Skip to content Skip to navigation

OpenStax-CNX

You are here: Home » Content » Low-Pass Fitler Implementation: Filter Specification

Navigation

Recently Viewed

This feature requires Javascript to be enabled.
 

Low-Pass Fitler Implementation: Filter Specification

Module by: Mark Butala. E-mail the author

Filter Specification

Figure 1
Depiction of the filter specifications.
Depiction of the filter specifications. (spec.png)
Table 1: Filter specifications
f p f p 0.1
f s f s 0.12
δ p δ p 0.5 dB
δ s δ s -60 dB
Δ τ g Δ τ g f ,|f| f p :|Δ τ g |9 f f f p Δ τ g 9

Please refer to Pictoralial filter specification for a pictorial description of how the various filter constraints correspond to the frequency response of a low-pass filter. Note that the Pictoralial filter specification does not imply that the system response must be equiripple. The constraints on the system response, to be discussed shortly, are on the maximum allowable peak errors. However, in general, an equiripple solution to a given filter specification will require the lowest filter order.

The full filter specification is given in filter specifications. The parameters f p f p and f s f s define the end of the pass-band and the beginning of the stop-band, respectively, on the frequency axis that has been normalized to 1. The parameters δ p δ p and δ s δ s define the maximum allowable ripple, in Decibels, in the pass-band and the stop-band, respectively. The parameter f ,|f| f p :|Δ τ g |9 f f f p Δ τ g 9 defines the maximum allowable deviation from a group delay of 9 in the pass-band. The parameter τ g τ g is the group delay of the system and is defined by the following:

τ g ω=dHωd x τ g ω x H ω
(1)

The parameter Δ τ g Δ τ g is defined as:

Δ τ g ω=max τ g ω |ω| ω p min τ g ω |ω| ω p Δ τ g ω ω ω p τ g ω ω ω p τ g ω
(2)

Thus, f ,|f| f p :|Δ τ g |9 f f f p Δ τ g 9 states that the group delay is not allowed to deviate more than 9 samples in the pass-band. A system that has constant group delay will have a phase response that is generalized linear-phase. Thus, deviation from constant group delay is a measure of the deviation of the phase response from linear. The MATLAB command grpdelay computes the group delay of a system as a function of frequency given the filter coefficients a a and b b.

Question:

For which of the three techniques discussed in filtering techniques must we verfiy explicitly that the group delay specification is met? All of them, some of them, or none of them?

Question:

Why do we only specify the filter coefficients for only the positive frequencies? What are we assuming? What does this imply about the coefficients a a and b b of the low-pass filter?

Content actions

Download module as:

Add module to:

My Favorites (?)

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

| A lens I own (?)

Definition of a lens

Lenses

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

What is in a lens?

Lens makers point to 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 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