Principles of Modern Radar - Volume 2 1891121537

Signal Analysis and ProcessingSelect Fourier Transforms and PropertiesContinuous Timex(t) X ( f ){A, − τ 2 ≤ t ≤ τ 20, otherwise{A cos(2π f 0 t), − τ 2 ≤ t ≤ τ 20, otherwise∞∑n=−∞δ D (t − nT)sin (π Bt)AB ≡ ABsinc (π Bt)π Btsin (π f τ)Aτ ≡ Aτsinc (π f τ)π f τAτ2 sinc[π( f − f 0)τ] + Aτ2 sinc[π ( f + f 0) τ]{∞∑k=−∞δ D ( f − k · PRF)A, − B 2 ≤ t ≤ B 20, otherwisex(t − t 0 ) e − j2π ft0 X ( f )e + j2π f0t x (t) X ( f − f 0 )Discrete Timex[n] X ( ˆf )Ae j2π ˆf0n , n = 0,...,N − 1 A 1 − e− j2π(ˆf − ˆf0)N∞∑n=−∞sin[ ]π ˆBnA ˆBπ ˆBn1 − e − j2π( ˆf − ˆf0) ≡ NAe− jπ(ˆf − ˆf0)(N−1) asinc( ˆf − ˆf 0 , N)Aδ[n − n 0 ] e − j2π ˆfn 0δ D (t − nT)∞∑k=−∞δ D ( f − k · PRF)[ ] { ∣ A, ˆf ∣ < ˆB≡ A ˆBsinc π ˆBn ˆB < ∣ ˆf ∣