Sign in

Not a member? | Forgot your Password?

Search Online Books



Search tips

Free Online Books

Free PDF Downloads

A Quadrature Signals Tutorial: Complex, But Not Complicated

Understanding the 'Phasing Method' of Single Sideband Demodulation

Complex Digital Signal Processing in Telecommunications

Introduction to Sound Processing

C++ Tutorial

Introduction of C Programming for DSP Applications

Fixed-Point Arithmetic: An Introduction

Cascaded Integrator-Comb (CIC) Filter Introduction

Chapters

FIR Filter Design Software

See Also

Embedded SystemsFPGA
Chapter Contents:

Search Introduction to Digital Filters

  

Book Index | Global Index


Would you like to be notified by email when Julius Orion Smith III publishes a new entry into his blog?

  

Example Zero-Phase Filter Design

Figure 10.1 shows the impulse response and frequency response of a length 11 zero-phase FIR lowpass filter designed using the Remez exchange algorithm.11.2 The matlab code for designing this filter is as follows:

N = 11;                % filter length - must be odd
b = [0 0.1 0.2 0.5]*2; % band edges
M = [1  1   0   0 ];   % desired band values
h = remez(N-1,b,M);    % Remez multiple exchange design
The impulse response h is returned in linear-phase form, so it must be left-shifted $ (N-1)/2=5$ samples to make it zero phase.

Figure 10.1: Impulse response and frequency response of a length 11 zero-phase FIR lowpass filter. Note that the frequency response is real because the filter is zero phase. Also plotted (in dashed lines) are the desired passband and stopband gains.
\includegraphics[width=\twidth ]{eps/remezexa}

Figure 10.2 shows the amplitude and phase responses of the FIR filter designed by remez. The phase response is zero throughout the passband and transition band. However, each zero-crossing in the stopband results in a phase jump of $ \pi $ radians, so that the phase alternates between zero and $ \pi $ in the stopband. This is typical of practical zero-phase filters.

Figure: Amplitude response and phase response of the length 11 zero-phase FIR lowpass filter in Fig.10.1.
\includegraphics[width=\twidth ]{eps/remezexb}


Previous: Phase in the Stopband
Next: Elementary Zero-Phase Filter Examples

Order a Hardcopy of Introduction to Digital Filters


About the Author: Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.


Comments


No comments yet for this page


Add a Comment
You need to login before you can post a comment (best way to prevent spam). ( Not a member? )