Lowpass filter specification
D = fdesign.lowpass
D = fdesign.lowpass(SPEC)
D = fdesign.lowpass(SPEC,specvalue1,specvalue2,...)
D = fdesign.lowpass(specvalue1,specvalue2,specvalue3,specvalue4)
D = fdesign.lowpass(...,Fs)
D = fdesign.lowpass(...,MAGUNITS)
D = fdesign.lowpass(SPEC) constructs object D and sets the Specification property to the string in SPEC. Entries in the SPEC string represent various filter response features, such as the filter order, that govern the filter design. Valid entries for SPEC are shown below. The strings are not case sensitive.
'Fp,Fst,Ap,Ast' (default spec)
The string entries 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 Fp and Fst are transition regions where the filter response is not explicitly defined.
D = fdesign.lowpass(SPEC,specvalue1,specvalue2,...) constructs an object D and sets the specification values at construction time using specvalue1, specvalue2, and so on for all of the specification variables in SPEC.
D = fdesign.lowpass(specvalue1,specvalue2,specvalue3,specvalue4) constructs an object D with values for the default Specification property string 'Fp,Fst,Ap,Ast' using the specifications you provide as input arguments specvalue1,specvalue2,specvalue3,specvalue4.
'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 MAGNUNITS 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.
Lowpass filter a discrete-time signal consisting of two sine waves.
Create a lowpass filter specification object. Specify the passband frequency to be 0.15π radians/sample and the stopband frequency to be 0.25π radians/sample. Specify 1 dB of allowable passband ripple and a stopband attenuation of 60 dB.
Query the valid design methods for your filter specification object, d.
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 radians/sample and amplitudes of 1 and 0.25 respectively. Filter the discrete-time signal with the FIR equiripple filter object, Hd.
n = 0:159; x = 0.25*cos((pi/8)*n)+sin((pi/4)*n); y = filter(Hd,x); Domega = (2*pi)/160; freq = 0:(2*pi)/160:pi; xdft = fft(x); ydft = fft(y); plot(freq,abs(xdft(1:length(x)/2+1))); hold on; plot(freq,abs(ydft(1:length(y)/2+1)),'r','linewidth',2); legend('Original Signal','Highpass Signal', ... 'Location','NorthEast'); ylabel('Magnitude'); xlabel('Radians/Sample');
Create a filter of order 10 with a 6-dB frequency of 9.6 kHz and a sampling frequency of 48 kHz.
d=fdesign.lowpass('N,Fc',10,9600,48000); designmethods(d) % only valid design method is FIR window method Hd = design(d); % Display filter magnitude response fvtool(Hd);
Zoom in on the magnitude response to verify that the -6 dB point is at 9.6 kHz.
If you have the DSP System Toolbox software, you can specify the shape of the stopband and the rate at which the stopband decays. The following example requires the DSP System Toolbox.
Create an FIR equiripple filter with a passband frequency of 0.2π radians/sample, a stopband frequency of 0.25π radians/sample, a passband ripple of 1 dB, and a stopband attenuation of 60 dB. Design the filter with a 20 dB/rad/sample linear stopband.
D = fdesign.lowpass('Fp,Fst,Ap,Ast',0.2,0.25,1,60); Hd = design(D,'equiripple','StopBandShape','linear','StopBandDecay',20); fvtool(Hd);