Skip to content Skip to navigation

Connexions

You are here: Home » Content » Multirate Filtering: Filter-Design Exercise in MATLAB

Navigation

Lenses

What is a lens?

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

This content is ...

Affiliated with (What does "Affiliated with" mean?)

This content is either by members of the organizations listed or about topics related to the organizations listed. Click each link to see a list of all content affiliated with the organization.

Also in these lenses

  • Real-Time DSP with MATLAB display tagshide tags

    This module is included inLens: DSP with MATLAB lens
    By: Bhaskar BhattacharyaAs a part of collection:"Digital Signal Processing Laboratory (ECE 420 55x)"

    Comments:

    "Real-Time DSP with MATLAB"

    Click the "Real-Time DSP with MATLAB" link to see all content selected in this lens.

    Click the tag icon tag icon to display tags associated with this content.

Recently Viewed

This feature requires Javascript to be enabled.

Tags

(What is a tag?)

These tags come from the endorsement, affiliation, and other lenses that include this content.

Multirate Filtering: Filter-Design Exercise in MATLAB

Module by: Douglas L. Jones, Swaroop Appadwedula, Matthew Berry, Mark Haun, Jake Janovetz, Michael Kramer, Dima Moussa, Daniel Sachs, Brian Wade. E-mail the authors

User rating (How does the rating system work?)
Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

:
(0 ratings)

Summary: You will design a low-pass finite impulse-response filter using the zero-placement method in MATLAB. The filter can be used as an anti-aliasing and anti-imaging filter in a multirate system.

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

Filter-Design Exercise

Using the zero-placement method, design the FIR filters for the multirate system in Multirate Filtering: Introduction. Recall that the z z-transform of a length- N N FIR filter is a polynomial in z-1 z -1 , and that this polynomial can be factored into N−1 N 1 roots.

Hz= h 0 + h 1 z-1+ h 2 z-2+⋯= z 1 −z-1 z 2 −z-1 z 3 −z-1⋯ H z h 0 h 1 z -1 h 2 z -2 ⋯ z 1 z -1 z 2 z -1 z 3 z -1 ⋯ (1)

Use this relation to design a low-pass filter (for the anti-aliasing and anti-imaging filters of the multirate system) by placing twelve complex zeros on the unit circle at ±3π8 ± 3 8 , ±π2 ± 2 , ±5π8 ± 5 8 , ±3π4 ± 3 4 , ±7π8 ± 7 8 , and ±π ± . This filter that you have just designed will serve for both FIR 1 and FIR 3. For filter FIR 2 (operating at the decimated rate), use four equally-spaced zeros on the unit circle located at ±π4 ± 4 and ±3π4 ± 3 4 . Be sure to adjust the resulting filter coefficients to ensure that the gain does not exceed one at any frequency.

Design your filters by writing a MATLAB script to compute the filter coefficients from the given zero locations. The MATLAB function poly is very useful for this; type help poly in MATLAB for details.

Once you have determined the coefficients of the filters, use MATLAB function freqz to plot the frequency responses. You will find that the frequency response of these filters has a large gain. Adjust the resulting filter coefficients to ensure that the largest frequency gain is less than or equal to one by dividing the coefficients by an appropriate value. Do the frequency responses match your expectations based on the locations of the zeros in the z-plane?

Content actions

Give Feedback:

E-mail the module authors | Rate module ( How does the rating system work?)

Rating system

Ratings

Ratings allow you to judge the quality of modules. If other users have ranked the module then its average rating is displayed below. Ratings are calculated on a scale from one star (Poor) to five stars (Excellent).

How to rate a module

Hover over the star that corresponds to the rating you wish to assign. Click on the star to add your rating. Your rating should be based on the quality of the content. You must have an account and be logged in to rate content.

(0 ratings)

Download:

Module PDF

Add module to:

My Favorites (?)

'My Favorites' is a special kind of lens which you can use to bookmark modules and collections directly in Connexions. 'My Favorites' can only be seen by you, and collections saved in 'My Favorites' can remember the last module you were on. You need a Connexions account to use 'My Favorites'.

| A lens (?)

Definition of a lens

Lenses

A lens is a custom view of Connexions content. You can think of it as a fancy kind of list that will let you see Connexions through the eyes of organizations and people you trust.

What is in a lens?

Lens makers point to Connexions materials (modules and collections), creating a guide that includes their own comments and descriptive tags about the content.

Who can create a lens?

Any individual Connexions member, a community, or a respected organization.

What are tags? tag icon

Tags are descriptors added by lens makers to help label content, attaching a vocabulary that is meaningful in the context of the lens.

| External bookmarks