channel spectral characteristics
TRANSCRIPT
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8/14/2019 Channel Spectral Characteristics
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Channel Spectral Characteristics
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Some Polyphase Filter Options
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FDM-to TDM Standard Channelizer:Collection of Downconverters
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FDM-to TDM Polyphase Channelizer:Input Commutator, M-Path Filter, and FFT
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Conventional Channelizer Application
Channelize and Downsample to Nyquist Rate,Interpolate to Two Times Symbol Rate
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Enhanced Channelizer SolutionReplace Interpolator Function With Buffer Addressing
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Standard Downconverter:
Heterodyne, Filter, Resample
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Equivalency Theorem
Heterodyne and Low Pass Filter Same asBand Pass Filter and Heterodyne
kk
kk
k
k
jrN
r
jn
jrjnN
r
N
r
rnj
nj
erhrnxe
erhernx
rhernx
nhenxkny
)()(
)()(
)()(
)(])([),(
1
0
1
0
1
0
)(
=
=
=
=
=
=
=
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Slide Heterodyne Through Filter:Convert Low-Pass to Band-Pass
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Slide Heterodyne Through Downsampler:Alias Frequency of Heterodyne
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Select Input Center Frequency That Aliasesto DC Under Resampling
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Noble IdentityInterchange Order of Filter and Resample
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M-Path Partition of FIR Filter
)1(321
1
0
)1()3()2()1()0(
)()(
=
+++++=
=
N
N
n
n
ZNhZhZhZhh
ZnhZH
L
L
MMMMMM
L
L
L
L
+++
+++
+++
+++
+++=
++
++
++
+
++
++
++
++
)13()12()1(
)32()3(3
)22()2(2
)12()1(1
)02(
)()()(
)()()3(
)()()2(
)()()1(
)()()0()(
13121
323
222
121
020
MMM
MM
MM
MM
MM
ZhZhZh
ZhZhZh
ZhZhZh
ZhZhZh
ZhZhhZH
MMM
MM
MM
MM
MM
)()()()()( )1()1(
2
2
1
1
0
M
M
MMMM
ZHZZHZZHZZHZH
++++= LL
=
=
=
+==
1
0
1)/(
0
1
0
)()()(M
r
MN
n
nMrM
r
M
r
rZnMrhZZHZZH
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Example of Polyphase (M-Path) Partition
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Block Diagram of M-Path Filter
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Pull Resamplers Through Filters in Each path
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Delays and Synchronous Rersamplers
are Equivalent to Input Commutator
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Input Series in Each Path of M-Path Filter
have Offset Time Origins
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Path Filters are Interpolators: Computing
Output Samples with Common Time Origin
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Phase Response of Paths in
Ten Stage Polyphase Filter
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-9
-8
-7
-6
-5
-4
-3
-2
-1
0Spectral Phase Response of Ten Polyphase Filters
Normaled F reque ncy (f/fs )
NormalizedPhase(/2)
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Group Delay of Paths in
Ten-Stage Polyphase Filter
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5-9
-8.8
-8.6
-8.4
-8.2
-8
-7.8
-7.6
-7.4
-7.2
-7Spe ctral Group Delay Res pons e of Ten P olyphase Filters
Norma led F reque ncy (f/fs )
NormalizedDelay(T/Ts)
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Modulation Property for Z-Transform
)(H(Z)G(Z)
then
])[(
])[1(])[2(])[1()0(
)1()2()1()0()(
and
)(
)1()2()1()0()(
if
j-eZ
1
0
)1()1(221
)1()1(221
1
0
)1(21
ZeH
Zenh
ZeNhZehZehh
ZeNhZehZehhZG
Znh
ZNnZhZhhZH
j
Z
N
n
nj
NNjjj
NNjjj
N
n
n
N
=
=
=
==
=
++++=
++++=
=
++++=
L
L
L
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Polyphase Partition of Band-Pass Filter
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Spectral Response of Signal in
Resampled Pass Band Filter
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Performance Specifications for
50-Channel Polyphase Channelizer
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Required Spectral Response of Channel
Filter at Output and at Input Rates
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Time and Frequency Response of
Remez Filter Design
0 100 200 300 400 500
-0.005
0
0.005
0.01
0.015
0.02
0.025
Impulse Res ponse , P rototype Filte r
-10 0 10 20 30 40 50 60
-5
0
5
10x 10
-4 Impulse Response, Detail
-30 -20 -10 0 10 20 30-80
-70
-60
-50
-40
-30
-20
-10
0
10
Normalize d Freque nc y f/fChannel
logmagnitu
de(dB)
Frequency Response, Prototype Filter
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Time and Frequency response of Remez
Filter Design with Modified End Points
0 100 200 300 400 500-0.005
0
0.005
0.01
0.015
0.02
0.025
Impulse Res ponse , Prototype Filter
-10 0 10 20 30 40 50 60-5
0
5
10x 10
-4 Impulse Res ponse, Detail
-30 -20 -10 0 10 20 30-80
-70
-60
-50
-40-30
-20
-10
0
10
Normalized Frequency f/fChannel
logmagnitu
de(dB)
Frequency Re spons e, P rototype Filter
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Time and Frequency Response of Prototype
Filter at Output Sample Rate
0 50 100 150 200 250 300 350 400 450 500-5
0
5
10
15
20
x 10-3 Impuls e Res ponse, P rototype F ilter
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2-80
-70
-60
-50
-40
-30
-20
-10
0
10
Norma lized Freq uency f/fChannel
logmagnitud
e(dB)
Frequency Resp onse, Prototype and Replicates at Output Rate
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Commutators for Standard Input Buffer and
for Circular Input Buffer
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Standard Polyphase Channelizer and
Modified Channelizer with Circular Buffers
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Content of 64-Point Circular Input Buffer for
Two Successive 48 Point Input Blocks
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Shifting Time Origin for Input Data of
Polyphase Filter and of Resetting FFT
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Contents of Transfer Circular Buffer
Aligning Origins for Successive Input Blocks
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Input Time and Spectrum to
30 Channel, 40 Point FFT Channelizer
300 350 400 450 500 550 600 650 700 750 800
-100
-50
0
50
100real part of com pos ite time s ignal
-20 -15 -10 -5 0 5 10 15 20-60
-50
-40
-30
-20
-10
0
10Spe c trum: compos ite time s ignal
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Time Series from 30 Channel Channelizer
0 100 200-10
0
10
0 100 200-10
0
10
0 100 200-10
0
10
0 100 200-10
0
10
0 100 200-10
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10
0 100 200-10
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10
0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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0 100 200-10
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10
0 100 200-10
0
10
0 100 200-10
0
10
0 100 200-10
0
10
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Spectra for 30 Channel Channelizer
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
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-1 0 1-60
-40
-20
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-1 0 1-60
-40
-20
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-1 0 1-60
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-20
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-1 0 1-60
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-20
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-1 0 1-60
-40
-20
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-1 0 1-60
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-20
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-1 0 1-60
-40
-20
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-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
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-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
-1 0 1-60
-40
-20
0
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Input Time and Spectrum to
50 Channel, 64 Point FFT Channelizer
600 650 700 750 800 850 900 950 1000-1
-0.5
0
0.5
1Composite Time Signal
S ample Index
Amplitude
-6000 -4000 -2000 0 2000 4000 6000-60
-50
-40
-30
-20
-10
0
10Spectrum
Frequency (kHz)
LogMagnitude(dB)
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Time Series from 50 Channel
Matched Filter Channelizer
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
0 100 200-1
0
1
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Spectra from 50 Channel
Matched Filter Channelizer
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5-50
0
-0.5 0 0.5-50
0
-0.5 0 0.5-50
0
-0.5 0 0.5-50
0
-0.5 0 0.5-50
0
-0.5 0 0.5-50
0
-0.5 0 0.5-50
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-0.5 0 0.5-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
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-0.5 0 0.5
-50
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-0.5 0 0.5
-50
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-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0
-0.5 0 0.5
-50
0