EP1S80B956C7N Altera, EP1S80B956C7N Datasheet - Page 596

• Manufacturer Part Number: EP1S80B956C7N
• Description: IC STRATIX FPGA 80K LE 956-BGA
• Manufacturer: Altera
• Series: Stratix®r

Specifications of EP1S80B956C7N

• Number Of Logic Elements/cells: 79040
• Number Of Labs/clbs: 7904
• Total Ram Bits: 7427520
• 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: Lead free / RoHS Compliant
• Number Of Gates: -

Finite Impulse Response (FIR) Filters
7–18
Stratix Device Handbook, Volume 2
Inserting zeros between the samples creates reflections of the original
spectrum, thus, a low pass filter is needed to filter out the reflections.
Figure 7–10. Block Diagram Representation of Interpolation
To see how interpolation filters work, consider the Nyquist Sampling
Theorem. This theorem states that the maximum frequency of the input
to be sampled must be smaller than f
frequency, to avoid aliasing. This frequency, f
Nyquist frequency (F
analog to digital converter (ADC), it needs to be low pass filtered using
an analog anti-aliasing filter to prevent aliasing. If the input frequency
spectrum extends close to the Nyquist frequency, then the first alias is also
close to the Nyquist frequency. Therefore, the low pass filter needs to be
very sharp to reject this alias. A very sharp analog filter is hard to design
and manufacture and could increase passband ripple, thereby
compromising system performance.
The solution is to increase the sampling rate of the ADC, so that the new
Nyquist frequency is higher and the spacing between the desired signal
and the alias is also higher. Zero padding as described above increase the
sample rate. This process also known as upsampling (oversampling)
relaxes the roll off requirements of the anti-aliasing filter. Consequently, a
simpler filter achieves alias suppression. A simpler analog filter is easier
to implement, does not compromise system performance, and is also
easier to manufacture.
Similarly, the digital to analog converter (DAC) typically interpolates the
data before the digital to analog conversion. This relaxes the requirement
on the analog low pass filter at the output of the DAC.
The interpolation filter does not need to run at the oversampled
(upsampled) rate of f
are zeros, so they do not contribute to the output.
Figure 7–11
interpolation for a specific case where the original signal spectrum is
limited to 2 MHz and the interpolation factor (I) is 4. The Nyquist
frequency of the upsampled signal must be greater than 8 MHz, and is
chosen to be 9 MHz for this example.
shows the time and frequency domain representation of
sample rate f s
Input
n
s
). Typically, before a signal is sampled using an
I. This is because the extra sample points added
I
s
/2, where f
LPF
s
/2, is also known as the
Output
sample rate I * f s
s
is the sampling
Altera Corporation
September 2004