3-Stage Filter wit 1 Bit Input for a Delta-Sigma Modulator (MATLAB->VHDL)

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%CASCADE of a CIC Desimation Filter and a (polyphase) FIR
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% CIC Filter specifications
D = 1; % Differential delays in the filter.
Nsecs = 4; % Filter sections
R = 128; % Decimation factor
iwl = 1; %input word length
%owl = 26;%output word length

hcic = dsp.CICDecimator('DecimationFactor',R,'DifferentialDelay',D,'NumSections',Nsecs); %
% lock object with desired input
step(hcic , fi(zeros(128,1),0,1,0));
info(hcic)

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%plot and analyze the theoretical magnitude response of the CIC filter
Fs_in = 1e6;
h2 = fvtool(hcic,'Fs',Fs_in);
h2.Color = 'White';


%Normalizing the CIC filter response to have 0 dB gain at DC 
h2.NormalizeMagnitudeto1 = 'on';


%the CIC has about -0.xx dB of attenuation (droop) at xx Hz, 
%which is within the bandwidth of interest. 
%A CIC filter is essentially a cascade of boxcar filters and therefore has a sinc-like response 
%which causes the droop. This droop needs to be compensated by the FIR filter in the next stage.

%axis([0 2 -2 0]);

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% FIR Filter specifications
Fs     = 8e3; % Sampling frequency 1024kHz/128
Apass  = 0.1;     % dB
Astop  = 100;       % dB
Fpass  = 1e3;     % Hz passband-edge frequency
Fstop  = 2e3;    % Hz stopband-edge frequency

% Design decimation filter. D and Nsecs have been defined above as the
% differential delay and number of sections, respectively.
hcfir = dsp.CICCompensationDecimator('SampleRate',Fs,...
    'CICRateChangeFactor',R,'CICNumSections',Nsecs,...
    'CICDifferentialDelay',D,'PassbandFrequency',Fpass,...
    'StopbandFrequency',Fstop,'PassbandRipple',Apass,...
    'StopbandAttenuation',Astop);


info(hcfir)

%Cascading the CIC with the inverse sinc filter we can see if we eliminated 
%the passband droop caused by the CIC.

hcas1 = cascade(hcic,hcfir);
h2 = fvtool(hcic,hcfir,hcas1,'Fs',[Fs_in,Fs_in/128,Fs_in]);
h2.Color = 'White';
h2.NormalizeMagnitudeto1 = 'on';
%axis([0 2 -2 0.8]);
legend(h2,'hcic','hcfir','cascade');

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N = 29;       % 30 taps
Fs = 4e3;  % 4 kHz
Fpass = 1e3;
Fstop = 1.6e3;

d = fdesign.decimator(2,'lowpass','N,Fp,Fst',N,Fpass,Fstop,Fs);
% Give more weight to passband
hpfir = design(d,'equiripple','Wpass',2,'SystemObject',true);


hpfir.FullPrecisionOverride = false;
hpfir.OutputDataType = 'custom';
hpfir.RoundingMethod = 'nearest';
hpfir.OverflowAction = 'Saturate';
hpfir.CustomOutputDataType = numerictype([],29,-12);
%We can use the info method to view the filter details.

info(hpfir)

hcas = cascade(hcic,hcfir,hpfir);
h3 = fvtool(hcas,'Fs',Fs_in);
h3.Color = 'White';
h3.NormalizeMagnitudeto1 = 'on';
h3.NumberofPoints = 8192*3;
axis([0 50 -250 50]);  % Zoom-in

%hdlfilterserialinfo(hcas,'InputDataType',numerictype(1,1))%display valid serial partitions