代做FFT algorithm留学生作业、代写C/C++程序设计作业、代做NEWMAT作业、代写C/C++实验作业
This programming assignment is about using the Fast Fourier Transform
(FFT) algorithm to clean-up/process financial data. I am only going to cover the
computational aspects of this procedure. To learn about the theory behind what
we are going to do, you might want to look at Oppenheim and Schafer’s classic
text. We will use the implementation of the FFT algorithm in NEWMAT.
I am going to give you the required “functional basics” for what an FFT
is etc. There is a lot more to this topic than what I am going to cover here.
The easiest way to get to the foundations of FFT is this – any periodic signal
x(t) with period T (i.e. x(t + T) = x(t) for any t) can be written as a sum-ofsinewaves
(click this wikipedia page for an illustrative example). That is,
x(t) = C0 +X∞i=1
. (1)
The terms Ai and Bi denote the amplitude (i.e. strength) of the sinewave/-
cosinewave whose frequency is i
T Hz – the larger these numbers are, the more
“significant” is the “contribution” of this frequency-component to the value of
x(?). To be a little more precise, the larger the value of pA2i + B2i
, there is a
larger contribution from the i
T Hz component.
In essence, we are are going to take the ticker data for a given duration (in
our case, it is for a day), and we are going to assume that it is a single-period
of a (fictitious) periodic waveform. Consequently, we can write this ticker data
“pattern” as a sum of sinewaves and cosinewaves. The summation is over a
large number of such terms, but some of the sinewaves/cosinewaves might have
a small contribution (i.e. pA2i + B2i
is small, compared to the rest) – we just
drop them – and we get a (smoother) “approximation” of the ticker data pattern.
Such filtered/smoothened version of the data can be used in numerous ways –
one of them is to do short-term prediction, possibly. Another, could be to come
up with triggers for automated-trades, but that requires some experimentation
on your part.
If the ticker data has n-many entries over a time period of T, it turns out we
can generate the values of Ai and Bi (0 ≤ i ≤ n) from the Fast-Fourier Transform
(FFT) routine. The version in NEWMAT (click here for the NEWMAT
documentation) that we will use has the format RealFFT(X, F, G);, where X is
the (real-valued) ticker data array, and F (resp. G) is the real-part (imaginarypart)
of the FFT of X. With reference to equation 1, it can be shown that for
1 ≤ i ≤n2 + 1,
C0 =1n
F(1); Ai =2n
F(i + 1); Bi =2n
G(i + 1).
1
To reconstruct the filtered tick data, you pick those components of F and G
that contribute significantly (compared to the others) to the original signal.
You compute a magnitude array whose i-th entry is p
F(i)
2 + G(i)
2. Following
this, you sort the entries of magnitude and pick the top-5, top-10, top-15 values
of magnitude (and these are the sinewave and cosinewave components that are
the “strongest” in the original tick data). After you picked the top, stronger
components, in the F and G arrays, you zero-out the remaining entries of the F
and G arrays, as their contributions are insignificant. You reconstruct the signal
using the inverse of the FFT, which is RealFFTI(F, G, X); in the NEWMAT
library. This is how the red, black, blue curves of figure 2 are generated.
In this programming assignment you are going to reconstruct a filteredversion
of a (highly noisy/fluctuating) price-path of an instrument1
.
Using the hint.cpp provided on Compass, and the video instructions, I want
you to write a C++ program that takes the ticker/price-path data and takes as
command-line inputs: (1) the #significant-terms in the fourier-series/fourierexpansion
of the price-path, (2) the #data-points in the ticker-data, (3) input-
file name that contains the ticker-data, and (4) the output-file that should contain
the filtered-data (after the program completes). A sample output is shown
in figure 1. The video instructions also tell you how to generate a sample output
as shown in figure 2.
Here is what I want from you for this programming assignment
1. A short write-up that explains what your code does. No more than a page.
2. C++ code with appropriate Class definitions along the lines of hint.cpp
that accomplishes what is required.
1You can get the second-by-second price-path of GOOG and MSF T recorded at COB
on 23 August, 2017. The GOOG data has 378 data-points, while the MSF T data has 390
data-points.
2
Figure 1: A sample output.
3
0 50 100 150 200 250 300 350 400
920
921
922
923
924
925
926
927
928
929
930 GOOG Price Path on 23 August 2017
GOOG
GOOG 5 Terms
GOOG 10 Terms
GOOG 15 Terms
(a) The original, and fitered-price-paths for GOOG on 23 August 2017
0 50 100 150 200 250 300 350 400
72.5
72.6
72.7
72.8
72.9
73
73.1
73.2 MSFT Price Path on 23 August 2017
MSFT
MSFT 5 Terms
MSFT 10 Terms
MSFT 15 Terms
(b) The original, and fitered-price-paths for MSFT on 23 August 2017
Figure 2: The original, and fitered-price-paths for GOOG and MSFT on 23
August 2017.
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