Generating Multitone FSK Using a Quadrature Modulator

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Buck Dean
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1 Generating Multitone FSK Using a Quadrature Modulator Page 1 of 7 Generating Multitone FSK Using a Quadrature Modulator By In recent columns (click on the Archives botton at the top of this page to link to them) I described how to use a quadrature modulator to generate quiet carriers, and 2- and 4-Level FSK. We then laid the groundwork for our investigation into multitone FSK. In this column, we ll look at the time-domain method of generating this signal. The Time-Domain Method The time-domain method extends the discussion of 4L-FSK. In that discussion you found that to generate a tone at some frequency that is offset f m from the carrier f RF, you apply sine and cosine waves at a frequency f m into the modulator s I and Q ports. The phase relationship between the I and Q signals determines whether the output signal is above or below the RF signal. You can generate a single sinewave of frequency f RF + f m1 by setting I(t) = cos (2f m1 t) and Q(t) = sin(2f m1 t). Superposition applies in a quadrature modulator, so by setting I( t) cos 2 f t Q( t) sin 2 f t m1 m1 cos 2 f t sin 2 f t m2 m2 you ll see two tones at the modulator output at frequencies f RF + f m1 and f RF + f m2. You can then extend this concept to generate the 8-tone signal of Fig 9 s multitone FSK signal. Let s consider an example system with a 10-kHz bit rate and a 1250-Hz symbol rate. As in the previous examples, set the spacing between each tone to twice the symbol rate, in this case 2500 Hz. Sitting down with a cup of coffee and a copy of the 8-level multitone frequency plan of Fig 8 in, Digital Modulation Techniques Using a Quadrature Modulator, you can generate the following table, which maps each bitstream to the proper I(t) and Q(t) waveforms: Bit Number Zero Frequency One Frequency B 0 f B0,0 = Hz I(t) = cos[2(-18750)t] Q(t) = sin[2(-18750)t] Q(t)=sin[2(-18750)t] I(t)=cos[2(-18750)t] Q(t)=sin[2(-18750)t f B0,1 = Hz I(t) = cos[2(-16250)t] Q(t) = sin[2(-16250)t] f B1,0 = Hz I(t) = cos[2(-13750)t] Q(t) = sin[2(-13750)t] f B1,1 = Hz I(t) = cos[2(-11250)t] Q(t) = sin[2(-11250)t]

2 Generating Multitone FSK Using a Quadrature Modulator Page 2 of B 1 B 2 B 3 B 4 B 5 B 6 B 7 f B2,0 = Hz I(t) = cos[2(-8750)t] Q(t) = sin[2(-8750)t] f B3,0 = Hz I(t) = cos[2(-3750)t] Q(t) = sin[2(-3750)t] f B4,0 = 1250 Hz I(t) = cos[2(1250)t] Q(t) = sin[2(1250)t] f B5,0 = 6250 Hz I(t) = cos[2(6250)t] Q(t) = sin[2(6250)t] f B6,0 = Hz I(t) = cos[2(11250)t] Q(t) = sin[2(11250)t] f B7,0 = Hz I(t) = cos[2(16250)t] Q(t) = sin[2(16250)t] f B2,1 = Hz I(t) = cos[2(-6250)t] Q(t) = sin[2(-6250)t] f B3,1 = Hz I(t) = cos[2(-1250)t] Q(t) = sin[2(-1250)t] f B4,1 = 3750 Hz I(t) = cos[2(3750)t] Q(t) = sin[2(3750)t] f B5,1 = 8750 Hz I(t) = cos[2(8750)t] Q(t) = sin[2(8750)t] f B6,1 = Hz I(t) = cos[2(13750)t] Q(t) = sin[2(13750)t] f B7,1 = Hz I(t) = cos[2(18750)t] Q(t) = sin[2(18750)t] The symbol B 7 B 6 B 5 B 4 B 3 B 2 B 1 B 0 = maps to frequencies f B7,1, f B6,1, f B5,0, f B4,0, f B3,0, f B2,1, f B1,0 and f B0,0 or Hz, Hz, 6250 Hz, 1250 Hz, Hz, Hz, Hz and Hz, respectively. Next arithmetically add all the I(t) waveforms to produce an aggregate I symbol (t), and then perform the same operation to produce an aggregate Q symbol (t): Isymbol t cos 2 fb0,0 cos 2 f B1,0 cos 2 f cos 2 f B2,1 B3,0 cos 2 f cos 2 f B4,0 B5,0 cos 2 f cos 2 f B6,1 B7,1 cos cos cos cos cos cos cos cos Qsymbol t sin 2 fb0,0 sin 2 fb1,0 sin 2 f sin 2 f B2,1 B3,0 sin 2 f sin 2 f B4,0 B5,0 sin 2 f sin 2 f B6,1 B7,1 sin sin sin sin sin sin sin sin Fig 1 shows I symbol (t) and Q symbol (t). It isn t intuitively obvious that these are the correct I(t) and Q(t) waveforms because they are made up of eight superimposed sine waves but trust me, the math works. Note that I(t) and Q(t) will be different for each symbol we send. Fig 2 shows the modulator output spectrum for the single symbol Note the eight output tones and their

3 Generating Multitone FSK Using a Quadrature Modulator Page 3 of 7 frequencies, which indicate the symbol sent. Fig 2 is actually the FFT of the complex waveform shown in Fig 1. Fig 1 The I(t) and Q(t) required to produce the 8-Level multitone FSK symbol corresponding to B 7 B 6 B 5 B 4 B 3 B 2 B 1 B 0 =

4 Generating Multitone FSK Using a Quadrature Modulator Page 4 of 7 Fig 2 The frequency spectrum of the 8-Level multitone FSK symbol corresponding to B 7 B 6 B 5 B 4 B 3 B 2 B 1 B 0 = Repeating this process for many random symbols generates the spectrum shown in Fig 3. There are 16 tones present in the peak representing the two possible states of each of the eight bits that make up a symbol.

5 Generating Multitone FSK Using a Quadrature Modulator Page 5 of 7 Fig 3 The frequency spectrum for an 8-Level multitone FSK symbol modulated with many random symbols. Note the 16 spikes that each correspond to one possible frequency emitted by the modulator. Finally, Fig 4 shows the time-frequency spectrogram of an 8-Level multitone FSK signal over a 5-symbol period. During the first symbol [ ], which runs from 400 sec, each of the eight tones are at their lower frequency. The next symbol, running from +400 sec to sec, is [ ] and each of the eight tones are at their higher frequency. The pattern continues with the subsequent symbols.

Generating Multitone FSK Using a Quadrature Modulator Page 6 of 7 Fig 4 Spectrogram (time-frequency plot) of an 8-Level multitone FSK signal over a 5-symbol period.

6 Generating Multitone FSK Using a Quadrature Modulator Page 6 of 7 Fig 4 Spectrogram (time-frequency plot) of an 8-Level multitone FSK signal over a 5-symbol period. The symbols used to modulate the signal were: Next time, we ll look at the FFT method of generating multilevel FSK, then we ll examine quadrature modulators and phase-modulated signals. Author Biography was born and raised in Ohio, which explains a lot. He went to the University of Akron for his undergraduate work in electrical engineering and completed his MSEE at the Johns Hopkins University in He designed and taught several RFrelated courses at Johns Hopkins University. He is also the author of Wireless Receiver Design for Digital Communications (ISBN-13: ) and of Radio Receiver

7 Generating Multitone FSK Using a Quadrature Modulator Page 7 of 7 Design (ISBN-13: ) with Tom Vito. You can reach Kevin at mcckevin@mcclaning.com. Bibliography Bingham, John A.C., The Theory and Practice of Modem Design, John Wiley and Sons, Inc., ISBN Ziemer, R.E., and Tranter, W.H., Principles of Communications: Systems, Modulation and Noise, Fourth Edition. John Wiley and Sons, Inc., ISBN

Generating 4-Level and Multitone FSK Using a Quadrature Modulator

Generating 4-Level and Multitone FSK Using a Quadrature Modulator Page 1 of 9 Generating 4-Level and Multitone FSK Using a Quadrature Modulator by In a reent olumn (lik on the Arhives botton at the top