FREQUENCY DOMAIN OF SAMPLES AT fS_IN FREQUENCY DOMAIN OF THE INTERPOLATION
參數(shù)資料
型號: AD1896AYRSZ
廠商: Analog Devices Inc
文件頁數(shù): 11/28頁
文件大小: 0K
描述: IC CONV SAMPLE RATE ASYNC 28SSOP
標準包裝: 1
類型: 采樣率轉(zhuǎn)換器
應(yīng)用: 車載音頻,處理,接收器
安裝類型: 表面貼裝
封裝/外殼: 28-SSOP(0.209",5.30mm 寬)
供應(yīng)商設(shè)備封裝: 28-SSOP
包裝: 管件
產(chǎn)品目錄頁面: 776 (CN2011-ZH PDF)
REV. A
AD1896
–19–
FREQUENCY DOMAIN OF SAMPLES AT fS_IN
FREQUENCY DOMAIN OF THE INTERPOLATION
FREQUENCY DOMAIN OF fS_OUT RESAMPLING
FREQUENCY DOMAIN AFTER
RESAMPLING
IN
OUT
fS_IN
fS_OUT
INTERPOLATE
BY N
LOW-PASS
FILTER
ZERO-ORDER
HOLD
fS_IN
220
fS_IN
220
fS_IN
220
fS_IN
SIN(X)/X OF ZERO-ORDER HOLD
Figure 6. Frequency Domain of the Interpolation and
Resampling
HARDWARE MODEL
The output rate of the low-pass filter of Figure 5 would be the
interpolation rate, 2
20
192000 kHz = 201.3 GHz. Sampling at
a rate of 201.3 GHz is clearly impractical, not to mention the
number of taps required to calculate each interpolated sample.
However, since interpolation by 2
20 involves zero-stuffing 220– 1
samples between each fS_IN sample, most of the multiplies in
the low-pass FIR filter are by zero. A further reduction can be
realized by the fact that since only one interpolated sample is
taken at the output at the fS_OUT rate, only one convolution
needs to be performed per fS_OUT period instead of 2
20 convo-
lutions. A 64-tap FIR filter for each fS_OUT sample is sufficient
to suppress the images caused by the interpolation.
The difficulty with the above approach is that the correct inter-
polated sample needs to be selected upon the arrival of fS_OUT.
Since there are 2
20 possible convolutions per f
S_OUT period, the
arrival of the fS_OUT clock must be measured with an accuracy
of 1/201.3 GHz = 4.96 ps. Measuring the fS_OUT period with a
clock of 201.3 GHz frequency is clearly impossible; instead,
several coarse measurements of the fS_OUT clock period are made
and averaged over time.
Another difficulty with the above approach is the number of
coefficients required. Since there are 2
20 possible convolutions
with a 64-tap FIR filter, there needs to be 2
20 polyphase coeffi-
cients for each tap, which requires a total of 2
26 coefficients. To
reduce the amount of coefficients in ROM, the AD1896 stores a
small subset of coefficients and performs a high order interpola-
tion between the stored coefficients. So far the above approach
works for the case of fS_OUT > fS_IN. However, in the case when
the output sample rate, fS_OUT, is less than the input sample
rate, fS_IN, the ROM starting address, input data, and the length
of the convolution must be scaled. As the input sample rate
rises over the output sample rate, the antialiasing filter’s cutoff
frequency has to be lowered because the Nyquist frequency of
the output samples is less than the Nyquist frequency of the
input samples. To move the cutoff frequency of the antialiasing
filter, the coefficients are dynamically altered and the length
of the convolution is increased by a factor of (fS_IN/fS_OUT).
This technique is supported by the Fourier transform property
that if f(t) is F(
w), then f(k t) is F(w/k). Thus, the range of
decimation is simply limited by the size of the RAM.
THE SAMPLE RATE CONVERTER ARCHITECTURE
The architecture of the sample rate converter is shown in
Figure 7. The sample rate converter’s FIFO block adjusts the
left and right input samples and stores them for the FIR filter’s
convolution cycle. The fS_IN counter provides the write address
to the FIFO block and the ramp input to the digital servo
loop. The ROM stores the coefficients for the FIR filter convo-
lution and performs a high order interpolation between the
stored coefficients. The sample rate ratio block measures the
sample rate for dynamically altering the ROM coefficients and
scaling of the FIR filter length as well as the input data. The
digital servo loop automatically tracks the fS_IN and fS_OUT
sample rates and provides the RAM and ROM start addresses
for the start of the FIR filter convolution.
RIGHT DATA IN
LEFT DATA IN
FIFO
ROM A
ROM B
ROM C
ROM D
HIGH
ORDER
INTERP
DIGITAL
SERVO LOOP
FIR FILTER
SAMPLE RATE
RATIO
fS_IN
COUNTER
SAMPLE RATE RATIO
EXTERNAL
RATIO
fS_IN
fS_OUT
L/R DATA OUT
Figure 7. Architecture of the Sample Rate Converter
The FIFO receives the left and right input data and adjusts the
amplitude of the data for both the soft muting of the sample rate
converter and the scaling of the input data by the sample rate
ratio before storing the samples in the RAM. The input data is
scaled by the sample rate ratio because as the FIR filter length
of the convolution increases, so does the amplitude of the
convolution output. To keep the output of the FIR filter from
saturating, the input data is scaled down by multiplying it by
(fS_OUT/fS_IN) when fS_OUT < fS_IN. The FIFO also scales the input
data for muting and unmuting of the AD1896.
The RAM in the FIFO is 512 words deep for both left and right
channels. An offset to the write address provided by the fS_IN
counter is added to prevent the RAM read pointer from ever
overlapping the write address. The offset is selectable by the
GRPDLYS, group delay select, signal. A small offset, 16, is
added to the write address pointer when GRPDLYS is high,
and a large offset, 64, is added to the write address pointer when
GRPDLYS is low. Increasing the offset of the write address pointer
is useful for applications when small changes in the sample rate
ratio between fS_IN and fS_OUT are expected. The maximum deci-
mation rate can be calculated from the RAM word depth and
GRPDLYS as (512 – 16)/64 taps = 7.75 for short group delay and
(512 – 64)/64 taps = 7 for long group delay.
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