PDSP16510AMA Datasheet, PDF (18/23 Pages) Mitel Networks Corporation – Stand Alone FFT Processor

PDSP16510A MA
Fig. 11. External Window Generator
overcome by using more data samples. This may not always
be possible because of other system constraints.
A common rule of thumb defines the resolution of an FFT
system as half the full width of the mainlobe. The width of the
mainlobe for a rectangular window is two frequency bins; for
the Hamming window it is four bins; for the Blackman-Harris
window it is six bins.
The latter two windows are actually supported by the
PDSP16510. These are constructed on the fly as needed, and
take the general form;
A - Bcosx + Ccos2x where x = 2πn n = 0 to N-1
N
For the Hamming window A = 0.54, B = 0.46, C = 0
For the Blackman-Harris window, A = 0.42323, B = 0.49755,
C = 0.07922
These windows can be applied to any of the transform
size options, except the 16 x 16 complex variant. When the
latter is specified the rectangular window option MUST be
selected, or the device will be configured in an internal test
mode.
If other operators are required these must be applied
externally. This can be conveniently achieved with either a
PDSP16112 or a PDSP16116, both of which are complex
multipliers but with different accuracies. Fig. 11 shows how
either one can be configured to perform two separate multipli-
cations with one input common to both. This arrangement is
necessary to perform the window function on complex inputs.
Important features of the windows generated by
PDSP16510, and other commonly used windows, are illus-
trated in Table 7. The results are obtained from the reference
quoted, which should be consulted for a full mathematical
treatment. The significance of each parameter is outlined
below;
Highest Side Lobe Level
The inherent rectangular window has sidelobes which
are only 13dB down from the mainlobe. These severely limit
the dynamic range. The object of the window is to improve this
situation with better side load attenuation.
Mid-Point Loss
In line with the filter concept it is possible to conceive of
an additional processing loss for a tone of frequency mid-way
between two bins. This is defined as the ratio of the coherent
gains of two tones, one at the mid-point and one at the sample
point. It is expressed in dB in Table 8.
Overall loss
An overall figure for the reduction in signal to noise ratio
can be obtained by adding the mid-point loss to the reciprocal
of the equivalent noise power bandwidth in dB. It is a measure
of the ability of the window to detect single tones in broadband
noise. The variance between windows is less than 1dB.
6.0dB Bandwidth
This figure, expressed in bin widths, represents the ability
of the window to resolve two tones and should be as close to
unity as possible. As the highest sidelobe level is reduced, this
parameter tends to get worse, and a compromise must be
used when choosing a window.
Window
Operator
Rectangular
Hamming
Dolph-Chebyshev
[C = 3.5]
Kaiser-Bessel
[C = 3]
Blackman
Blackman-Harris
[3 term]
Highest
Mid-Point
Side Lobe Loss dB
Overall
Loss dB
-13
3.92
3.92
-43
1.78
3.1
-70
1.25
3.35
-69
1.02
3.55
-58
1.1
3.47
-67
1.13
3.45
6dB
Bandwidth
Overlap Correlation
75%
50%
1.21
75
50
1.81
70.7
23.5
2.17
60.2
11.9
2.39
53.9
7.4
2.35
56.7
9
1.81
57.2
9.6
Table 7. Window Performance ( from The use of Windows for Harmonic Analysis. F J Harris. Proc IEEE Vol 66. Jan 1978 )
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