[B,A] = butter(5,0.5/(Fs/2),'high');

clear clc home load ACCfilter load ElapsedTime %definitions Fs = 32; t = ElapsedTime; % sampling range yno = ACCfilter; [B,A] = butter(5,0.5/(Fs/2),'high'); y = filter(B,A,yno); %plot in time domain subplot(2, 1, 1); % plot(t, y,'r'); grid on % plot with grid title('Acceleration vs Time') xlabel('Time (s)'); % time expressed in seconds hold on plot(t,yno,'g') %FFT section Y = fft(y); % compute Fourier transform enter n = length(y); % Amp = abs(Y )/n; % absolute value and normalize %if n is even the fft will be symmetric %the first n/2 + 1 points will be unique and the rest are symmetrically %redundant. Point 1 is the DC component. Point n/2 +1 is the nyquist %component %1 2 3 4 5 6 7 8 %4 3 2 1 0 -1 -2 -3 % if n is odd the nyquist component is not evaluated. The number of unique % points is (n+1)/2 %1 2 3 4 5 6 7 8 9 %5 4 3 2 1 -1 -2 -3 -4 %create the frequency axis NumUniquePts=ceil((n+1)/2); % the positive frequencies freq=(0:NumUniquePts-1)*Fs/(n-1); %mirror the positive frequencies but make them negative then adjust some things %to look right freq2= -1*freq(end:-1:1); if mod (n,2)==0 freq2(1)=[]; end freq3=[freq, freq2]; freq3'; size(freq3); if mod(n,2)==1 freq3(n+1)=[]; end if mod(n,2)==0 freq3(n)=[]; end %store freq3 in a column freq3c = freq3'; %plot acceleration in frequency domain subplot(2, 1, 2); plot(freq, Amp(1 : NumUniquePts),'b.'); grid on % plot amplitude spectrum enter xlabel('Frequency (Hz)'); % 1 Herz = number of cycles per second enter ylabel('Acceleration Amplitude'); % amplitude as function of frequency enter %Omega Arithmetic to convert acceleration to velocity %uses complete frequency vector from above V=Y./(2*pi*freq3c*1i); %result=[freq3',Y',G'] %use this line to look at freq3, Y, and G next to each other % Get rid of infinities resulting from divisions by zero to prepare for % ifft V(1)=[1]; if mod(n,2)==0 V(n)=[1]; end %go back to time domain with the velocity inversedVno=ifft(V); [B,A] = butter(5,0.5/(Fs/2),'high'); inversedV = filter(B,A,inversedVno); figure plot(t,real(inversedV),'b') hold on title('Velocity vs Time'); % amplitude as function of time xlabel('Time (s)'); % time expressed in seconds ylabel('FFT Velocity'); % FsdirV=100; %sampling rate % dtdirV = 1/Fs; % % etdirV = 3; % end of the interval % tdirV = 0 : dt : et; % sampling range % ydirV = -cos(4*pi*t)/(2*pi);% define the signal % plot(t,ydirV,'g') %Omega Arithmetic to convert velocity to displacement D=V./(2*pi*freq3c*1i); % Get rid of infinities resulting from divisions by zero to prepare for % ifft D(1)=[1]; if mod(n,2)==0 D(n)=[1]; end %go back to time domain with the displacement inversedDno=ifft(D); [B,A] = butter(5,0.5/(Fs/2),'high'); inversedD = filter(B,A,inversedDno);