Digital Signal Processing Reference
In-Depth Information
L
samples
x
[
n
]
L
1
n
N
samples
m
1
N
samples
m
2
N
samples
m
3
N
samples
m
4
x
1
[
n
]
x
2
[
n
]
N
1
0
n
0
n
N
samples
N
samples
Figure 12.34
Blocks of data for a periodogram spectrum estimate.
feasible, and the sample estimate of the autocorrelation is calculated for each
from (12.53):
x
m
[n]
N- 1
1
N
a
r
Nm
[p] =
x
m
[n]x
m
[p + n], p = 0, 1, Á , N - 1.
n= 0
An FFT algorithm is then used to compute the energy spectral density esti-
mate (12.54) for that sample sequence
S
xm
[k] =
5
r
Nm
[p]
6
.
In the
averaging periodogram method,
the energy spectral density sequences,
for several sample sequences are averaged together to give the periodogram
estimate
S
xm
[k],
M
q
1
S
x
=
S
xm
[k].
(12.55)
m= 0
In this section, we look at applications of the DFT. We saw ways that we can use the
DFT for digital signal processing in and for providing an estimate of the Fourier
transform of a signal.
12.7
THE DISCRETE COSINE TRANSFORM
Closely related to the DFT is the discrete cosine transform (DCT). Instead of the
exponential kernel (or basis function)
e
-j2pkn
>
N
