Problem 6.30 A space probe sends a containing 500 times 500 elements, each conta

Question

Problem 6.30

A space probe sends a containing 500 times 500 elements, each containing a brightness scale with 256 possible levels. This scale requires eight are binary digits. Thus, altogether 8 times 500 times 500 = 2 times 10^6 pulses are required to the picture for transmission. Suppose that the transmitter uses a bandwidth of 1000 Hz. (For the faint signals from distant space probes the bandwidth must be kept small to reduce the effects of electronic noise that is present at all frequencies.) Roughly how long is needed to send one picture? Note that the center-to-center separation of adjacent pulses must be at least 2 Delta t (the total width of any one pulse). (a) By inspection of Fig. 6.19, deduce the fundamental frequency in the Fourier series of F (t). (b) What would you suggest is the highest harmonic that has a substantial amplitude? What is its frequency?

Explanation / Answer

6.30] a] The most fundamental frequency will give the overall structure to the signal. It is the regular component of the signal with the shortest frequency. Here, this is the signal with time period 5 ms

so, the fundamental frequency is f = 1/T = 1/5ms = 200 Hzo = 1/To = 1/5ms = 200 Hz

b] The highest harmonic will be the regular component of the signal with the highest frequency.

Here, there are 4 small oscillations in 5 ms

so time for 1 oscillations is: 5ms/4 = 1.25 ms

=> f = 1/1.25ms = 800 Hz = 4(fo).

therefore, this frequency is the fourth harmonic (3rd overtone).

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