This preview shows page 1. Sign up to view the full content.
Unformatted text preview: l into the frequency domain, the IDFT is used
to map a signal in the frequency domain into time domain. Because, the DFT is an
orthogonal transformation, the inverse is computed using the Hermitian operator .
The cost of inverting an
matrix is proportional to
, the cost of multiplying a
matrix by a vector is proportional to
. We will further diminish the computation cost
of multiplying a matrix times a vector by using the FFT (Fast Fourier Transform). ¡4 X 4 4 4 3.1.2 Zero padding The DFT allows us to transform an points time series into frequency coefﬁcients
, where the index is associated to the discrete frequency , 45 0 4 0¢
4
0
$¢
4
BGEF4D) " " ) B )
0¢
5
44" #IA' § 7 ) 7 $£§ 7 3 1 § 60 0
$¢ 7 5
¤ the frequency axis is sampled every
radians. At this point it appears that
is controlled by the number of samples of the time series . Zero padding can be used to
, in this case we deﬁne a new time series that condecrease the frequency interval
sists of the original time series foll...
View
Full
Document
 Winter '12
 Sacchi

Click to edit the document details