Digital IIR Filter Design (DSP Blockset)

Design and implement an IIR filter.

Library

Filter Designs, in Filtering

Description

The Digital IIR Filter Design block designs a discrete-time (digital) IIR filter in a lowpass, highpass, bandpass, or bandstop configuration, and applies the filter to the input using the Direct-Form II Transpose Filter block in the Filter Realizations library. The Design method parameter allows you to specify Butterworth, Chebyshev type I, Chebyshev type II, and elliptic filter designs. Note that for the bandpass and bandstop configurations, the actual filter length is twice the Filter order parameter value.


Filter Design	Description
Butterworth	The magnitude response of a Butterworth filter is maximally flat in the passband and monotonic overall.
Chebyshev type I	The magnitude response of a Chebyshev type I filter is equiripple in the passband and monotonic in the stopband.
Chebyshev type II	The magnitude response of a Chebyshev type II filter is monotonic in the passband and equiripple in the stopband.
Elliptic	The magnitude response of an elliptic filter is equiripple in both the passband and the stopband.

The design and band configuration of the filter are selected from the Design method and Filter type pop-up menus in the dialog box. For each combination of design method and band configuration, an appropriate set of secondary parameters is displayed.

The table below lists the available parameters for each design/band combination. For lowpass and highpass band configurations, these parameters include the passband edge frequency f_np, the stopband edge frequency f_ns, the passband ripple R_p, and the stopband attenuation R_s. For bandpass and bandstop configurations, the parameters include the lower and upper passband edge frequencies, f_np1 and f_np2, the lower and upper stopband edge frequencies, f_ns1 and f_ns2, the passband ripple R_p, and the stopband attenuation R_s. Frequency values are normalized to the Nyquist frequency, and ripple and attenuation values are in dB.


	Lowpass	Highpass	Bandpass	Bandstop
Butterworth	Order, f_np	Order, f_np	Order, f_np1, f_np2	Order, f_np1, f_np2
Chebyshev Type I	Order, f_np, R_p	Order, f_np, R_p	Order, f_np1, f_np2, R_p	Order, f_np1, f_np2, R_p
Chebyshev Type II	Order, f_ns, R_s	Order, f_ns, R_s	Order, f_ns1, f_ns2, R_s	Order, f_ns1, f_ns2, R_s
Elliptic	Order, f_np, R_p, R_s	Order, f_np, R_p, R_s	Order, f_np1, f_np2, R_p, R_s	Order, f_np1, f_np2, R_p, R_s

The digital filters are designed using the Signal Processing Toolbox's filter design commands butter, cheby1, cheby2, and ellip.

The Frame-based inputs parameter allows you to choose between sample-based and frame-based operation.

Sample-Based Operation

When the check box is not selected (default), the block assumes that the input is a 1-by-N sample vector or M-by-N sample matrix. Each of the N vector elements (or M*N matrix elements) is treated as an independent channel, and the block filters each channel over time.

Frame-Based Operation

When the Frame-based inputs check box is selected, the block assumes that the input is an M-by-N frame matrix. Each of the N frames in the matrix contains M sequential time samples from an independent signal. The Number of channels parameter specifies the number of independent channels (columns), N, in the matrix. The block filters each channel independently over time. Frame-based operation provides substantial increases in throughput rates, at the expense of greater model latency.

In both sample-based and frame-based modes, the output is the same size as the input.

Dialog Box

The parameters displayed in the dialog box vary for different design/band combinations. Not all of the parameters shown above (and listed below) are visible in the dialog box at any one time.

Design method: The filter design method: Butterworth, Chebyshev type I, Chebyshev type II, or Elliptic.
Filter type: The type of filter to design: Lowpass, Highpass, Bandpass, or Bandstop.
Filter order: The order of the filter for lowpass and highpass configurations. For bandpass and bandstop configurations, the length of the final filter is twice this value.
Passband edge frequency: The normalized passband edge frequency for the highpass and lowpass configurations of the Butterworth, Chebyshev type I, and elliptic designs.
Lower passband edge frequency: The normalized lower passband frequency for the bandpass and bandstop configurations of the Butterworth, Chebyshev type I, and elliptic designs.
Upper passband edge frequency: The normalized upper passband frequency for the bandpass and bandstop configurations of the Butterworth, Chebyshev type I, or elliptic designs.
Stopband edge frequency: The normalized stopband edge frequency for the highpass and lowpass band configurations of the Chebyshev type II design.
Lower stopband edge frequency: The normalized lower stopband frequency for the bandpass and bandstop configurations of the Chebyshev type II design.
Upper stopband edge frequency: The normalized upper stopband frequency for the bandpass and bandstop filter configurations of the Chebyshev type II design.
Passband ripple: The passband ripple, in dB, for the Chebyshev type I and elliptic designs.
Stopband ripple: The stopband attenuation, in dB, for the Chebyshev type II and elliptic designs.
Frame-based inputs: Selects frame-based operation.
Number of channels: For frame-based operation, the number of columns (channels) in the input matrix.

References

Antoniou, A. Digital Filters: Analysis, Design, and Applications. 2nd ed. New York, NY: McGraw-Hill, 1993.

Oppenheim, A. V. and R. W. Schafer. Discrete-Time Signal Processing. Englewood Cliffs, NJ: Prentice Hall, 1989.

Proakis, J. and D. Manolakis. Digital Signal Processing. 3rd ed. Englewood Cliffs, NJ: Prentice-Hall, 1996.