Post on 22-Jan-2018
Two Channel Analysis
Tejus Adiga M
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Transmultiplexers
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• TDM - FDM• FDM - TDM
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Transmultiplexers (FDM to TDM)• A/D Converter: Sampling rate: 96khz – 12 channels of 4khz each.• Frequency Translation: Band pass to Baseband all 12 channels.• Decimator: Reduce redundancy in each channel due to 12x oversampling to 4k• Commutate: Multiplex 12 channel samples of each 4k samples/sec to form 96k
samples/sec TDM signal.• Sub band Decomposition: N point DFT as Filter bank of N band pass filters; each DFT
value representing approximate value of each sub band.• Twidel Factor:
𝑊𝑁𝑘𝑛 = cos
2𝜋𝑘𝑛
𝑁+ 𝑗 𝑠𝑖𝑛
2𝜋𝑘𝑛
𝑁
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Transmultiplexers (TDM to FDM)
Problem with only re-scalingDownsampler Upsampler
X[n] X[2n] x1[n]Downsampler Upsampler
X[n] X[2n] x1[n]H(ω) G(ω)
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The Lost Information (Recedue)X[2n] x1[n]
Downsampler UpsamplerX[n]
H(ω) G(ω)
-E[n]
• E[n] error is significant • Losses occur in H(w) and G(w)
as they are LPFs; High frequency components are lost.
• PERFECT RECONSTRUCTION:• In parallel keep track of High
pass Frequencies filtered by LPFs and add it to the up sampled output x1[n].
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Quadrature Mirror Filter (QMF)
Xa0
X1[n]
Downsampler Upsampler
X[n]
H1(ω) G1(ω)
H2(ω) G2(ω)Downsampler Upsampler
ΣXa1
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Removing Aliasing
H0(z) = H(z)H1(z) = H(-z)G0(z) = H(z)G1(z) = -H(-z)
H0(w) = H(w)H1(w) = H(w-π)G0(w) = H(w)G1(w) = - H(w-π)
h0[n] = h[n]h1[n] = (-1)n h[n]g0[n] = h[n]g1[n] = (-1)n h[n]
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