Bandpass Modulation and Demodulation 3-Digital Communications-Lecture Slides, Slides of Digital Communication Systems

Download Bandpass Modulation and Demodulation 3-Digital Communications-Lecture Slides and more Slides Digital Communication Systems in PDF only on Docsity! Chapter 4: Bandpass Modulation and Demodulation ® docsity.com Today’s Agenda Review Differential Phase Shift Keying D8PSK Example docsity.com 7 If v,(t) = Acos(@)t + 45°) and w,(t) = Acos(@pt — 45°) : Decision: 1. Calculate z,(t) as 2) = fr) w (Oat 2. Find the quadrant of (Zp), 24) ® docsity.com  4.6 Complex Envelope = Areal bandpass waveform s(t) can be represented using complex notation sect s(t) =Re{g(e""} Where g(t) is known as the complex envelope, expressed as: = The magnitude of the complex envelope is: RN=|gMl=yr Orv = And its phase: I(t a(t) = tan! 2 x(t) = g(t) is called the baseband message or data in complex form and e/"0', the carrier wave in complex form ® docsity.com  = Then the modulation can be expressed as the product of the two s(t) = Re{[ x(t) + jv(t)] [cos @,f+ jsin @t]} = x(t)cos @,t—- y(t)sin @yt 4.6.1 Quadrature Implementation of a Modulator = Consider a baseband waveform g(t) appearing at discrete times k =1,2,..., Then g(t), x(t) and y(t) can be written as g,, x,,y,. Let x,=y, =0.707A; Then complex envelope can be expressed in discrete form as! g, =x, + jy, =0.707 A+ j0.707 A = The modulation process suggests: s(t) = Re{g, e”””} = Re{[ x, + jv, ] [cos o,f + jsin a,t]} = xX, COS W ,f- y, SM Oy 1 = 0.707 Acos w,f-0.707 Asin @,f = Acos [oy + 4) ® docsity.com  = Detector in general calculates the coordinates of the incoming signal by correlating it with locally generated waveforms such as: \2/T cosw,t and V2/T sinwgt Angie measured by datector ysl) Ld (ay : by} Stored signal vector (ag, bz) 6 Currently = The detector then measures the = _ ved signal vector angle between the currently received signal vector and the previously received signal vector. a th ym 20M fet, M in wylt) Fig 4.16 — Signal space for DPSK ® docsity.com  4.5.2 Detection of Binary PSK Differential Encoding message (first bit arbitrary), d, Sample Index,k 0 |1 12 6 |7 |8 |91]10 Information Message, a, 1 11 1 11 0 );0]1 Differentially Encoded 141 41 141 {0 1171 shift, 6, Corresponding phase 070 |0 Encoding Schemes d, = di, ® ay, d, = di ® ay, @ docsity.com  Decoding Scheme r(k) n a, =n, On, a(k) docsity.com