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)))));