Digital Signal Processing Reference
In-Depth Information
1
1
0
0
−1
−1
0
10
20
30
0
10
20
30
(a) Sample
(b) Bin
1
1
0
0
−1
−1
0
10
20
30
0
10
20
30
(c) Sample
(d) Bin
1
1
0
0.5
−1
0
0
10
20
30
0
10
20
30
(e) Sample
(f) Bin
Figure 3.13:
(a) and (c): Real and Imaginary correlators for Bin -1, shown after computing all bin values;
(b) and (d): Real and Imaginary parts of DFT for waveform at (a) and (c), with all bin values plotted; (e)
Truncated square wave serving as test signal; (f ) Magnitude of DFT, based on real and imaginary parts
plotted in (b) and (d).
mathematically, the Real DFT is a sort of corollary or special case of the complex DFT, which possesses
a symmetry that allows the scaling value to be equal for all bins.
Example 3.13.
Compute the DFT of a sawtooth wave.
The script (see exercises below)
LVxDF TComputeSawtooth
computes the DFT, step-by-step, of a truncated harmonic sawtooth which is synthesized using
N/
2
W
=
(
1
/k)
sin
(
2
πnk/N)
k
=
1
−
where
n
runs from 0 to
N
1. Note that both odd and even harmonics are included. The result from
running the script through all bin values is shown in Fig. 3.14.
Example 3.14.
Compute the DFT of a test signal using symmetric bin values.
