. Airborne radar. Airplanes; Guided missiles. 5-7] NARROW BAND NOISE 263 graph 5-6 in connection with the discussion of a square-law device. Using the results of that paragraph, the autocorrelation of r- is computed as follows: ri^ra^ a'^ + la^Xx + la^xi + arx^- + arx-^- -f- a?-y^ + a'-y-^ + 1ax\X'^ + .yi-j'2- +4^2—2 (5-81) = (^2 + 2cr2)2 + 4<72((72p2 + ^2^) = (2^2)2(1 + ^/yV)2 + (2a2)2[p2 + 2(.S'/A^)p]. The spectrum of the video signal plus noise has three components: (a) an impulse at zero frequency representing the d-c, (b) a continuous portion of the same shape as the spectrum of the co


. Airborne radar. Airplanes; Guided missiles. 5-7] NARROW BAND NOISE 263 graph 5-6 in connection with the discussion of a square-law device. Using the results of that paragraph, the autocorrelation of r- is computed as follows: ri^ra^ a'^ + la^Xx + la^xi + arx^- + arx-^- -f- a?-y^ + a'-y-^ + 1ax\X'^ + .yi-j'2- +4^2—2 (5-81) = (^2 + 2cr2)2 + 4<72((72p2 + ^2^) = (2^2)2(1 + ^/yV)2 + (2a2)2[p2 + 2(.S'/A^)p]. The spectrum of the video signal plus noise has three components: (a) an impulse at zero frequency representing the d-c, (b) a continuous portion of the same shape as the spectrum of the component x and y processes repre- senting beats between the signal and the noise, (c) a continuous portion somewhat wider than the spectrum of the x and y processes representing beats between various parts of the noise spectrum. Fig. 5-12 illustrates the Impulse Signal Power = a^/2 Noise Power ?=2D\N=u S/N= a2/2(7". 27r(ay4) Impulse 27rW' 47r W Signal Plus Noise Angular ^ 27rW"^ 1^ Frequency 27r (2(7^)2 Impulse / \ t 1 / t D 1 1 Noise Alone Angular Frequency Fig. 5-12 Power Density Spectra of the Square of the Envelope of a Sinusoidal Signal Plus Narrow-Band Noise. forms of the various spectra in a typical case. The spectrum of the x and y processes is assumed rectangular with bandwidth W. The density of the positive and negative portions of the narrow band spectrum is denoted by D. The d-c level is equal to twice the sum of the signal and noise powers. The portion of the continuous spectrum corresponding to (b) is rectangular, of half the width of the narrow band spectrum (considering only positive. Please note that these images are extracted from scanned page images that may have been digitally enhanced for readability - coloration and appearance of these illustrations may not perfectly resemble the original Povejsil, Donald J. Princeton, N. J. , Van Nostrand


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