Điều chế xung biên độ PAM

3F4 Pulse Amplitude Modulation (PAM) Dr. I. J. Wassell Introduction • The purpose of the modulator is to convert discrete amplitude serial symbols (bits in a binary system) a k to analogue output pulses which are sent over the channel. • The demodulator reverses this process Modulator Channel Demodulator Serial data symbols a k ‘analogue’ channel pulses Recovered data symbols Introduction • Possible approaches include – Pulse width modulation (PWM) – Pulse position modulation (PPM) – Pulse amplitude modulation (PAM) • We will only be considering PAM in these lectures PAM • PAM is a general signalling technique whereby pulse amplitude is used to convey the message • For example, the PAM pulses could be the sampled amplitude values of an analogue signal • We are interested in digital PAM, where the pulse amplitudes are constrained to chosen from a specific alphabet at the transmitter PAM Scheme H C ( ω ) h C (t) Symbol clock H T ( ω ) h T (t) Noise N( ω ) Channel + Pulse generator a k Transmit filter ∑ ∞ −∞= −= k ks kTtatx )()( δ ∑ ∞ −∞= −= k Tk kTthatx )()( Receive filter H R ( ω ), h R (t) Data slicer Recovered symbols Recovered clock )()()( tvkTthaty k k +−= ∑ ∞ −∞= Modulator Demodulator PAM • In binary PAM, each symbol a k takes only two values, say {A 1 and A 2 } • In a multilevel, i.e., M-ary system, symbols may take M values {A 1 , A 2 , A M } • Signalling period, T • Each transmitted pulse is given by )( kTtha Tk − Where h T (t) is the time domain pulse shape PAM • To generate the PAM output signal, we may choose to represent the input to the transmit filter h T (t) as a train of weighted impulse functions ∑ ∞ −∞= −= k ks kTtatx )()( δ • Consequently, the filter output x(t) is a train of pulses, each with the required shape h T (t) ∑ ∞ −∞= −= k Tk kTthatx )()( PAM • Filtering of impulse train in transmit filter Transmit Filter ∑ ∞ −∞= −= k Tk kTthatx )()( ∑ ∞ −∞= −= k ks kTtatx )()( δ )(th T )(tx s )(tx PAM • Clearly not a practical technique so – Use a practical input pulse shape, then filter to realise the desired output pulse shape – Store a sampled pulse shape in a ROM and read out through a D/A converter • The transmitted signal x(t) passes through the channel H C ( ω ) and the receive filter H R ( ω ). • The overall frequency response is H( ω ) = H T ( ω ) H C ( ω ) H R ( ω ) PAM • Hence the signal at the receiver filter output is )()()( tvkTthaty k k +−= ∑ ∞ −∞= Where h(t) is the inverse Fourier transform of H( ω ) and v(t) is the noise signal at the receive filter output • Data detection is now performed by the Data Slicer [...].. .PAM- Data Detection • Sampling y(t), usually at the optimum instant t=nT+td when the pulse magnitude is the greatest yields yn = y (nT + td ) = ∞ ∑ a h((n − k )T + t ) + v k = −∞ k d n Where vn=v(nT+td) is the sampled noise and td is the time delay required for optimum sampling • yn is then compared with threshold(s) to determine the recovered data symbols PAM- Data Detection TX . modulation (PAM) • We will only be considering PAM in these lectures PAM • PAM is a general signalling technique whereby pulse amplitude is used to convey the message • For example, the PAM pulses. analogue signal • We are interested in digital PAM, where the pulse amplitudes are constrained to chosen from a specific alphabet at the transmitter PAM Scheme H C ( ω ) h C (t) Symbol clock H T ( ω ). slicer Recovered symbols Recovered clock )()()( tvkTthaty k k +−= ∑ ∞ −∞= Modulator Demodulator PAM • In binary PAM, each symbol a k takes only two values, say {A 1 and A 2 } • In a multilevel, i.e.,