ifft returns NaN when plotting the impulse response function

Hello, I seem to be having issues using MATLAB's fft and ifft functions.

An impulse response function h(t) has the following formula: inj(t) * h(t) = AIF(t). We know that the graphs of inj(t) and AIF(t) are as followed. I wrote the following code to do the deconvolution but h(t) in the output graph is zero.

I realized that the h returns from ifft is NaN but I don't know how to correct the code. Thanks!

load("AIF_1.mat");
load("inj_1.mat");
inj_1 = inj(201:2400);
inj1_FFT = fft(inj_1);
AIF_1 = AIF(201:2400);
AIF1_FFT = fft(AIF_1);
h_FFT = AIF1_FFT ./ inj1_FFT;
h_FFT(isnan(h_FFT)==1) = 0;
h = ifft(h_FFT);
X = zeros(1,200)
ht = [X,h];
plot(time,real(ht));title('h(t)');

Answer 1

[Paul]

Hi 粤轩 杨,

It looks like h_FFT also has a few values that are inf, in addition to the NaNs

load("AIF_1.mat");
load("inj_1.mat");
inj_1 = inj(201:2400);
inj1_FFT = fft(inj_1);
AIF_1 = AIF(201:2400);
AIF1_FFT = fft(AIF_1);

h_FFT = AIF1_FFT ./ inj1_FFT;

sum(isnan(h_FFT))

ans = 3

sum(isinf(h_FFT))

ans = 2

% quick correction to get things to run, not sure if this is really what
% should be done
inj1_FFT(inj1_FFT == 0) = eps;

h_FFT = AIF1_FFT ./ inj1_FFT;

sum(isnan(h_FFT))

ans = 0

sum(isinf(h_FFT))

ans = 0

h = ifft(h_FFT);

X = zeros(1,200);
ht = [X,h];
plot(time,real(ht));title('h(t)');

[粤轩 杨]

Hi Paul,

The output graph is a little strange. But you finging of inf values in h_FFT made me realize that I didn't intercept the inj correctly.

After changing to

inj_1 = inj(200:2400)

the output graph is good!

Thank you for your inspiration!

Answer 2

[粤轩 杨]

There are two related attachments for your information. Thanks!

[粤轩 杨]

Just as mentioned above, the final code should be

load("AIF_1.mat");
load("inj_1.mat");
inj_1 = inj(200:2400);
inj1_FFT = fft(inj_1);
AIF_1 = AIF(200:2400);
AIF1_FFT = fft(AIF_1);
h_FFT = AIF1_FFT ./ inj1_FFT;
h = ifft(h_FFT);
X = zeros(1,199);
ht = [X,h];
plot(time,real(ht));title('h(t)');

And the output graph looks like