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Arbitrary response magnitude and phase filter specification object


d = fdesign.arbmagnphase
d = fdesign.arbmagnphase(specification)
d = fdesign.arbmagnphase(specification,specvalue1,specvalue2,...)
d = fdesign.arbmagnphase(specvalue1,specvalue2,specvalue3)
d = fdesign.arbmagnphase(...,fs)


d = fdesign.arbmagnphase constructs an arbitrary magnitude filter specification object d.

d = fdesign.arbmagnphase(specification) initializes the Specification property for specifications object d to specification. The input argument specification must be one of the choices shown in the following table. Specification options are not case sensitive.


Description of Resulting Filter


Single band design (default). FIR and IIR (n is the order for both numerator and denominator).


FIR multiband design where b defines the number of bands.


IIR single band design.

The following table describes the specification arguments.




Number of bands in the multiband filter.


Frequency vector. Frequency values specified in f indicate locations where you provide specific filter response amplitudes. When you provide f you must also provide h which contains the response values.


Complex frequency response values.


Filter order for FIR filters and the numerator and denominator orders for IIR filters (when not specified by nb and na).


Numerator order for IIR filters.


Denominator order for IIR filter designs.

By default, this method assumes that all frequency specifications are supplied in normalized frequency.

Specifying f and h

f and h are the input arguments you use to define the filter response desired. Each frequency value you specify in f must have a corresponding response value in h. This example creates a filter with two passbands (b = 4) and shows how f and h are related. This example is for illustration only. It is not an actual filter.

Define the frequency vector f as [0 0.1 0.2 0.4 0.5 0.6 0.9 1.0]

Define the response vector h as [0 0.5 0.5 0.1 0.1 0.8 0.8 0]

These specifications connectf and h as shown in the following table.

f (Normalized Frequency)

h (Response Desired at f)

















A response with two passbands—one roughly between 0.1 and 0.2 and the second between 0.6 and 0.9—results from the mapping between f and h. Plotting f and h yields the following figure that resembles a filter with two passbands.

The second example in Examples shows this plot in more detail with a complex filter response for h. In the example, h uses complex values for the response.

Different specification types often have different design methods available. Use designmethods(d) to get a list of design methods available for a given specification option and specifications object.

d = fdesign.arbmagnphase(specification,specvalue1,specvalue2,...) initializes the filter specification object with specvalue1, specvalue2, and so on. Use get(d,'description') for descriptions of the various specifications specvalue1, specvalue2, ...specn.

d = fdesign.arbmagnphase(specvalue1,specvalue2,specvalue3) uses the default specification option n,f,h, setting the filter order, filter frequency vector, and the complex frequency response vector to the values specvalue1, specvalue2, and specvalue3.

d = fdesign.arbmagnphase(...,fs) specifies the sampling frequency in Hz. All other frequency specifications are also assumed to be in Hz when you specify fs.


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Use fdesign.arbmagnphase to model a complex analog filter.

d = fdesign.arbmagnphase('n,f,h',100); % N=100, f and h set to defaults.

Figure Figure 1: Magnitude Response (dB) contains an axes object. The axes object with title Magnitude Response (dB), xlabel Normalized Frequency ( times pi blank r a d / s a m p l e ), ylabel Magnitude (dB) contains 2 objects of type line.

For a more complex example, design a bandpass filter with low group delay by specifying the desired delay and using f and h to define the filter bands.

n = 50;     % Group delay of a linear phase filter would be 25.
gd = 12;    % Set the desired group delay for the filter.
f1=linspace(0,.25,30); % Define the first stopband frequencies.
f2=linspace(.3,.56,40);% Define the passband frequencies.
f3=linspace(.62,1,30); % Define the second stopband frequencies.
h1 = zeros(size(f1));  % Specify the filter response at the freqs in f1.
h2 = exp(-1j*pi*gd*f2); % Specify the filter response at the freqs in f2.
h3 = zeros(size(f3));  % Specify the response at the freqs in f3.
D = design(d,'equiripple','SystemObject',true);

Figure Figure 2: Magnitude Response (dB) and Phase Response contains an axes object. The axes object with title Magnitude Response (dB) and Phase Response, xlabel Normalized Frequency ( times pi blank r a d / s a m p l e ), ylabel Magnitude (dB) contains an object of type line.

Version History

Introduced in R2011a