AM – DSB-SC (double sideband suppressed carrier)

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Modulator the modulated signal .AM – DSB-SC (double sideband suppressed carrier) Spectrum M ( f ) = F [m(t )] S ( f ) = F [m(t ) cos(2π f 0 t )] = F [m(t )] ∗ F [cos(2π f 0 t )] = = M ( f ) ∗ 1 [δ ( f − f 0 ) + δ ( f + f 0 )] = 2 = 1 M ( f − f0 ) + 1 M ( f + f0 ) 2 2 .AM – DSB-SC (double sideband suppressed carrier) fM Power of the modulating signal P= ∫ | M ( f ) |2 df S =...

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AM – DSB-SC (double sideband suppressed carrier) Modulator the modulated signal
AM – DSB-SC (double sideband suppressed carrier) M ( f ) = F [m(t )] Spectrum S ( f ) = F [m(t ) cos(2π f 0 t )] = F [m(t )] ∗ F [cos(2π f 0 t )] = = M ( f ) ∗ 1 [δ ( f − f 0 ) + δ ( f + f 0 )] = 2 = 1 M ( f − f0 ) + 1 M ( f + f0 ) 2 2
AM – DSB-SC (double sideband suppressed carrier) fM ∫ | M ( f ) |2 df P= Power of the modulating signal − fM S = ∫ | S ( f ) |2 df = 1 P + 1 P = 1 P Power of the modulated signal (DSB-SC) 4 4 2 (if the amplitude of the carrier signal =1)
AM – DSB-SC (double sideband suppressed carrier) Practical method of DSB-SC generation x(t ) = m(t ) [a1 cos(2π f 0t ) + a3 cos(2π 3 f 0t ) + a5 cos(2π 5 f 0t ) + …] = = a1m(t ) cos(2π f 0t ) + a3m(t )cos(2π 3 f 0t ) + a5 m(t )cos(2π 5 f 0t ) + … DSB-SC, carrier f0 DSB-SC, carrier 3f0 DSB-SC, carrier 5f0
AM – DSB-SC (double sideband suppressed carrier) The high – frequency components may be eliminated, using a filter: s (t ) = a1 m(t ) cos(2π f 0 t ) At the filter output:
AM – DSB-SC: demodulator Receiver with a synchronous detector band- low- pass pass filter filter DSBSC +noise bandwidth fM bandwidth B synchronous detector 1. DSC-SC signal without noise s (t ) = m(t ) cos(2π f 0 t ) - input of the synchronous detector: m(t ) cos 2 (2π f 0 t ) = m(t ) [ 1 + 1 cos(4π f 0 t )] - output of the synchronous detector : 2 2 s0 (t ) = 1 m(t ), =1P power S 0 moc - output of the low-pass filter: 2 4
AM – DSB-SC: demodulator P S P SNR0 = 0 = 4 = 2. signal to noise ratio at the output of the receiver N 0 η f M 2η f M P 2 S P =2= at the output of the channel SNR = = SNR0 N η f M 2η f M B   f fM SNR0,max = 1 + M SNR  −1 maximum resistance to channel noise   B 2 SNR0,max = [1 + 1 SNR ] − 1 > SNR0, DSBSC Here, bandwidth expansion B/fM =2 2 DSBSC receiver with a synchronous detector does not attain maximum resistance to channel noise
Application of the AM – DSB-SC: the analog stereo signal L(t), R(t) – left and right channel The composite stereo signal: f0 m(t ) = [ L(t ) + R(t )] + [ L(t ) − R (t )]cos(2π f 0t ) + a cos(2π t) 2 monoaural DSB-SC „pilot” signal f0=38kHz 19kHz m(t) with no « pilot» Decoder of the L(t) and R(t): 2 samplers
Application of the AM – DSB-SC: the analog stereo signal Spectrum of the composite stereo signal: monoaural „pilot” DSB-SC signal 19kHz f0=38kHz
AM – DSB (double sideband) Modulator the modulated signal
AM – DSB (double sideband) Spectrum of the DSB = Spectrum of the DSB SC + carrier spectrum Psd of the DSB SC and psd of the carrier signal are disjoint, so the power of DSB signal is a sum of the DSB SC and carrier powers. Generally, power of a sum of signals is not equal to the sum of corresponding powers. Power od the DSB signal: S = 0.5 + 0.5 P Due to transmission of the carrier, higher SNR of the channel is required, i.e. resistance to channel noise is lower for DSB than for DSB SC.
AM – DSB: envelope detector E.g. peak detector: Application of the DSB: commercial broadcast using long and medium waves (fM=4.5 kHz, B=9 kHz)
AM – SSB (single sideband) DSB-(SC) SSB-(SC) Modulation by filtering: H(f) = P/4 Power : S Filter ( upper SSB): Application of the SSB: communication using short waves
AM – SSB (single sideband) x m(t) + Modulation by phase SSB-SC cos(2πf0t) shift: ^ m(t) +/- HH(f) x sin(2πf0t) -: upper SSB +: lower SSB: Hilbert transform (phase shift by 90o) s (t ) = m(t )cos(2π f 0 t ) ± m(t )sin( 2π f 0 t ) ˆ =P Power: S
SSB receiver - synchronous detector m*(t)=s0(t)+n0(t) SSB+noise x LPF BPF cos(2πf0t) bandwidth bandwidth fM fM 1. (Upper) SSB without noise m(t )cos(2π f 0 t ) − m(t )sin(2π f 0 t ) ˆ - output of the bandpass filter (BPF) m(t )cos 2 (2π f 0 t ) − m(t )sin(2π f 0 t )cos(2π f 0 t ) = ˆ - output of the multiplier = m(t )[1 + 1 cos(4π f 0 t )]− m(t ) 1 sin(4π f 0 t ) ˆ2 2 2 s0 (t ) = 1 m(t ) S0 = 1 P power - output of the lowpass filter (LPF) 2 4
SSB receiver - synchronous detector m*(t)=s0(t)+n0(t) SSB+noise x LPF BPF cos(2πf0t) bandwidth bandwidth fM fM η fM N0 = 2. Noise only 4 S0 P S P - at the output of - at the output of SNR0 = = SNR = = the receiver the channel N0 η fM N η fM B =1 This is the maximum SNR0 at the bandwidth expansion fM
AM – SSB - spectra Receiver: synchronous detector upper SSB
AM – SSB - spectra lower SSB
AM – VSB (vestigial sideband) DSB VSB Modulator: H(f) Filter: Application of the VSB: terrestrial analog TV
Synchronous detector with phase error s0(t) s(t) x LPF BPF cos(2πf0t+φ) phase error 1. Reception of the DSBSC signal m(t )cos(2π f 0 t ) - output of the bandpass filter (BPF) m(t ) cos(2π f 0 t ) cos(2π f 0 t + φ ) = - output of the multiplier = 1 m(t )[cos φ + cos(4π f 0 t + φ )] 2 s0 (t ) = 1 m(t ) cos φ S 0 = 1 P cos 2 φ power - output of the lowpass filter (LPF) 2 4