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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