Using the DSP Blockset (DSP Blockset)

DSP Blockset

Classical IIR and FIR Filters, Discrete Time

The Digital FIR Filter Design and Digital IIR Filter Design blocks design and implement discrete-time filters with standard band configurations.

All of the digital filter designs let you specify a filter order. The other available parameters depend on the Filter type and band configuration, as shown below, where f_n0 = cutoff frequency, f_n1 = lower cutoff frequency, f_n2 = upper cutoff frequency, R_p = passband ripple in decibels, and R_s = stopband attenuation in decibels.

Configuration
FIR
Butterworth
Chebyshev I
Chebyshev II
Elliptic

Lowpass
f_n0
f_n0
f_n0, R_p
f_n0, R_s
f_n0, R_p, R_s

Highpass
f_n0
f_n0
f_n0, R_p
f_n0, R_s
f_n0, R_p, R_s

Bandpass
f_n1, f_n2
f_n1, f_n2
f_n1, f_n2, R_p
f_n1, f_n2, R_s
f_n1, f_n2, R_p, R_s

Bandstop
f_n1, f_n2
f_n1, f_n2
f_n1, f_n2, R_p
f_n1, f_n2, R_s
f_n1, f_n2, R_p, R_s

Configuration	FIR	Butterworth	Chebyshev I	Chebyshev II	Elliptic
Lowpass	f_n0	f_n0	f_n0, R_p	f_n0, R_s	f_n0, R_p, R_s
Highpass	f_n0	f_n0	f_n0, R_p	f_n0, R_s	f_n0, R_p, R_s
Bandpass	f_n1, f_n2	f_n1, f_n2	f_n1, f_n2, R_p	f_n1, f_n2, R_s	f_n1, f_n2, R_p, R_s
Bandstop	f_n1, f_n2	f_n1, f_n2	f_n1, f_n2, R_p	f_n1, f_n2, R_s	f_n1, f_n2, R_p, R_s

For all of the classical discrete-time filter design blocks, frequency parameters use normalized units. The unit frequency is the Nyquist frequency (half the sample frequency), so the band edge frequencies are always in the range [0 1].

The Digital IIR Filter Design block uses a direct-form II transposed representation. It inherits its sample rate from the driving block, and accepts only discrete-time inputs.

Both of these blocks use Signal Processing Toolbox functions to design the filter:

The FIR design uses the toolbox function fir1.
The Butterworth design uses the toolbox function butter.
The Chebyshev type I design uses the toolbox function cheby1.
The Chebyshev type II design uses the toolbox function cheby2.
The elliptic design uses the toolbox function ellip.

For more information on the filter design algorithms, see the Signal Processing Toolbox User's Guide.

Example: Chebyshev Type II Lowpass Filter

Create a model like the one shown below. The model generates a signal composed of two sine waves at different frequencies, and then removes the higher frequency component with a lowpass filter.

Construct the model using:

Sine Wave block from the DSP Sources library
Sum block from the Simulink Linear library
Digital IIR Filter Design block from the Filter Designs library
Mux block from the Simulink Signals & Systems library
Buffered FFT Frame Scope block from the DSP Sinks library

To try the model:

1.: Create a signal made up of two sinusoids (at 100 Hz and 400 Hz) by entering a two-element vector in the Frequency field of the Sine Wave block:

Amplitude = 10
Frequency = [100 400]
Phase = 0
Sample time = 0.001
Samples per frame = 1

2.: Set the Sum block's List of signs parameter to 1.

3.: Verify that the Buffered FFT Frame Scope block is set to inherit the sample period of the input, and to plot two channels of data:

Sample time of original time series = -1
Number of input channels = 2

4.: In the Digital IIR Filter Design dialog, specify a Chebyshev type II lowpass filter with a Stopband edge frequency of 250 Hz, to attenuate the sinusoid at 400 Hz but retain the sinusoid at 100 Hz. Note that the Nyquist frequency in this case is 500 Hz (half the sample frequency), so that the normalized Stopband edge frequency is 0.5.

Select Chebyshev II from Design Method.
Select Lowpass from Filter Type.
Filter Order = 8
Stopband edge frequency = 0.5
Stopband ripple = 20

5.: Set the Stop time in the Parameters dialog box to inf, and start the simulation by selecting Start from the Simulation menu.

6.: As the simulation begins running, right-click in the plot area of the scope, and select Autoscale from the pop-up menu. You can also change the styles and colors of the plotted lines by selecting either CH 1 or CH 2 from the right-click pop-up menu.

The Buffered FFT Frame Scope window displays both the original signal and the filtered result, which shows the expected attenuation of the 400 Hz component. Stop the simulation at any time by selecting Stop from the Simulation menu.

[ Previous | Help Desk | Next ]