% Script to construct a first derivative approximation filter
% using FFT methods.

clear
match   = 170;
transit = 84;
nfilt   = 25;
alpha   = 6.2;

% FFT properties
blksize = 1000;
nhfilt  = floor(nfilt/2);

% Build the ideal spectrum for a derivative operator
spect = zeros(1,blksize);
for term=2:blksize/2
  ideal(term)=((term-1)*pi*2/blksize);
  spect(term) = -j * ideal(term);
  spect(blksize+2-term)=-spect(term);
end

% Window to desired spectrum band
wind = platcos(match,transit,blksize);
spect = spect .* wind;
%figure(1)
%plot(1:1000,abs(spect(1:1000)),'k')
%title('Spectrum to fit')
%pause(1.5)

% Design filter
seq = real(ifft(spect));
filter(1:nhfilt)=seq(blksize+1-nhfilt:blksize);
filter(nhfilt+1:nfilt)=seq(1:nhfilt+1);
wind = kaiser(nfilt,alpha);
filter = filter' .* wind

% Verify design
[actual,w] = freqz(filter,[1],500);
actual = abs(actual');
figure(1)
plot(1:200,ideal(1:200),'g',1:500,actual(1:500),'b')
title('Compare designed filter to ideal')
%figure(2)
%diff=actual-ideal;
%plot(1:100,diff(1:100),'r')
%title('Fit error')