AUDFILTERS - Generates filters equidistantly spaced on auditory frequency scales

Usage

[g,a,fc,L]=audfilters(fs,Ls);
[g,a,fc,L]=audfilters(fs,Ls,...);

Input parameters

Output parameters

Description

[g,a,fc,L]=audfilters(fs,Ls) constructs a set of filters g that are equidistantly spaced on a perceptual frequency scale (see freqtoaud) between 0 and the Nyquist frequency. The filter bandwidths are proportional to the critical bandwidth of the auditory filters audfiltbw. The filters are intended to work with signals with a sampling rate of fs. The signal length Ls is mandatory, since we need to avoid too narrow frequency windows.

By default the ERB scale is chosen but other frequency scales are possible. Currently supported scales are 'erb', 'erb83', 'bark', 'mel' and 'mel1000', and can be changed by passing the associated string as an optional parameter. See freqtoaud for more information on the supported frequency scales.

By default, a Hann window shape is chosen as prototype frequency response for all filters. The prototype frequency response can be changed by passing any of the window types from firwin or freqwin as an optional parameter.

[g,a,fc,L]=audfilters(fs,Ls,fmin,fmax) constructs a set of filters between fmin and fmax. The filters are equidistantly spaced on the selected frequency scale. One additional filter will be positioned at the 0 and Nyquist frequencies each, so as to cover the full range of positive frequencies. The values of fmin and fmax can be instead specified using a key/value pair as:

[g,a,fc,L]=audfilters(fs,Ls,...,'fmin',fmin,'fmax',fmax)

Default values are fmin=0 and fmax=fs/2.

For more details on the construction of the filters, please see the given references.

Downsampling factors

The integer downsampling rates of the channels must all divide the signal length, filterbank will only work for input signal lengths being multiples of the least common multiple of the downsampling rates. See the help of filterbanklength. The fractional downsampling rates restrict the filterbank to a single length L=Ls.

[g,a]=audfilters(...,'regsampling') constructs a non-uniform filterbank with integer subsampling factors.

[g,a]=audfilters(...,'uniform') constructs a uniform filterbank where the integer downsampling rate is the same for all the channels. This results in most redundant representation which produces nice plots.

[g,a]=audfilters(...,'fractional') constructs a filterbank with fractional downsampling rates a. This results in the least redundant system.

[g,a]=audfilters(...,'fractionaluniform') constructs a filterbank with fractional downsampling rates a, which are uniform for all filters except the "filling" low-pass and high-pass filters which can have different fractional downsampling rates. This is useful when uniform subsampling and low redundancy at the same time are desirable.

Additional parameters

audfilters accepts the following optional parameters:

Examples:

In the first example, we construct a highly redudant uniform filterbank on the ERB scale and visualize the result:

[f,fs]=greasy;  % Get the test signal
[g,a,fc,L]=audfilters(fs,length(f),'uniform','M',100);
c=filterbank(f,g,a);
plotfilterbank(c,a,fc,fs,90,'audtick');

In the second example, we construct a non-uniform filterbank with fractional sampling that works for this particular signal length, and test the reconstruction. The plot displays the response of the filterbank to verify that the filters are well-behaved both on a normal and an ERB-scale. The second plot shows frequency responses of filters used for analysis (top) and synthesis (bottom).

[f,fs]=greasy;  % Get the test signal
L=length(f);
[g,a,fc]=audfilters(fs,L,'fractional');
c=filterbank(f,{'realdual',g},a);
r=2*real(ifilterbank(c,g,a));
norm(f-r)

% Plot the response
figure(1);
subplot(2,1,1);
R=filterbankresponse(g,a,L,fs,'real','plot');

subplot(2,1,2);
semiaudplot(linspace(0,fs/2,L/2+1),R(1:L/2+1));
ylabel('Magnitude');

% Plot frequency responses of individual filters
gd=filterbankrealdual(g,a,L);
figure(2);
subplot(2,1,1);
filterbankfreqz(gd,a,L,fs,'plot','linabs','posfreq');

subplot(2,1,2);
filterbankfreqz(g,a,L,fs,'plot','linabs','posfreq');