CQTFILTERS - CQT-spaced filters

Usage

[g,a,fc]=cqtfilters(fs,fmin,fmax,bins,Ls,varargin);

Input parameters

Output parameters

Description

[g,a,fc]=cqtfilters(fs,fmin,fmax,bins,Ls) constructs a set of band-limited filters g which cover the required frequency range fmin-fmax with bins filters per octave starting at fmin. All filters have (approximately) equal \(Q=f_c/f_b\), hence constant-Q. The remaining frequency intervals not covered by these filters are captured by two additional filters (low-pass, high-pass). The signal length Ls is mandatory, since we need to avoid too narrow frequency windows.

By default, a Hann window on the frequency side is chosen, but the window can be changed by passing any of the window types from firwin as an optional parameter. Run getfield(getfield(arg_firwin,'flags'),'wintype') to get a cell array of window types available.

Because the downsampling rates of the channels must all divide the signal length, filterbank will only work for multiples of the least common multiple of the downsampling rates. See the help of filterbanklength.

[g,a]=cqtfilters(...,'regsampling') constructs a non-uniform filter bank. The downsampling rates are constant in the octaves but can differ among octaves. This approach was chosen in order to minimize the least common multiple of a, which determines a granularity of admissible input signal lengths.

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

[g,a]=cqtfilters(...,'fractional') constructs a filter bank with fractional downsampling rates a. The rates are constructed such that the filter bank can handle signal lengths that are multiples of L, so the benefit of the fractional downsampling is that you get to choose the value returned by filterbanklength. This results in the least redundant system.

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

The filters are intended to work with signals with a sampling rate of fs.

cqtfilters accepts the following optional parameters:

Examples:

In the first example, we construct a highly redundant uniform filter bank and visualize the result:

[f,fs]=greasy;  % Get the test signal
[g,a,fc]=cqtfilters(fs,100,fs,32,length(f),'uniform');
c=filterbank(f,g,a);
plotfilterbank(c,a,fc,fs,90,'audtick');

In the second example, we construct a non-uniform filter bank with fractional sampling that works for this particular signal length, and test the reconstruction. The plot displays the response of the filter bank to verify that the filters are well-behaved both on a normal and an log 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]=cqtfilters(fs,100,fs,8,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');