EP1S40B956C5 Altera, EP1S40B956C5 Datasheet - Page 598

• Manufacturer Part Number: EP1S40B956C5
• Description: IC STRATIX FPGA 40K LE 956-BGA
• Manufacturer: Altera
• Series: Stratix®r

Specifications of EP1S40B956C5

• Number Of Logic Elements/cells: 41250
• Number Of Labs/clbs: 4125
• Total Ram Bits: 3423744
• Number Of I /o: 683
• Voltage - Supply: 1.425 V ~ 1.575 V
• Mounting Type: Surface Mount
• Operating Temperature: 0°C ~ 85°C
• Package / Case: 956-BGA
• Lead Free Status / RoHS Status: Contains lead / RoHS non-compliant
• Number Of Gates: -

Finite Impulse Response (FIR) Filters
7–20
Stratix Device Handbook, Volume 2
Table 7–9. Decomposition of a 16-Tap Interpolating Filter into Four Polyphase Filters
Output Sample
y(0), y(4)...
y(1), y(5)...
y(2), y(6)...
y(3), y(7)...
where:
This equation implies that the first polyphase filter, h
h(0), h(I), h(2I),..., h((P-1)I). The second polyphase filter, h
coefficients h(1), h(1+I), h(1+2I), ..., h(1+(P-1)I). Continuing in this way,
the last polyphase filter, hI
- 1) + 2I), ..., h((I - 1) + (P-1)I).
An example helps in understanding the polyphase implementation of
interpolation. Consider the polyphase representation of a 16-tap low pass
filter with an interpolation factor of 4. Thus, the output is given below:
Referring back to
the input are x(0), x(4), x(8,) and x(12). The first output, y(0), only depends
on h(0), h(4), h(8) and h(12) because x(i) is zero for i 0, 4, 8, 12.
shows the coefficients required to generate output samples.
Table 7–9
parallel polyphase filters. This is shown in
the filters are multiplexed to generate the overall output. The multiplexer
is controlled by a counter, which counts up modulo-I starting at 0.
It is illuminating to compare the computational requirements of the direct
implementation versus polyphase implementation of the low pass filter.
In the direct implementation, the number of computations per cycle
k = 0,1, …, I-1
n = 0,1, …, P-1
P = L/I = length of polyphase filters
L = length of the filter (selected to be a multiple of I)
I = interpolation factor
h(n) = original filter impulse response
y n
Coefficients Required
h(2), h(6), h(10), h(14)
h(3), h(7), h(11), h(15)
shows that this filter operation can be represented by four
h(0), h(4), h(8), h(12)
h(1), h(5), h(9), h(13)
=
i
15
=
0
h n iI
Figure 7–11 on page
–
x i
-1
(n), has coefficients h(I-1), h((I - 1) + N), h((I
Polyphase Filter Impulse Response
7–19, the only nonzero samples of
Figure
7–12. The outputs from
h
h
h
h
0
1
2
3
0
(n)
(n)
(n)
(n)
(n), has coefficients
Altera Corporation
September 2004
1
(n), has
Table 7–9