5. analog to digital conversion. ( pcm ,dm with short descriptions )
- 3. 4.3 Pulse Code Modulation (PCM) Delta Modulation (DM) • To change an analog signal to digital data we use two techniques, ANALOG-TO-DIGITAL CONVERSION
- 4. 4.4 Pulse Code Modulation (PCM)
- 5. 4.5 PCM
- 6. 4.6 Figure 1 Components of PCM encoder
- 7. 4.7 Sampling • Analog signal is sampled every TS secs. • Ts is referred to as the sampling interval. • fs = 1/Ts is called the sampling rate or sampling frequency. • There are 3 sampling methods: • Ideal - an impulse at each sampling instant • Natural - a pulse of short width with varying amplitude • Flattop - sample and hold, like natural but with single amplitude value • The process is referred to as pulse amplitude modulation PAM and the outcome is a signal with analog (non integer) values
- 8. 4.8 Figure 2 Three different sampling methods for PCM
- 9. 4.9 According to the Nyquist theorem, the sampling rate must be at least 2 times the highest frequency contained in the signal. Nyquist theorem
- 10. 4.10 Figure 3 Nyquist sampling rate for low-pass and bandpass signals
- 11. 4.11 Figure 4 Recovery of a sampled sine wave for different sampling rates
- 14. 4.14 Figure 5 Quantization and encoding of a sampled signal
- 15. 4.15 Quantization Levels • The midpoint of each zone is assigned a value from 0 to L-1 (resulting in L values) • Each sample falling in a zone is then approximated to the value of the midpoint.
- 16. 4.16 Quantization Error • When a signal is quantized, we introduce an error - the coded signal is an approximation of the actual amplitude value. • The difference between actual and coded value (midpoint) is referred to as the quantization error. • The more zones, the smaller which results in smaller errors. • BUT, the more zones the more bits required to encode the samples -> higher bit rate
- 17. 4.17 Encoding • The last step in PCM is encoding. • If the number of quantization levels is L, the number of bits is nb=log2 L. • The bit rate can be found from the formula. Bitrate = Sampling rate X Number of bites per sample= ƒs X nb
- 18. 4.18 Encoding • Bmin = c x N x 1/r = c x ƒs X nb x 1/r = 0.5 x ƒs X nb x 1/r = c x ƒs X nb
- 19. 4.19 Find the Transmission of a low pass analog signal using PCM
- 21. 4.21 Delta Modulation • This scheme sends only the difference between pulses, if the pulse at time tn+1 is higher in amplitude value than the pulse at time tn, then a single bit, say a “1”, is used to indicate the positive value. • If the pulse is lower in value, resulting in a negative value, a “0” is used. • This scheme works well for small changes in signal values between samples. • If changes in amplitude are large, this will result in large errors.
- 22. 4.22 Figure 6 Delta modulation components
- 23. 4.23 Figure 7 The process of delta modulation
- 24. 4.24 Thank you