PDSP16515A Datasheet, PDF (20/25 Pages) Mitel Networks Corporation – Stand Alone FFT Processor

PDSP16515A
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.
Overlap Correlation
In many practical systems the squared magnitudes of
successive transforms are averaged to reduce the variance of
the measurements. If, however, a windowed FFT is applied to
non overlapping partitions of the sequence, data near the
boundaries will be ignored since the window exhibits small
values at those points. To avoid this loss partitions are usually
overlapped by 50% or 75%, which might, at first sight, remove
the need to average successive transforms. If non-windowed
transforms are overlapped by 75% or 50%, then 75% or 50%
of the data will be correlated. When windows are applied,
however, the data common to both transforms will be operated
upon by different portions of the window waveform. The
difference in these portions will dictate the amount of
correlation between overlapped data. At 50% overlap Table 7
shows that with all windows the data is virtually independent,
and successive averaging would still be needed. At 75%
overlap figures are obtained which are closer to the 75%
correlation obtained with no window.
Examination of Table 7 shows that the Blackman-Harris
window gives performance very similar to that of the Kaiser-
Bessel and Dolph-Chebyshev windows. The latter two
windows can not be computed as they are needed since they
are mathematically too complicated. The values are normally
pre-computed and stored in a ROM; this would need to contain
1M bits to match the accuracy of the rest of the system.
Use of the Hamming window gives worse dynamic range than
the more complex windows, but it has less effect on the
overlap correlation and it has a smaller main lobe width.
Spectral Performance
There are two important parameters in the measurement of
spectral response: resolution and dynamic range. Resolution
defines how closely two sinusoids can be spaced in frequency
and still be identified; dynamic range defines how great the
difference in the amplitudes of the sinusoids may be and yet
the smaller one still identified. Resolution is determined by the
observation time [i.e. the width of the frequency bin] and the
window operator that is used. Dynamic range is also
determined by the window operator, but in a hardware
implementation it is also influenced by the number of bits used
to represent the data throughout the calculation.
The hardware effects include the accuracy of the A/D
converter, the number of bits representing the window
operator and the twiddle factors, and the way the growth in
word length is handled as the FFT calculation proceeds. The
obvious way to overcome these limitations is to use floating
point arithmetic; but in real life the accuracy of the A/D
converter is fixed and the sample size is limited. Floating point
arithmetic is thus an overkill solution for the majority of
applications. This is especially true for transform sizes up to
1024 points, which is the intended application area.
Figures given for the dynamic range of a system must be
carefully interpreted, since there is no exact definition of the
measurement. Three different ways of measuring dynamic
range have been investigated using 1024 point transforms.
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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