1. Pulse Modulation 1

2. Introduction In Continuous Modulation C.M. a parameter in the sinusoidal signal is proportional to m(t) In Pulse Modulation P.M. a parameter in the pulse train is proportional to m(t) In analog P.M. the parameter (amplitude, position, duration) is varied in a continuous manner In digital P.M. the values are discrete values P.M. is a transition between analog modulation and digital modulation 2

3. Kinds of Pulse Modulation PAMPulse Amplitude Modulation PDMPulse Duration Modulation (or)PWMPulse Width Modulation PPMPulse Position Modulation PCM Pulse Code Modulation 3

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5. Natural Sampling The sampled signal consists of a sequence of pulses of varying amplitude whose tops are not flat but follow the shape of the waveform of the signal m(t). 5

6. The sampled signal consists of a sequence of pulses of flat tops amplitude. It will make distortion for recovered signal, but the distortion will not be noticeable when the number of samples are large, 6 Flat-Top Sampling

7. Pulse Amplitude Modulation (PAM) The amplitudes of regularly spaced pulses are varied in proportion to the corresponding sampling values of a continuous message Similar to natural sampling: the message signal is multiplied by a train of rectangular pulses. The top of each modulated rectangle is maintained not flat 7

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9. Two operations evaluated in the generation of PAM: - Instantaneous sampling every T s - Lengthening the duration of the sample to some constant value T. To reconstruct the signal, we need an equalizer (since the sample and hold filter used at the transmitter alter the shape of the signal) plus the reconstruction filter 9

10. Reconstruction filter Equalizer PAM signal The reconstruction filter is an ideal L.P.F having a cut off frequency equals to the signal bandwidth. The equalizer frequency response: H eq (f) = 1/ | H 0 (f)| = 1 / [ T sinc (fT ) = π f / [ sin (π f T) ] 10

11. Quantization Process Quantization is to approximate each sample to the nearest level. Amplitude quantization: The process of transforming the sample amplitude m(nT s ) of a message signal m(t) at time t = nT s into a discrete amplitude v(nT s ) taken from a finite set of possible amplitudes Quantizer g(.) Continuous sample m Discrete sample v 11

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13. Define: L Total number of amplitude levels used in the quantizer m k discrete amplitudes k = 1,2 …L (decision levels, thresholds ) v k representation (or reconstruction) levels I k quantizer interval m k-1 mkmk m k+1 m k+2 v k-2 v k-1 v k v k+1 I k 13

14. Step size (quantum): spacing between two representation levels The quantizer O/P v = v k if the input signal m belongs to the interval I k 14

15. Uniform (linear) Quantization The representation levels are uniformly spaced  Mid-tread: Origin in the middle of staircase  Mid-rise: Origin in the middle of rising part of staircase Mid-tread Mid-rise 15

16. Quantization Noise for Uniform Quantization The use of quantization introduces an error between the I/P signal m(t) and the signal at quantizer output m q (t). This error is known as: quantization error or (e), where: e = m(t) – m q (t) 16

17. If m(t) is in the range ( - m max, m max ) Then the Step size of the quantizer : S = 2 m max / L Assume that the quantization error is uniformly distributed within each quantization range, then its p.d.f f(m) will be:f 1 (m)+f 2 (m)+ f 3 (m)+….+ f L (m) = 1 / S f(m) 17 Quantization Noise for Uniform Quantization f 2 (m) f 1 (m) f 4 m) f 3 (m) f 1 (m) f L (m) m s

18. σ Q 2 =Quantization noise = mean square value of the error = m max 2 / [ 3 L 2 ] [S=2m max /L] If ‘n’ is the number of bits per sample L = 2 n S = 2m max / 2 n σ Q 2 = m max 2 2 -2n / 3 18

19. Let P = average power of the message signal m(t) Assuming m(t) is uniformly distributed from –m max to m max Output signal to noise ratio = SNR o/p = P / σ Q 2 = 3 P 2 2n / m max 2 = 3 K (2) 2n Where: K = P / m max 2 = 1/3 [SNR o/p ]= 10 log [(2) 2n ] = 6n (dB) 19

20. Non-Uniform quantization (Companding) Why? Low amplitudes happens more frequently than larger ones Since the mean square error is proportional to the step size, we need to decrease the step size for lower values than larger values. This is accomplished by using a compressor at the transmitter and an expander at the receiver The combination of a compressor and an expander is called compander 20

21. Two types of compressors may be used: A law and μ law refer to the parameter which appear in the equation of compression and expansion.  -Law A-Law 21 Non-Uniform quantization (Companding)

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25. Dynamic Range: is the difference in dB between max. signal level, and min. signal level having accepted output SNR. To improve dynamic range Companding is used to keep SNR high for low signal level as well as for high signal level 25 Non-Uniform quantization (Companding)

26. 26 Non-Uniform quantization (Companding) Output SNR (dB) Companded Un-Companded S i (dB) normalized input signal power in dB 30 -18-480 10 dB 48

27. Example: For acceptable voice transmission the received signal have a ratio SNR > 30 dB. The companded system has dynamic range of input signal=48 dB. The un-companded system has dynamic range of input signal=18 dB for the same condition of SNR>30 dB The penalty paid is at max. amplitude of input signal, SNR is less 10 dB after companding. 27 Non-Uniform quantization (Companding)