PDSP16510AMA Datasheet, PDF (19/23 Pages) Mitel Networks Corporation – Stand Alone FFT Processor

Arithmetic Accuracy
16 bit,unconditional
scaling
24 bit arithmetic with
unconditional scaling,
16 bit inputs
16 bit inputs with
PDSP16510 block FP
Full 32 bit Floating point
with 16 bit inputs
Max Tone Slot Noise
WRT Noise Test
60
44
88
67
74
61
93
82
2 Tones
with
Freq Spread
45
65
63
67
Table 8. Comparative Dynamic Range Measurements
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 correla-
tion 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 win-
dows 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. Resolu-
tion 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 deter-
mined 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 opera-
tor and the twiddle factors, and the way the growth in word
PDSP16510A MA
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.
The ‘best’ dynamic range figures will be obtained with
single tone measurements, and these results are often quoted
to indicate the need for greater bit accuracies. The measure
is the ratio of a full scale sinusoid to the average noise level
and the results will be essentially independent of the window
operator. The results given by the PDSP16510 are compared
to various other configurations in the first column of Table 8.
With this method the dynamic range is bound to improve as
more bits are used to represent the data. Theoretically 6 dB of
dynamic range will be obtained for every bit representing the
input data, if the internal arithmetic accuracy gives no degra-
dation in performance. In practice this improvement has no
significance since the incoming waveforms will be much more
complex than a single sinusoid.
An alternative method of determining dynamic range is
with a slot noise test. White noise is passed through a narrow-
band notch filter, several frequency bins wide, and the FFT
computed. There is no noise in the filtered slot at the input to
the FFT, but there is noise in the frequency bins corresponding
to the width of the notch. Dynamic range is measured as the
difference in dB of the average signal power and the average
noise power and can be considered to give more useful
results. Comparative results from various configurations are
also given in the second column of Table 8. The performance
with 24 bit data is seen to be little better than that obtained with
the PDSP16510. This can be attributed to the scaling scheme,
word growth, and rounding method used within the device.
When two nearby tones are to be capable of detection,
the window operator will dictate the performance of the
system. The final column in Table 8 illustrates the results
obtained using two sinusoids of different amplitudes, with the
larger one residing mid-way between two frequency bins, and
the smaller 5.5 bins away. The two frequencies are five bins
apart to avoid the effects of the mainlobe widths. The dB
figures given are the difference in amplitude between the two
signals when the smaller one is still just detectable as a
separate peak from the larger one.
This technique illustrates the performance of the window,
since the amount by which sidelobe structure of the larger
signal swamps the mainlobe of the smaller signal will effect
whether the smaller signal is detected. The theoretical attenu-
ation of the highest sidelobe levels, with respect to the
mainlobe, for the window options provided by the PDSP16510
have been given in Table 7, and represent the dynamic range
that can be obtained if arithmetic effects are ignored. The
results in the final column in Table 8 are the practical results
given by the device, and as with the slot noise test indicate that
the arithmetic scheme used by the PDSP16510 is equivalent
to using 24 bit data. The Blackman Harris window was used
in all cases.
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