09-19-2018
Quote:
Originally Posted by
Corona688
Absolutely. I don't post code for people to not use it.
It's a kind of naive implementation though. Usually better to read values from stdin, but knowing how audioscope works I knew you'd need batches. That'd obscure how it really works a bit though. Maybe better as this, people can populate the arrays as they please.
It's not truly an FFT either, just a DFT -- which gives the same result but takes much more time to do so. Notice how it must do N*N loops for N input. FFT accomplishes the same with N log N loops.
Still, I hope it has its uses. And I'm grateful for you writing one in shell. That's the first DFT I've seen written in a language I really understand.
Yes it is technically a DFT but most people don't know what the difference is and FFT is what they know most, so I used that term. I will upload to AMINET as a DFT however.
And naive it is too, but I could stay with python and use the builtin import
cmath version I have got to eliminate the 'scipy' and 'scipyIO' dependencies. I really didn't want to use python although my code works from Python 1.4.0 to the current 3.7.0.
Thanks a lot matey, will post the URL for you to see when I have uploaded it...
Bazza...
------ Post updated 19-09-18 at 06:19 AM ------
Hi Corona688...
Uploaded to the AMINET site at around 9:30pm UK local time last night, 18-09-2018.
At around 6:00am today 19-09-2018 UK local time it was added and has had 2 downloads, dls, already. It will be on show for 14 days and I expect at least 150 dls in that time.
Aminet - dev/gcc/DFT-FFT.awk.txt
Thanks a lot...
Bazza.
(Consider this thread wrapped up.)
I have no idea why it added my separate post to the end of this one...
This User Gave Thanks to wisecracker For This Post:
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math::fourier(n) Tcl Math Library math::fourier(n)
__________________________________________________________________________________________________________________________________________________
NAME
math::fourier - Discrete and fast fourier transforms
SYNOPSIS
package require Tcl 8.4
package require math::fourier 1.0.2
::math::fourier::dft in_data
::math::fourier::inverse_dft in_data
::math::fourier::lowpass cutoff in_data
::math::fourier::highpass cutoff in_data
_________________________________________________________________
DESCRIPTION
The math::fourier package implements two versions of discrete Fourier transforms, the ordinary transform and the fast Fourier transform. It
also provides a few simple filter procedures as an illustrations of how such filters can be implemented.
The purpose of this document is to describe the implemented procedures and provide some examples of their usage. As there is ample litera-
ture on the algorithms involved, we refer to relevant text books for more explanations. We also refer to the original Wiki page on the sub-
ject which describes some of the considerations behind the current implementation.
GENERAL INFORMATION
The two top-level procedures defined are
o dft data-list
o inverse_dft data-list
Both take a list of complex numbers and apply a Discrete Fourier Transform (DFT) or its inverse respectively to these lists of numbers. A
"complex number" in this case is either (i) a pair (two element list) of numbers, interpreted as the real and imaginary parts of the com-
plex number, or (ii) a single number, interpreted as the real part of a complex number whose imaginary part is zero. The return value is
always in the first format. (The DFT generally produces complex results even if the input is purely real.) Applying first one and then the
other of these procedures to a list of complex numbers will (modulo rounding errors due to floating point arithmetic) return the original
list of numbers.
If the input length N is a power of two then these procedures will utilize the O(N log N) Fast Fourier Transform algorithm. If input length
is not a power of two then the DFT will instead be computed using a the naive quadratic algorithm.
Some examples:
% dft {1 2 3 4}
{10 0.0} {-2.0 2.0} {-2 0.0} {-2.0 -2.0}
% inverse_dft {{10 0.0} {-2.0 2.0} {-2 0.0} {-2.0 -2.0}}
{1.0 0.0} {2.0 0.0} {3.0 0.0} {4.0 0.0}
% dft {1 2 3 4 5}
{15.0 0.0} {-2.5 3.44095480118} {-2.5 0.812299240582} {-2.5 -0.812299240582} {-2.5 -3.44095480118}
% inverse_dft {{15.0 0.0} {-2.5 3.44095480118} {-2.5 0.812299240582} {-2.5 -0.812299240582} {-2.5 -3.44095480118}}
{1.0 0.0} {2.0 8.881784197e-17} {3.0 4.4408920985e-17} {4.0 4.4408920985e-17} {5.0 -8.881784197e-17}
In the last case, the imaginary parts <1e-16 would have been zero in exact arithmetic, but aren't here due to rounding errors.
Internally, the procedures use a flat list format where every even index element of a list is a real part and every odd index element is an
imaginary part. This is reflected in the variable names by Re_ and Im_ prefixes.
The package includes two simple filters. They have an analogue equivalent in a simple electronic circuit, a resistor and a capacitance in
series. Using these filters requires the math::complexnumbers package.
PROCEDURES
The public Fourier transform procedures are:
::math::fourier::dft in_data
Determine the Fourier transform of the given list of complex numbers. The result is a list of complex numbers representing the (com-
plex) amplitudes of the Fourier components.
list in_data
List of data
::math::fourier::inverse_dft in_data
Determine the inverse Fourier transform of the given list of complex numbers (interpreted as amplitudes). The result is a list of
complex numbers representing the original (complex) data
list in_data
List of data (amplitudes)
::math::fourier::lowpass cutoff in_data
Filter the (complex) amplitudes so that high-frequency components are suppressed. The implemented filter is a first-order low-pass
filter, the discrete equivalent of a simple electronic circuit with a resistor and a capacitance.
float cutoff
Cut-off frequency
list in_data
List of data (amplitudes)
::math::fourier::highpass cutoff in_data
Filter the (complex) amplitudes so that low-frequency components are suppressed. The implemented filter is a first-order low-pass
filter, the discrete equivalent of a simple electronic circuit with a resistor and a capacitance.
float cutoff
Cut-off frequency
list in_data
List of data (amplitudes)
BUGS, IDEAS, FEEDBACK
This document, and the package it describes, will undoubtedly contain bugs and other problems. Please report such in the category math ::
fourier of the Tcllib SF Trackers [http://sourceforge.net/tracker/?group_id=12883]. Please also report any ideas for enhancements you may
have for either package and/or documentation.
KEYWORDS
FFT, Fourier transform, complex numbers, mathematics
math 1.0.2 math::fourier(n)