FDM(Telephony). Laboratory exercises using MATLAB

Frequency-Division Multiplexing Experiment no. ____

II. Introduction1 A number of analog telephone signals can be multiplexed onto one channel using frequency-division multiplexing. Since these signals are analog so it is better to use different frequencies to combine them into one channel, and to save bandwidth of channel (either be wired or wireless) only one sideband is to be utilized. The available spectrum is divided among different information – voice or data. However, in telephony, conversation requires only 3 kHz of bandwidth – as opposed to 15 kHz for accurate retrieval of original signal. Hence, only one sideband is necessary and that could be either be the upper- or lower-sideband SSB. In FDM, the channels are divided into groups forming a hierarchical structure. The lowest of these groups is called (simply) group, which consists of 12 LSB channels occupying 60 kHz to 108 kHz. A group is also called an A (analog) channel bank. Five of these groups can be multiplexed together to form a supergroup, which occupies the spectrum from 312 kHz to 552 kHz and contain 60 voice channels. If the bandwidth of the channel (wire or wireless) permits, then ten supergroup can form mastergroup with frequency from 564 kHz to 3084 kHz and a capacity of 600 voice channels. For satellite communication, you can have jumbogroup (6 mastergroups or 3600 voiceband channels) or superjumbogroup (3 jumbogroups or 10,800 voiceband channels.)

Comm.5: FDM

I. Objectives To demonstrate the frequency-division multiplexing as it is used in analog telephony.

III. Tools and Equipment (1) PC (1) MATLAB (1) mouse IV. Procedure 1. Open MATLAB and Simulink. Build the Simulink element of group consisting 12 LSB channels. Refer to Figure 1. 2. Use the following Simulink element by using the find browser located in Simulink toolbar.

1

Blake, 2002. kindly include in your telephony and microwave design for 5th year ece students

1gm

Sine wave (carrier signal) Product DIR FIR Filter Design (bandpass)

Spectrum Scope

DIR FIR Filter Design (lowpass)

Parameters Amp: 1; Bias: 0; Frequency: 2*π*4e3; Phase: 0; Sample Time: 1/(256e3) Amp: 1; Bias: 0; Frequency: 2*π*108e3; Phase: 0; Sample Time: 1/(256e3) No inputs: 2; Element-wise Bandpass filter; Filter order: 64; Lower cutoff frequency: 104/130; Upper cutoff frequency: 108/130; Window type: Hamming Scope Properties: Buffer size: 512; Buffer overflow: 64; FFT length: check; FFT length: 512; No spectral ave: 8 Display Property: (Same) Axis Properties: Frequency Units: Hz; Frequency Range: [0…Fs/2]; Min Y Limit and Max Y Limit: (as is) Low-pass Filter; Filter order:128; Cutoff frequency: 3.3/4; Window type: Hamming

Comm.5: FDM

Simulink Element Sine wave (modulating signal)

Table 1 Group Using FDM

2gm

fir 1

fir 1 B-FFT

Product

3.3kkHz lowpass filter

104 -108 kHz bandpass filter

108 kHz carrier1

ch 2

fir 1

ch 2: 4kHz mod wave 1

fir 1

fir 1

B-FFT

ch 1: 3.3kHz mod wave

Product 1

ch 12 :4kHz mod wave 2

3.3kkHz lowpass filter 11

fdm out

fir 1

B-FFT Ch 12 Spectrum 1

60 -64 Hz bandpass filter 2

fir 1

fir 1

B-FFT Ch 2 Spectrum

100 -104 kHz bandpass filter 2

ch 12 ch 12

Product 11

64 kHz carrier1

ch 2 ch 2

3.3kkHz lowpass filter 1

Ch 1 Spectrum

FDM Spectrum

ch 11:4kHz mod wave 2

3.3kkHz lowpass filter 10

ch 11 ch 11

B-FFT

Product 10

Ch 11 Spectrum 1

64 -68 Hz bandpass filter 3

104 kHz carrier2

ch 3: 4kHz mod wave 2

3.3kkHz lowpass filter 2

fir 1

68 kHz carrier2

ch 3 ch 3 ch 3

Product 2

fir 1 B-FFT

ch 10 :4kHz mod wave 1

Ch 3 Spectrum 1

96 -100 kHz bandpass filter 1

fir 1

ch 10 ch 10

Product 9

3.3kkHz lowpass filter 9

B-FFT Ch 10 Spectrum 2

68 -72 Hz bandpass filter 2

100 kHz carrier3 72 kHz carrier1

fir 1

ch 4: 4kHz mod wave 1

fir 1

ch 4

3.3kkHz lowpass filter 3

fir 1

ch 4

Product 3

fir 1

ch 9 ch 9

B-FFT Ch 4 Spectrum 2

92 -96 kHz bandpass filter 3

ch 9:4kHz mod wave 2

Product 8

3.3kkHz lowpass filter 8

B-FFT Ch 9 Spectrum 1

72 -76 Hz bandpass filter 1

Comm.5: FDM

fir 1

96 kHz carrier4 fir 1

ch 5: 4kHz mod wave 2

3.3kkHz lowpass filter 4

fir 1

76 kHz carrier2 ch 5 ch 5

Product 4

fir 1

fir 1

B-FFT Ch 5 Spectrum 3

88 -92 kHz bandpass filter 1

ch 8:4kHz mod wave 1

ch 8 ch 8

Product 7

3.3kkHz lowpass filter 7

76 -80 Hz bandpass filter 2

B-FFT Ch 8 Spectrum 2

92 kHz carrier5 fir 1

ch 6: 4kHz mod wave 1

3.3kkHz lowpass filter 5

fir 1

Product 5 84 -88 kHz bandpass filter 2

ch 6 ch 6

fir 1

80 kHz carrier1 fir 1

B-FFT Ch 6 Spectrum 4

ch 7:4kHz mod wave 2

ch 7 ch 7

3.3kkHz lowpass filter 6

Product 6

80 -84 Hz bandpass filter 1

B-FFT Ch 7 Spectrum 1

88 kHz carrier1 84 kHz carrier2

3. Your output should show channels from 60 to 108 kHz and that it can be shown through the output spectrum. Double click the icon for output (or final) spectrum and observe the output. 4. Sketch your FFT spectra output of 12 channels of a group. 5. Figure 2 shows the formation of (partial) supergroup. A supergroup consists of 5 groups occupying 312 – 552 kHz. Simulate a supergroup by cre-creating the block diagram of Figure 3 using Simulink. Use a modulating wave of 84 kHz for each group, with corresponding carrier for each group: 420 kHz, 468 kHz, 516 kHz, 564 kHz, and 612 kHz. The bandpass filter for each group will be: 312-360 kHz, 360408 kHz, 408-456 kHz, 456-504 kHz, and 504-552 kHz. Complete the block diagram of Figure 3 and simulate it. You may ask your instructor to confirm if your output is correct.

3gm

fir 1 group 1: 84 kHz mod wave

gr1 gr1

B-FFT

Product

Ch 1 Spectrum

312 -360 kHz bandpass filter

FDM supergroup

420 kHz carrier1

B-FFT

group 2: 384 kHz mod wave 1

gr2 gr2

Product 1 360 -408 kHz bandpass filter 1

B-FFT Ch 2 Spectrum 2

468 kHz carrier2

6. Draw the completed block diagram of supergroup and its FDM output

Comm.5: FDM

fir 1

FDM out Spectrum 1

V. Questions and Problems 1. Discregarding the guardband of mastergroup, form a sketch showing the formation of mastergroup. A mastergroup consists of 10 supergroups with a frequency range of 564 kHz to 3084 kHz and contains 60 voice channels. 2. Simulate the one you make in Question no. 1. Include it in your microwave design.

4gm