Week 6

Question 1

What is used to defeat radar in battlefield situations

Answer 1

Smoke and obscurants

Question 2

Doppler radar on missile

Answer 2

As target moves relative to surface to air missile (SAM) carrying a fusing radar, fd changes

Question 3

Typical Doppler shifts

Answer 3

20 Hz to 2000 Hz

Question 4

Coherent processing interval

Answer 4

CPI or dwell time

Time over which pulses encounter the target

Question 5

Rules of Fourier transformations

Answer 5

Infinite complex sinusoid - impulse function

Rectangular pulse - sinc function

Multiplication in one domain - convolution in the other

Infinite pulse train in one domain - infinite pulse train in the other

Wide feature in one domain - narrow feature in the other

Question 6

Increasing time scales and decreasing frequency scales for finite RF pulse train

Answer 6

RF wave period - RF wave frequency

Pulse width - pulse bandwidth

PRI - PRF

CPI - spectral line bandwidth

Question 7

Spectrum of a single pulse

Answer 7

Nulls at 1/τ

Question 8

Rayleigh width

Answer 8

Distance from the peak to the first null (1/τ)

Question 9

3dB width

Answer 9

Measured between the half power (1/sqrt(2)) points across the peak

Question 10

Spectrum of infinite pulse train

Answer 10

Generate an infinite train of rectangular pulses in the time domain by consoling the rectangular pulse with an infinite train of impulses in the time domain

I’m frequency domain this corresponds to multiplying the FT of the rectangular pulse and the FT of the infinite train of impulses

Rectangular pulse of length τ &laquo_space;FT&raquo_space; sinc of width 1/τ

Infinite train of impulses with separation PRI &laquo_space;FT&raquo_space; infinite train of impulses with separation PRF

Multiplication in frequency domain produces an infinite pulse train with a magnitude that is modulated by the sinc function

Infinite pulse train produces an infinite series of spectral lines weighted by the spectrum of a single pulse

Broad sinc function has been resolved into narrow spectral lines (separation of spectral lines equal to the PRF)

Train of rectangular pulses cannot really be infinite in time

Question 11

Spectrum of finite pulse train

Answer 11

Truncating the infinite pulse train to Td (the CPI)

In time domain, this amounts to multiplication of the infinite train of pulses by a longer rectangular pulse of length Td

In frequency domain, this is equivalent to a convolution of the spectral lines with a second, narrower sinc function

Infinitely sharp spectral lines have broadened into sinc functions with a main lobe width determined by 1/Td

Main spectral line at f=0 has a sub-spectrum of secondary peaks lying between -PRF/2 and PRF/2

Question 12

Spectrum of modulated finite pulse train

Answer 12

Add the carrier frequency by multiplying the finite train of pulses in the time domain by a sinusoid of frequency f0
-equivalent to a convolution in the frequency domain with the double Dirac delta function (shifts the waveform peaks to f0 and -f0)

Question 13

Spectrum of modulated finite pulse train: frequency scales

Answer 13

Bandwidth of spectral lines (1/Td)

Spacing of spectral lines (PRF=1/Tp)

Bandwidth of the single-pulse sinc envelopes (1/τ)

Center frequencies of those envelopes (f0 = 1/T0)