesign.highpass('Fst,Fp,Ast,Ap',0.3,0.35,60,1); Hd1 = design(D,'equiripple','StopBandShape','linear','StopBandDecay',20); Hd2 = design(D,'equiripple','StopBandShape','linear','StopBandDecay',40);

Visualize the magnitude responses of the filters.

hfvt = fvtool([Hd1 Hd2]); legend(hfvt,'20 dB/rad/sample','40 dB/rad/sample')