Anonymous function handle incosistence problem with Fourier functions

Hello, during some optics simulation I dared to shorten my code (a .m type) by making fourier transform an anonymous function as such:

F = @(x)  fftshift(fft(ifftshift(x)));
iF = @(x)  ifftshift(ifft(fftshift(x)));
poow = @(x) abs(x).^ 2;

with these I would Transform, inverse transform and Find the intensity of the signal but for a reason I don't know it only works when I post it in the command window... sometimes.

here is an example of it in action:

L = 15; % mm
F = 100; % mm
f0 = 1/100e-3; % lp/mm
f1 = 1/300e-3; % lp/mm
dx = 4e-3; % mm
t = 0:dx:L-dx; % mm
n = length(t);
f = -1/(2*dx):1/L:(1/(2*dx)-1/L);
object = chirp(t,f0,t(end),f1,"quadratic");
I = poow(object);

%% transform the object and display
object_ = F(object);

Array indices must be positive integers or logical values.

I_object_ = poow(object_);

Now, the problem is as you might see here is that the error this time is:

Array indices must be positive integers or logical values.

but on my machine its:

Error: File: LiveEditorEvaluationHelperE1735339498.m Line: 57 Column: 7

Invalid expression. Check for missing or extra characters.

Error in LiveEditorEvaluationHelperE1735339498>@(x)fftshift(fft(ifftshift(x))) (line 3)

F = @(x) fftshift(fft(ifftshift(x)));

^

this error happens to all previewed anonymous functions.

I have checked if a simpler handle would work and it does only crash when calling these 3 specific ones when running the script.

[Stephen23]

"Array indices must be positive integers or logical values."

is caused by these two lines:

F = 100; % mm
..
object_ = F(object);

where you incorrectly think that you are calling a function, but in fact you are indexing into a scalar numeric.

To debug the other error message please upload your code by clicking the paperclip button. Did you copy that code from a website or something similar?

Answer 1

[Matt J]

Aside from what Stephen mentions,

(1) the time and frequency axes need to have a common origin at the center of the array.

(2) ifftshift always comes first, in both F and iF, when processing centered signals.

F = @(x)  fftshift(fft(ifftshift(x)));
iF = @(x)  fftshift(ifft(ifftshift(x)));
poow = @(x) abs(x).^ 2;

L = 15; % mm
%F = 100; % mm
f0 = 1/100e-3; % lp/mm
f1 = 1/300e-3; % lp/mm
dx = 4e-3; % mm

%Set up axes
n=ceil(2*L/dx);
df=1/n/dx;
ax=-ceil((n-1)/2):+floor((n-1)/2); %normalized axis
t=ax*dx; %time axis
f=ax*df; %frequency axis


object=zeros(size(t));
object(t>=0) = chirp(t(t>=0),f0,t(end),f1,"quadratic");
I = poow(object);

%% transform the object and display
object_ = F(object);
I_object_ = poow(object_);


figure; plot(t,object); 

●

figure; plot(f,abs(object_))