Filter Requirements and Specification

Filter design is the process of creating the filter coefficients to meet specific filtering requirements. Filter implementation involves choosing and applying a particular filter structure to those coefficients. Only after both design and implementation have been performed can data be filtered. The following chapter describes filter design and implementation in Signal Processing Toolbox software.

The goal of filter design is to perform frequency dependent alteration of a data sequence. A possible requirement might be to remove noise above 200 Hz from a data sequence sampled at 1000 Hz. A more rigorous specification might call for a specific amount of passband ripple, stopband attenuation, or transition width. A very precise specification could ask to achieve the performance goals with the minimum filter order, or it could call for an arbitrary magnitude shape, or it might require an FIR filter. Filter design methods differ primarily in how performance is specified.

To design a filter, the Signal Processing Toolbox software offers two approaches: object-oriented and non-object oriented. The object-oriented approach first constructs a filter specification object, fdesign, and then invokes an appropriate design method. To illustrate the object-oriented approach, design and implement a 5–th order lowpass Butterworth filter with a 3–dB frequency of 200 Hz. Assume a sampling frequency of 1 kHz. Apply the filter to input data.

Fs=1000; %Sampling Frequency
time = 0:(1/Fs):1; %time vector
% Data vector
x = cos(2*pi*60*time)+sin(2*pi*120*time)+randn(size(time));
d=fdesign.lowpass('N,F3dB',5,200,Fs); %lowpass filter specification object
% Invoke Butterworth design method
Hd=design(d,'butter');
y=filter(Hd,x);

The non-object oriented approach implements the filter using a function such as butter and firpm. All of the non-object oriented filter design functions operate with normalized frequencies. Convert frequency specifications in Hz to normalized frequency to use these functions. The Signal Processing Toolbox software defines normalized frequency to be in the closed interval [0,1] with 1 denoting π radians/sample. For example, to specify a normalized frequency of π/2 radians/sample, enter 0.5.

To convert from Hz to normalized frequency, multiply the frequency in Hz by two and divide by the sampling frequency. To design a 5–th order lowpass Butterworth filter with a 3–dB frequency of 200 Hz using the non-object oriented approach, use butter:

Wn = (2*200)/1000; %Convert 3-dB frequency
% to normalized frequency: 0.4*pi rad/sample
[B,A] = butter(5,Wn,'low');
y = filter(B,A,x);

Filter Design and Implementation

IIR Filter Design

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