PDSP16515GCPR datasheet(19/27 Pages) MITEL

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PDSP16515A

A - Bcosx + Ccos2x where x = (2

πn)/N, n = 0 to N-1

For Hamming, A = 0.54, B = 0.46, C = 0

For Blackman-Harris, 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

multiplications 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

PDSP16515A, and other commonly used windows, are

illustrated 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.

BIT 14:13

These bits allow four dump size options to be provided.

Individual frequency bins are not accessible.

BIT 15

Under normal circumstances DAV would be expected to go

invalid when a transform has been dumped. In some

applications, however, it may be necessary to read the outputs

more than once. When this bit is set, DAV will remain valid until

the next INEN input, and will indicate that the transformed data

still remains in the internal buffer. As soon as the next INEN is

received the transformed data will be overwritten. Whilst DAV

remains active the output tri-states will be enabled.

Window Operators

Since only a finite segment of a signal can be observed and

processed at any one time, it is impossible to obtain pure

spectral lines. Discontinuities are introduced at the

boundaries of the observation interval which lead to spectral

leakage. Windows are weighting functions applied to the data

in order to reduce these discontinuities at the boundaries.

In the time domain the signal has to be observed through a

finite window as a matter of accord. This is in fact equivalent

to multiplying the signal with a set of uniform weights i.e. a

rectangular window operator. In the frequency domain the

spectrum of the data will be the spectrum of this weighting

function shifted to the sinusoidal frequencies of the

components in the data.

The rectangular window has a Fourier Transform which is a

SINC(X) function. This has sidelobes which are only 13dB

down from the main lobe. This severely limits the dynamic

range of the system since a second sinusoid in close proximity

would have its main lobe swamped by this side lobe. This

would occur if its amplitude was a mere 13dB down from the

first sinusoid.

Window operators are thus mathematically constructed to

cancel these sidelobes as far as possible. Unfortunately this

is normally done at the expense of making the main lobe

spread over more frequency bins. This reduces the ability of

the system to resolve two frequencies, and can only be

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

PDSP16515A. These are constructed on the fly as needed,

and take the general form:

PDSP16515

AUX

POWER

ON RESET

PARAMETERS

PDSP16116

COMPLEX

MULTIPLIER

SYSTEM

CLOCK

REAL

DATA

IMAG'

DATA

WINDOW

PROM

ZERO

COUNTER

CLK

FIRST

SAMPLE

CLOCK

CLR

Figure. 9. External Window Generator

PDSP16515GCPR Datasheet(PDF) 19 Page - Mitel Networks Corporation

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