Principles of Modern Radar - Volume 2 1891121537

22 CHAPTER 2 Advanced Pulse Compression Waveform ModulationsTt gdδRRpulse repetition intervalgroup delayrange resolutionrange window extent2.1.3.2 Stretch ProcessingVariables associated with stretch processing are as follows:x (t) transmit waveformf 1 center frequency of first oscillatorβ LFM waveform’s swept bandwidthθ 1 phase of the first local oscillatorf 2 center frequency of the second oscillatorθ 2 phase of the second local oscillatorLO 2,tx second oscillator signal used to synthesize transmit signalt rcv time delay on receive, referenced to the center of the range windowLO 1,rcv first oscillator signal applied on receiveLO 2,rcv second oscillator signal applied on receivex r (t) received signaly (t) received signal after mixer stagest d time delay relative to the center of the range windowϕ residual video phaseθ composite phase after deramp operationf b beat frequencyY () spectrum of the deramped signalY M () spectrum magnituded d =−τ (1 − |t d |/τ) peak location of sinc’s main lobe peak null location of sinc’s first nullδ difference between peak and null in radians per secondδ f difference between peak and null in hertzδt d time-delay resolutionSNR loss signal-to-noise ratio losst rw time duration associated with a range windowB F low-pass filter bandwidthY (ω) spectrum of the sampled signaly (n) sampled received signaln sample indexN number of samples collected from a single point scattererY M (ω) magnitude of the spectrumr range delay relative to the center of the range windowδω Rayleigh resolution in radians per samplek discrete Fourier transform (DFT) bin indexY (k) discrete Fourier transformM discrete Fourier transform sizeN noise number of samples containing thermal noise collectedover the receive windowSNR β signal-to-noise ratio using a filter with bandwidth β