CHAPTER 1 Pulse Code Modulation 1 TOPICS Sampling

CHAPTER 1: Pulse Code Modulation 1

TOPICS ¡ ¡ ¡ ¡ Sampling theorem Nuquist criteria Sample and hold circuit Quantization PCM transmitter and receiver Delta Modulation Adaptive DM DPCM 2

1. 1 Sampling theorem ¡ For periodic waveforms, the duration of the waveform before it repeats is called the period of the waveform. ¡ In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous-time signals (often called "analog signals") and discrete-time signals (often called "digital signals"). It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth. Sampling Theorem: “A bandlimited signal can be 3 reconstructed exactly if it is sampled at a rate atleast twice the maximum frequency component in ¡

Sampling process…. . V Information signal Pulse train Wt multiplication Sampled signal 4

1. 2 Nyquist criteria…. . Statemene: “the sampling frequency should be at least double than the highest frequency component present in the information signal” Sampling freq. Fs>>>2 Fi Fs=sampling freq. in Hz Fi=infoemation signal in Hz

1. 3 Quantization Statemene: “Quantization is the process of converting a continuous range of values into a finite range of discreet values. This is a function of analog-to-digital converters, which create a series of digital values to represent the original analog signal. ” 6

1. 3 Quantization…… -Sampling results in a series of pulses of varying amplitude values ranging between two limits: a min and a max. -The amplitude values are infinite between the two limits. -We need to map the infinite amplitude values onto a finite set of known values. -This is achieved by dividing the distance between min and max into L zones, each of height = (max - min)/L 7

1. 4 PCM encoder / decoder Encoder(transmitter)

Decoder(receiver)

1. 6 Delta Modulation -Next form of pulse modulation -Transmits information only to indicate whether the analog signal that is being encoded goes up or goes down -The Encoder Outputs are highs or lows that “instruct” whether to go up or down, respectively -DM takes advantage of the fact that voice signals do not change abruptly -The analog signal is quantized by a one-bit ADC (a comparator implemented as a comparator) -The comparator output is converted back to an analog signal with a 1 -bit DAC, and subtracted from the input after passing through an integrator The shape of the analog signal is transmitted as follows: a "1" indicates that a positive excursion has occurred since the last sample, and a "0" indicates that a negative excursion has occurred since the last sample.

DM Block Diagram 11

1. 6 Delta Modulation…. .

Slope Overloading problem…. . in DM 13

slope overhead distortion ¡ granular noise ¡

1. 7 Adaptive DM Adaptive Delta Modulation (ADM) is another voice coding scheme; a mature technique that should be considered for these applications because of its bit error robustness and its low implementation cost. ADM quantizes the difference between the current sample and the predicted value of the next sample.

1. 8 Differential PCM -Sampling at higher then Nyquist rate creates correlation between samples (good and bad) -Difference between samples has small variance – smaller than the variance of the signal itself -Encoded signal contains redundant information -Can be used to a positive end – remove redundancy before encoding to get a more efficient signal to be transmitted

DPCM system. (a) Transmitter. (b) Receiver