将加速度转换为位移记录时，将离散傅立叶变换与二重积分技术进行比较附matlab代码.zip

function y1 = ASD(y0,dt, indIn, indOut,varargin) % y1 = ASD(y0,dt, indIn, indOut,varargin) converts accleration, displacement % of velocity data into another of these three types. % % Inputs: % * y0: double: [1xN] or [Nx1] vector of the acceleration, displacement or % velocity response of a structure % * dt: double [1x1]: time step (seconds) % * indIn: double [1x1]: either 3 (acceleration) 2 (velocity) or 1 % (displacement). It corresponds to the type of data usd in y0. If y0 is % an acceleration record, then indIn should be 1 % * indOut: double [1x1]: either 1, 2 or 3. If one wish to transform an % acceleration record (indIn = 3) into a dispalcement record, then indOut % should be indOut = 1 % *varargin: % |x| 'zeropadding': double [1x1], either 1 (with zero padding) or % 0 (without zero padding) for the fft method) % |x|'method': string: either 'fft' or 'TD' % |x|'window': type of window for the fft method (rectwin by % default) % % % Outputs: % *y1: double: [1xN] or [Nx1] vector of the acceleration, displacement or % velocity response of the structure, obtained from y0. If indOut = 1, y1 % is a displacement. If indOut = 2, y1 is a velocity and if indOUt = 3, % y1 is an acceleration. % % Author: E. Cheynet - UiB - last modified: 2020-02-16 % % see also cumtrapz fft fftshift detrend %% Inputparseer p = inputParser(); p.CaseSensitive = false; p.addOptional('zeropadding',1); p.addOptional('method','fft'); p.addOptional('window','rectwin'); % by default: no windowing p.parse(varargin{:}); %%%%%%%%%%%%%%%%%%%%%%%%%% zeropadding = p.Results.zeropadding ; % zero padding: either 1 or 0 method = p.Results.method; % either 'fft' or 'TD' windowName = p.Results.window; % type of windowing used (none by default) %% Main part if indIn >3 || indIn <1 || indOut > 3 || indOut<1 error(' ''indOut'' and ''indOut'' must be either 1 ,2 or ') end if strcmpi(method,'fft') y0 = y0(:); % Forced to be a column vector N0 = numel(y0); if zeropadding==1 N = 2^nextpow2(N0); y0 = [y0;zeros(N-N0,1)]; elseif zeropadding==0 N = N0; else error(' ''zeropadding'' must be either ''1'' or ''0'' '); end tmax = dt.*N; % max duration f0 = 1/tmax; % lowest frequency recorded fs = 1/dt; % sampling frequency y0 = window(windowName,N).*y0; % Windowing of the time series % Use of the two-sided FFT f = [-fs/2:f0:fs/2-f0]'; Y = fftshift(fft(y0)); Y(f~=0) = Y(f~=0).*(2*pi*1i.*f(f~=0)).^(indOut-indIn); Y(f==0) = 0; y1 = real(ifft(ifftshift(Y))); if zeropadding==1, y1 = y1(1:N0); end elseif strcmpi(method,'TD') % IF fft is not used N = numel(y0); t = (0:N-1).*dt; if indIn-indOut == 2 % acc to displ with double integration method y1 = detrend(cumtrapz(t,y0)); y1 = detrend(cumtrapz(t,y1)); elseif indIn-indOut == 1 % acc to vel or vel to displ y1 = detrend(cumtrapz(t,y0)); elseif indIn-indOut == 0 y1 = y0; elseif indIn-indOut == -2 % displ to acc y0 = [0;0;y0(:)]; % pad with zero y1 = diff(y0,2)./dt.^2; elseif indIn-indOut == -1 % displ to vel or vel to acc y0 = [0;y0(:)]; % pad with zero y1 = diff(y0)./dt; else error('unknown error') end else error(' The method must be either ''fft'' or ''TD'' '); end return