The following is a working code that uses 32-component polyphase decomposition of the associated 32-channel anslysis and synthesis filterbanks. As I have already commented, the speed gain is not dramatic in this cae due to short signal and filter lengths. However further architectural improvements as well as coding optimizaiton can provide better results.

% S0 - Load the prototype lowpass filter impulse response h0[n]:
% --------------------------------------------------------------
load h2.mat;         % h[n] is the prototype lowpass filter of length 512
L = length(h);

% S1 - Create the 32 x 512 filter-bank hha[k,n] by cosine modulation from protoype :
% ----------------------------------------------------------------------------------
numbands = 32;                 % number of banks (channels)
n=0:L-1;

hha=zeros(numbands,L);         % bank of filters hha[k,n] = 32 x 512 array.
for k=0:1:numbands-1 
   hha(k+1,:) = h.*cos( ( (2*k+1)*pi*(n-16) ) / (2*numbands) );
end


% S2 - Create the 32-polyphase components hhap[k,m,n] , for each one of 32 analysis filters hha[k,n]:
% ---------------------------------------------------------------------------------------------------
numpoly = numbands;             % polyphase component number = decimation ratio = number of channels
hhap = zeros(numbands,numpoly, L/numpoly);  % hhap = 32 x 32 x 512/32 , 3D ANALYSIS filter bank array

M = numpoly;                    % polyphase system decimation ratio
for k=1:numbands
    for m = 1:numpoly
        hhap(k,m,:) = hha(k,m:M:end);       % create the m-th polyphase component of k-th channel filter
    end
end


% S3 - Design the 32 x 512  synthesis (cmplementary) filter bank :
% ----------------------------------------------------------------
numbands = 32;                  % number of banks
n=0:L-1;
hhs = zeros(numbands,L);        % bankd of filters
for k=0:1:numbands-1 
   hhs(k+1,:) = h.*cos( ( (2*k+1)*pi*(n+16) ) / (2*numbands) );
end


% S4 - Obtain the 32-polyphase components hhsp[k,m,n] , for each one of 32 synthesis filters hhs[k,n]:
% ----------------------------------------------------------------------------------------------------
numpoly = numbands;             % polyphase component number = decimation ratio = number of channels
hhsp = zeros(numbands,numpoly, L/numpoly);  % hhap = 32 x 32 x 512/32 , 3D ANALYSIS filter bank array
M = numpoly;                    % polyphase system decimation ratio
for k=1:numbands
    for m = 1:numpoly
        hhsp(k,m,:) = hhs(k,m:M:end);       % create the m-th polyphase component of k-th channel filter
    end
end


% S5 - Generate the test input signal
% -----------------------------------
N = 2*1024;
wav_in = cos(0.01791*pi*[0:N-1]);        % pure sine tone

% S6 - Apply test signal to the filterbank,  using the filterband approach :
% --------------------------------------------------------------------------
yyd = zeros( numbands, floor(N/numbands));   % decimated outputs..
M = numbands;
for k=1:1:numbands
    %temp = conv( wav_in,hha(k,:));          % THESE STEPS are now implemented as a POLYPHASE filter    
   
    temp = conv([wav_in(1:M:end),0] , hhap(k,1,:));
    for m=2:M
        temp = temp + conv([0,wav_in(M-m+2:M:end)],hhap(k,m,:));   
    end
    yyd(k,:) = temp(L/(2*M)+1 : L/(2*M)+N/numbands);
end

% S7 - Apply synthesis filterbanks on the decimated signal :
% ----------------------------------------------------------
ys = zeros(1, N);

for k=1:numbands
    temp = zeros(1, N+L-1);
    for m = 1:numpoly
        temp(m:numbands:end-31) = conv( yyd(k,:) , hhsp(k,m,:) );
    end
    
    ys = ys + temp(L/2+1:L/2+N);    
end
ys = numbands*ys;
 

% SX - DISPLAY RESULTS:
% ---------------------
L = length(h);
figure,subplot(2,1,1)
stem([0:L-1],h);title('The Prototype Lowpass Filter');
subplot(2,1,2)
plot(linspace(-1,1,4*L),20*log10(abs(fftshift(fft(h,4*L)))));
grid on;

figure
plot(linspace(-1,1,4*L),20*log10(abs(fftshift(fft(hha(1,:),4*L)))));
hold on
for k=2:numbands
    plot(linspace(-1,1,4*L),20*log10(abs(fftshift(fft(hha(k,:),4*L)))));
end
title('32 CHANNEL FILTERBANK');

figure,subplot(2,1,1)
plot(wav_in);title('input signal')
subplot(2,1,2)
plot(linspace(-1,1,4*N),20*log10(abs(fftshift(fft(wav_in,4*N)))));

figure,subplot(2,1,1)
plot(ys);title('Synthesized Back');
subplot(2,1,2)
plot(linspace(-1,1,4*N),20*log10(abs(fftshift(fft(ys,4*N)))));

The following is a working code that uses 32-component polyphase decomposition of the associated 32-channel anslysis and synthesis filterbanks. As I have already commented, the speed gain is not dramatic in this cae due to short signal and filter lengths. However further architectural improvements as well as coding optimizations can provide better results.

% S0 - Load the prototype lowpass filter impulse response h0[n]:
% --------------------------------------------------------------
load h2.mat;         % h[n] is the prototype lowpass filter of length 512
L = length(h);

% S1 - Create the 32 x 512 analysis filter-bank hha[k,n] by cosine modulation from protoype :
% -----------------------------------------------------------------------------------------
numbands = 32;                 % number of banks (channels)
n=0:L-1;

hha=zeros(numbands,L);         % bank of filters hha[k,n] = 32 x 512 array.
for k=0:1:numbands-1 
   hha(k+1,:) = h.*cos( ( (2*k+1)*pi*(n-16) ) / (2*numbands) );
end


% S2 - Create the 32-polyphase components hhap[k,m,n] , for each one of 32 analysis filters hha[k,n]:
% ---------------------------------------------------------------------------------------------------
numpoly = numbands;             % polyphase component number = decimation ratio = number of channels
hhap = zeros(numbands,numpoly, L/numpoly);  % hhap = 32 x 32 x 512/32 , 3D ANALYSIS filter bank array

M = numpoly;                    % polyphase system decimation ratio
for k=1:numbands
    for m = 1:numpoly
        hhap(k,m,:) = hha(k,m:M:end);       % create the m-th polyphase component of k-th channel filter
    end
end


% S3 - Design the 32 x 512  synthesis (complementary) filter bank :
% -----------------------------------------------------------------
numbands = 32;                  % number of banks
n=0:L-1;
hhs = zeros(numbands,L);        % bank of filters
for k=0:1:numbands-1 
   hhs(k+1,:) = h.*cos( ( (2*k+1)*pi*(n+16) ) / (2*numbands) );
end


% S4 - Obtain the 32-polyphase components hhsp[k,m,n] , for each one of 32 synthesis filters hhs[k,n]:
% ----------------------------------------------------------------------------------------------------
numpoly = numbands;             % polyphase component number = interpolation ratio = number of channels
hhsp = zeros(numbands,numpoly, L/numpoly);  % hhap = 32 x 32 x 512/32 , 3D ANALYSIS filter bank array
M = numpoly;                    % polyphase system decimation ratio
for k=1:numbands
    for m = 1:numpoly
        hhsp(k,m,:) = hhs(k,m:M:end);       % create the m-th polyphase component of k-th channel filter
    end
end


% S5 - Generate the test input signal
% -----------------------------------
N = 2*1024;
wav_in = cos(0.01791*pi*[0:N-1]);        % pure sine tone

% S6 - Apply test signal to the filterbank: ANALYSIS STAGE :
% -----------------------------------------------------------
yyd = zeros( numbands, floor(N/numbands));   % decimated outputs..
M = numbands;
for k=1:1:numbands       
    temp = conv([wav_in(1:M:end),0] , hhap(k,1,:));
    for m=2:M
        temp = temp + conv([0,wav_in(M-m+2:M:end)],hhap(k,m,:));   
    end
    yyd(k,:) = temp(L/(2*M)+1 : L/(2*M)+N/numbands);
end

% S7 - Apply SYNTHESIS filterbank on the decimated signal :
% ---------------------------------------------------------
ys = zeros(1, N);

for k=1:numbands
    temp = zeros(1, N+L-1);
    for m = 1:numpoly
        temp(m:numbands:end-31) = conv( yyd(k,:) , hhsp(k,m,:) );
    end
    
    ys = ys + temp(L/2+1:L/2+N);    
end
ys = numbands*ys;
 

% SX - DISPLAY RESULTS:
% ---------------------
L = length(h);
figure,subplot(2,1,1)
stem([0:L-1],h);title('The Prototype Lowpass Filter');
subplot(2,1,2)
plot(linspace(-1,1,4*L),20*log10(abs(fftshift(fft(h,4*L)))));
grid on;

figure
plot(linspace(-1,1,4*L),20*log10(abs(fftshift(fft(hha(1,:),4*L)))));
hold on
for k=2:numbands
    plot(linspace(-1,1,4*L),20*log10(abs(fftshift(fft(hha(k,:),4*L)))));
end
title('32 CHANNEL FILTERBANK');

figure,subplot(2,1,1)
plot(wav_in);title('input signal')
subplot(2,1,2)
plot(linspace(-1,1,4*N),20*log10(abs(fftshift(fft(wav_in,4*N)))));

figure,subplot(2,1,1)
plot(ys);title('Synthesized Back');
subplot(2,1,2)
plot(linspace(-1,1,4*N),20*log10(abs(fftshift(fft(ys,4*N)))));