PDSP16510A MA

18

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

Highest

Mid-Point

Overall

6dB

Overlap Correlation

Operator

Side Lobe

Loss dB

Loss dB

Bandwidth

75%

50%

Rectangular

-13

3.92

3.92

1.21

75

50

Hamming

-43

1.78

3.1

1.81

70.7

23.5

Dolph-Chebyshev

-70

1.25

3.35

2.17

60.2

11.9

[C = 3.5]

Kaiser-Bessel

-69

1.02

3.55

2.39

53.9

7.4

[C = 3]

Blackman

-58

1.1

3.47

2.35

56.7

9

Blackman-Harris

-67

1.13

3.45

1.81

57.2

9.6

[3 term]

Table 7. Window Performance ( from The use of Windows for Harmonic Analysis. F J Harris. Proc IEEE Vol 66. Jan 1978 )

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 = 2

πn 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