Implementation of FFT and IFFT in Matlab
in [Matlab]
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From: Saurabh on 18 Mar 2010 06:37 Hello I have a rectangular function defined as follows tstop = 10E-3; t=-0.1:dt:0.1; p_i=(1/2)*(sign(t)-sign(t-tstop)); input = figure; plot(t,p_i) rge = 0.05; axis([-rge rge 0 1]); xlabel('time') ylabel('amplitude') title('Input step function') Then I take a Centered FFT [pw,frequencyRange] = centeredFFT(p_i,1/dt); positiveFFT = figure; stem(frequencyRange,abs(pw)); % set(positiveFFT,'Position',[500,500,500,300]) xlabel('Freq (Hz)') ylabel('Amplitude') title('Using the positiveFFT function') grid axis([0 500 0 0.05]); xlabel('frequency') ylabel('amplitude') title('FFT of the input step function') where the function centeredFFT is function [X,freq]=centeredFFT(x,Fs) %this is a custom function that helps in plotting the two-sided spectrum %x is the signal that is to be transformed %Fs is the sampling rate N=length(x); %this part of the code generates that frequency axis if mod(N,2)==0 k=-N/2:N/2-1; % N even else k=-(N-1)/2:(N-1)/2; % N odd end T=N/Fs; freq=k/T; %the frequency axis %takes the fft of the signal, and adjusts the amplitude accordingly X=fft(x)/N; % normalize the data X=fftshift(X); %shifts the fft data so that it is centered Now I want to take IFFT of the function but i do not get back the same input signal orignal_signal = ifft(YfreqDomain); time = ifft(frequencyRange); reterived = figure plot( time,orignal_signal) in Could any one guide in simple terms where I am wrong ? I also tried this orignal_signal = ifft(ifftshift(YfreqDomain)); time = ifft(ifftshift(frequencyRange)); reterived = figure plot( time,orignal_signal) but could not reterive back original signal
From: Rune Allnor on 18 Mar 2010 06:40 On 18 Mar, 11:37, "Saurabh " <saura...(a)student.ethz.ch> wrote: > but could not reterive back original signal Try this: N = 100; x = randn(N,1); X = fft(x); y = real(ifft(X)); d = max(abs(y-x)) d should now contain a very small number (on the order of 1e-15), which means that y == x, except for numerical round-off. Rune
From: Wayne King on 18 Mar 2010 06:54 "Saurabh " <saurabhs(a)student.ethz.ch> wrote in message <hnsvof$2f0$1(a)fred.mathworks.com>... > Hello > > I have a rectangular function defined as follows > tstop = 10E-3; > t=-0.1:dt:0.1; > p_i=(1/2)*(sign(t)-sign(t-tstop)); > input = figure; > plot(t,p_i) > rge = 0.05; > axis([-rge rge 0 1]); > xlabel('time') > ylabel('amplitude') > title('Input step function') > > Then I take a Centered FFT > > [pw,frequencyRange] = centeredFFT(p_i,1/dt); > positiveFFT = figure; > stem(frequencyRange,abs(pw)); > % set(positiveFFT,'Position',[500,500,500,300]) > xlabel('Freq (Hz)') > ylabel('Amplitude') > title('Using the positiveFFT function') > grid > axis([0 500 0 0.05]); > xlabel('frequency') > ylabel('amplitude') > title('FFT of the input step function') > > where the function centeredFFT is > > function [X,freq]=centeredFFT(x,Fs) > %this is a custom function that helps in plotting the two-sided spectrum > %x is the signal that is to be transformed > %Fs is the sampling rate > > N=length(x); > > %this part of the code generates that frequency axis > if mod(N,2)==0 > k=-N/2:N/2-1; % N even > else > k=-(N-1)/2:(N-1)/2; % N odd > end > T=N/Fs; > freq=k/T; %the frequency axis > > %takes the fft of the signal, and adjusts the amplitude accordingly > X=fft(x)/N; % normalize the data > X=fftshift(X); %shifts the fft data so that it is centered > > Now I want to take IFFT of the function but i do not get back the same input signal > > orignal_signal = ifft(YfreqDomain); > time = ifft(frequencyRange); > reterived = figure > plot( time,orignal_signal) > in > > Could any one guide in simple terms where I am wrong ? > > I also tried this > > orignal_signal = ifft(ifftshift(YfreqDomain)); > time = ifft(ifftshift(frequencyRange)); > reterived = figure > plot( time,orignal_signal) > > but could not reterive back original signal Hi, if you want the signal back, why not just % you never give us dt by the way tstop = 10E-3; dt=1e-3; t=-0.1:dt:0.1; p_i=(1/2)*(sign(t)-sign(t-tstop)); Pdft = fft(p_i); p_m=ifft(Pdft,'symmetric'); norm(p_m-p_i) Wayne
From: Saurabh on 18 Mar 2010 07:20 well sorry for missing dt which is 1E-6..... I am new to matlab but the thing is that if I just use the code Pdft = fft(p_i); plot (abs(Pdft)) or Pdft = fft(p_i); stem(abs(Pdft)) I do not get what is expected so I have not used your remaining code since Fourier transform is not right . Because my input signal is a box card function and mathematically i know what its output is going to be that is a sinc function and the way i am using centeredFFT i do get a sync function . I need to use FFT and IFFT in my program so that is why i am looking to how to use them correctly hence making a simple test program that i put up where I have a input boxcar and by taking its Fourier Transform I do get a sync function now to see how ifft works i should get back box car function . But i do not . the suggestion which you gave does not convince me since Pdft is not a sync function and x axis give me no information about the frequency . Could you elaborate your answer ? and suggest me possibly How could I recover back Box car after doing ifft with the sync function Regards "Wayne King" <wmkingty(a)gmail.com> wrote in message <hnt0ob$gvm$1(a)fred.mathworks.com>... > "Saurabh " <saurabhs(a)student.ethz.ch> wrote in message <hnsvof$2f0$1(a)fred.mathworks.com>... > > Hello > > > > I have a rectangular function defined as follows > > tstop = 10E-3; > > t=-0.1:dt:0.1; > > p_i=(1/2)*(sign(t)-sign(t-tstop)); > > input = figure; > > plot(t,p_i) > > rge = 0.05; > > axis([-rge rge 0 1]); > > xlabel('time') > > ylabel('amplitude') > > title('Input step function') > > > > Then I take a Centered FFT > > > > [pw,frequencyRange] = centeredFFT(p_i,1/dt); > > positiveFFT = figure; > > stem(frequencyRange,abs(pw)); > > % set(positiveFFT,'Position',[500,500,500,300]) > > xlabel('Freq (Hz)') > > ylabel('Amplitude') > > title('Using the positiveFFT function') > > grid > > axis([0 500 0 0.05]); > > xlabel('frequency') > > ylabel('amplitude') > > title('FFT of the input step function') > > > > where the function centeredFFT is > > > > function [X,freq]=centeredFFT(x,Fs) > > %this is a custom function that helps in plotting the two-sided spectrum > > %x is the signal that is to be transformed > > %Fs is the sampling rate > > > > N=length(x); > > > > %this part of the code generates that frequency axis > > if mod(N,2)==0 > > k=-N/2:N/2-1; % N even > > else > > k=-(N-1)/2:(N-1)/2; % N odd > > end > > T=N/Fs; > > freq=k/T; %the frequency axis > > > > %takes the fft of the signal, and adjusts the amplitude accordingly > > X=fft(x)/N; % normalize the data > > X=fftshift(X); %shifts the fft data so that it is centered > > > > Now I want to take IFFT of the function but i do not get back the same input signal > > > > orignal_signal = ifft(YfreqDomain); > > time = ifft(frequencyRange); > > reterived = figure > > plot( time,orignal_signal) > > in > > > > Could any one guide in simple terms where I am wrong ? > > > > I also tried this > > > > orignal_signal = ifft(ifftshift(YfreqDomain)); > > time = ifft(ifftshift(frequencyRange)); > > reterived = figure > > plot( time,orignal_signal) > > > > but could not reterive back original signal > > Hi, if you want the signal back, why not just > > % you never give us dt by the way > tstop = 10E-3; > dt=1e-3; > t=-0.1:dt:0.1; > p_i=(1/2)*(sign(t)-sign(t-tstop)); > Pdft = fft(p_i); > p_m=ifft(Pdft,'symmetric'); > norm(p_m-p_i) > > Wayne
From: Matt J on 18 Mar 2010 07:37
A few comments about things that could be contributing to the problem: > %takes the fft of the signal, and adjusts the amplitude accordingly > X=fft(x)/N; % normalize the data =============== This doesn't seem like an appropriate normalization. If you'e trying to approximate the continuous Fourier transform, the appropriate normalization would be X=fft(x)*Fs; %Equation 1 Also, if you invert Equation 1, you get x=ifft(X)/Fs; %Equation 2 which shows that later, when you take the ifft, you have to undo the normalization you did in Equation 1 to get the original signal back again. > X=fftshift(X); %shifts the fft data so that it is centered > > Now I want to take IFFT of the function but i do not get back the same input signal > > orignal_signal = ifft(YfreqDomain); > time = ifft(frequencyRange); ================= I'm baffled as to why you think you can or need to use the IFFT to generate the time axis. You already created a time axis, t, early in the code. |