How to create local copy of an FFT object?

[Maxim]

Hello!

I am working with the builtin FFT Fast Fourier Transform of Sagemath,
and have coded (based on the work of P. Lutus here :
http://vps.arachnoid.com/sage/fourier.html) a function that takes an
fftobject to plot the spectrum of a function.

My problem is that when I pass the fftobject, I don't know how to make
a local copy of this object inside the scope of my function. The
result if that after my first call of this function, the fftobject
gets modified (globally) when I run fftobject.fordward_transform() on
it. This is not what I want, because I want to reuse this same object
unchanged further in my code.

I'm new at Python, so I do not know a lot about this. I have first
tried to to something as :
fftobject_copy = fftobject
But it would just create a pointer to fftobject, and still allow the
function to modify its content. I tried to use the list copy :
fft_object_copy = fftobject[:]
But it would loose it's FFT specific functions, such as in
"fftobject.forward_transform()".

So, how can I make a local copy of an FFT object? An example of my
code is following.
Many thanks!

## My functions declaration. Notice the fft_unilateral(fftobj)
function, where I'm trying to make a local copy of
## fftobj.
# magnitude of 2-component cartesian vector
def mag(x):
return sqrt(x[0]^2+x[1]^2)

def nextpow2(i):
n = 2
while n < i: n = n * 2
return n

def fft_unilateral(fftobj):
# fftobj_copy = fftobj[:] <== Trying to create a local copy of
fftobj here!
fftobj_copy = fftobj # <== fftobj_copy is not a copy but a
pointer to fftobj!
fftobj_copy.forward_transform()
lfft = len(fftobj_copy)
dt = 1.0/lfft
list = map(lambda x:(2*mag(x))*dt,fftobj_copy[:lfft/2])
list[0]=list[0]/2
return list

# frequency unilateral domain plot
def fft_plot(fftobj,line_color='blue',labels=
('Frequence','Amplitude')):
list = fft_unilateral(fftobj)
return list_plot
(list,rgbcolor=line_color,plotjoined=True,axes_labels=labels)

# Power Spectrum Density plot
def psd_plot(fftobj,line_color='blue',labels=
('Frequence','Amplitude')):
list = fft_unilateral(fftobj)
for i in range(len(list)):
list[i]=list[i]^2
return list_plot
(list,rgbcolor=line_color,plotjoined=True,axes_labels=labels)

## Begin main program
# Define time domain function (AM without overmodulation here)
m(t)= cos(2*pi*100*t)
p(t)= cos(2*pi*1000*t)
AM1(t)=(1 + 0.5*m(t))*p(t)

# Create
samples=4000
lfft=nextpow2(samples)
# samples = sampling frequency
# Create fft object
fft_a=FFT(lfft)
# Fill fftobject with time domain data
for t in range(lfft):
fft_a[t] = AM1(t/lfft)

## Finally, ready to fire it up.
# If you have succeded to create a local copy in the fft_unilateral
function, then the two following PSDs are
# identical. If not, then they differ.
fft_plot(fft_a,line_color='blue',labels=('$f$ (Hz)','$|\Phi(f)|$'))

# Copy to new cell
fft_plot(fft_a,line_color='blue',labels=('$f$ (Hz)','$|\Phi(f)|$'))

[Maxim]

Ok. I've found a way (to copy an fft object) :

lfft = len(fftobj)
fftobj_copy = FFT(lfft)
for i in range(lfft):
fftobj_copy[i]=fftobj[i]

If you see things which I could / should do another way in my code,
feel free to post your suggestions!