Design ConsiderationsIn the design of an
y telemetry system, such features as bit rate, accuracy, precision, error rate, and bandwidth must be firmly specified. Proper choices for such factors are products of the application of information theory to the problem.4
This report is concerned with the heuristic development of the basic features of pulse-frequency modulation, an information encoding technique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and
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Let us investigatea few factors which are necessary in a PFM telemetry system. Let the maximum value of the analog time function f ( t ) be defined as the full-scale value F, of the channel. I F, is divided into N equal parts, the magnitude F,/N represents the precision of the system. f This is the smallest discernible change between two samples of f ( t ) The value of N is determined by the requirements of the experiment being telemetered. For small scientific satellites a precision factor 1/N of 0.01, o r 1 percent of the full-scale value, is normally considered adequate. For experiments, such as the flux-gate magnetometer, which depend on the measuring of the modulation of the magnetic field by the satellite's spin, precisions to 0.1 percent are desirable, although accuracy better than 1percent is not necessary. For analog signals encoded with PFM, the precision is a function of the signal-to-noise ratio. At close range, the precision is an order of magnitude better than at maximum range. This feature, which will be discussed later in more detail, is equivalent to encoding with a variable bit-rate.
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""_DATA CHANNEL 1 SYNC PULSE DATA CHANNEL 2
DATA CHANNEL 15
Figure 2-Pulse-frequency-modulation format: (a) telemetry frame; (b) sequence.
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This report is concerned with the heuristic development of the basic features of pulse-frequency modulation, an information encoding technique which has been used in a number of spacecraft. The primary advantages are its noise-immunity characteristics and
Since the frequency of the pulse contains the signal information, a measurement precision of 1percent, for example, requires that the detection system be able to discern 100 different frequencies. The total frequency band B is therefore divided into 100 equal parts. The separation between frequencies, Af, is B/lOO. The power spectra of the pulses (Appendix A) have zeros of power density on each side of the center frequency at multiples of the reciprocal of T the pulse length. T is determined by the sampling rate necessary to telemeter the highest frequency of f t ) at least better than at the Nyquist rate. The zeros of the power spectrum then should f a l l at multiples of B/lOO, o r A f,= I/T. This gives the relation between the bandwidth, precision, and pulse length,
where
1/N
is the precision constant.
The above analysis was made on the basis of the sampling time of a single channel f (t ) determining the pulse length T. Since time-division multiplexing is used, the pulse length must be shortened in proportion to the number of commutated channels. Therefore the bandwidth B will increase in proportion to the numberof commutated channels.
In effect, the application of Equation 2 predicts that the samplewill assume any one of N, in this case 100, discrete amplitudes. The power spectrum for any one of these amplitudes is centered in one of the 100 equal parts of width A f, in the band B.A first-order solution to the detection p
roblem is to arrange 100 contiguous bandpass filters with bandwidth A f,= 1/~ cover the bandwidth B A maximum-likelihood detector on the outputs to of the filters can select the filter with the greatest output. The signal is thus quantized into one of 100 possible levels. The original amplitude of a sample would not necessarily cause the frequency to fall exactly in the center of any one of the 100 filters. The output would still be greater in one filter than in an adjacent filter. As the amplitude of the sample is changed, the maximum-likelihood detector indicates that the adjacentfilter has acquired the signal only when its response has an amplitude greater than the output of the original filter. With a good signal-to-noise ratio the filter output which is greatest can be gated into a discriminator in order thatthe frequency might be measured with better than 1 percent precision.
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Rather than samplings only at times nT, the frequency of the pulse can be a continuous representation of the amplitude of the sample for the whole duration of the pulse, T By using a discriminator on the output of the contiguous filters, not only can the average amplitude during the time T be determined but also the rate of change of amplitude. Having the latter information is equivalent to doubling the sampling rate (Reference 9). These topics will be discussed in detail later.
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For data encoded as digital information, the minimum number of filters required in the detection system is the same as the number of frequency levels encoded. Filters for these frequency levels as well as filters contiguous to these discrete frequencies are tied together a"greatest of" conin figuration as in Figure 3. This allows some latitude in the stability of each discrete frequencytemperature drift or aging of the digital oscillator might cause a discrete frequency to f a l l outside