cascade

Cascade digital filters

Since R2026a

Syntax

dOut = cascade(d1,d2,...,dn)

dOut = cascade(___,SampleRate=Fs)

Description

dOut = cascade(d1,d2,...,dn) cascades n digital filters into a digital filter cascade, dOut. You can cascade between 2 and 15 digitalFilter objects.

dOut = cascade(___,SampleRate=Fs) specifies the sample rate for the cascaded filter.

Examples

Cascade Lowpass and Bandstop IIR Filters

Design a lowpass IIR filter with passband and stopband frequencies of 0.65π rad/sample and 0.80π rad/sample, respectively. The passband ripple is 1 dB and the stopband attenuation is 50 dB. Plot the filter response.

d1 = designfilt("lowpassiir", ...
    PassbandFrequency=0.65,StopbandFrequency=0.80, ...
    PassbandRipple=1,StopbandAttenuation=50);
freqz(d1)

Design a bandstop IIR filter with passband ripples of 1 dB and stopband attenuation of 50 dB. The passband frequencies are 0.25π rad/sample and 0.34π rad/sample. The stopband frequencies are 0.36π rad/sample and 0.45π rad/sample. Plot the filter response.

d2 = designfilt("bandstopiir", ...
    PassbandFrequency1=0.25,StopbandFrequency1=0.34, ...
    StopbandFrequency2=0.36,PassbandFrequency2=0.45, ...
    PassbandRipple1=1,StopbandAttenuation=50, ...
    PassbandRipple2=1);
freqz(d2)

Cascade the lowpass IIR and bandstop IIR filters to form a cascaded filter. Plot the filter response.

d3Norm = cascade(d1,d2)

d3Norm = 
 digitalFilter cascade with properties:

   Stages:
                 Stage1: [1×1 digitalFilter]
                 Stage2: [1×1 digitalFilter]

   Specifications:
    NormalizedFrequency: 1

 Use filterAnalyzer to visualize filter
 Use filter to filter data

freqz(d3Norm)

Set the sample rate to 20 Hz and cascade the lowpass IIR and bandstop IIR filters to form a cascaded filter.

Fs = 20;
d3Freq = cascade(d1,d2,SampleRate=Fs)

d3Freq = 
 digitalFilter cascade with properties:

   Stages:
                 Stage1: [1×1 digitalFilter]
                 Stage2: [1×1 digitalFilter]

   Specifications:
    NormalizedFrequency: 0
             SampleRate: 20

 Use filterAnalyzer to visualize filter
 Use filter to filter data

Input Arguments

d — Digital filter

digitalFilter object

Digital filter, specified as a digitalFilter object. Use designfilt to generate a digital filter based on frequency-response specifications.

Example: d = designfilt("lowpassiir",FilterOrder=3,HalfPowerFrequency=0.5) specifies a third-order Butterworth filter with normalized 3 dB frequency 0.5π rad/sample.

Fs — Sample rate of cascaded filter

"auto" (default) | "normalized" | positive scalar

Sample rate of the cascaded filter, specified as one of these:

• "auto" — cascade automatically sets the sample rate of the cascaded filter.

  • If all the digital filter inputs use normalized frequency, then cascade sets all the stages of dOut to use normalized frequency.

  • If some of the digital filter inputs have a common sample rate of F_s Hz and the rest of them use normalized frequency, then cascade uses F_s to set the sample rate of dOut.

  • If at least two of the digital filter inputs have a different sample rate, cascade errors out.

• "normalized" — cascade sets all the stages of dOut to use normalized frequency.

• Positive scalar — cascade uses the value specified in this argument to set the sample rate of dOut, in Hz.

Data Types: char | string | single | double

Output Arguments

dOut — Digital filter cascade

digitalFilter object

Digital filter cascade, returned as a digitalFilter object.

More About

Digital Filter Cascades

A digital filter can be represented as a single stage or as a cascade of multiple stages. Accordingly, a digitalFilter object can represent either a single-stage digital filter or a cascade of digital filters (digital filter cascade).

Assume these filters: a bandstop FIR filter d1, bandpass IIR filter d2, and a Hilbert transformer FIR filter d3. The following block diagram represents the digital filter cascade d, which has three stages: d1, d2, and d3.

To create a digital filter cascade, use the cascade function. For example, the following code creates a digital filter cascade with stages d1, d2, and d3 from their corresponding digitalFilter objects.

d = cascade(d1,d2,d3);

You can cascade filters in multiple hierarchy levels. That way, you can get a multi-level digital filter cascade. In a multi-level digital filter cascade, each stage can have multiple substages. For example, the bandpass IIR filter d2 can be represented as a cascade of a lowpass IIR filter d21 and a highpass IIR filter d22. The following code creates a two-level cascaded filter with stages d1, d2, and d3, where d2 is a digital filter cascade with stages d21 and d22. All the inputs are digitalFilter objects.

d2 = cascade(d21,d22);
d = cascade(d1,d2,d3);

Version History

Introduced in R2026a