Sampling And Waveform Coding

A Home Assignment Blog on

“ sampling and waveform coding”

 Submitted to B.G.Tarlekar sir

Vishwakarma Institute of Technology, Pune

(An Autonomous Institute Affiliated to Savitribai Phule Pune University)

In partial fulfilment of the requirements of

B.Tech.

In

Electronics and Telecommunication Engineering

By

                   Student Name        Roll No          Gr.No

1       ShrinathPalwankar             65             11920105

2        Manav Wacchewar            58             11810712

3        Nikhil Shete                      53                11811174

4.        Sarang Patil                     52                11810738

5.        Prathamesh Kulkarni       59                1710485

Academic Year 2019-20 / SEM II

SY B.Tech ET B

Subject: ET2015/ DIGITAL SYSTEM

Department of Electronics and Telecommunication Engineering

                                                           SAMPLING:

                                                              Theory:-
                               

                                    Sampling theory is a subset of communications theory.

                                               want to record signal, not noise 

                                   Quantization: Conversion from analog to discrete values

                                   Coding: Assigning a digital word to every discrete value

                                                  Thermometer code, Gray code...

                                                      Quantization adds noise

                                                 Analog signal is continuous

                                              Digital representation is approximate

                                                      Difference (error) is noiselike

                                                   Quantizing a signal

                                                      1) We sample it

                                                      2) We encode the samples 

                                                  Questions-

                                                      How fast do we sample?

                                                      How do we so this in hardware?

                                                      What resolution do we need?

                                                           Shannon's sampling theorem

 If endless , band-limited signal contains no frequency components above fc, then we will recover the first signal without distortion if we sample at a rate of at least 2fc samples

 ✦ 2fc is called the Nyquist rate

 ✦ Real life

 ➭ Sample at 2.5fc or faster

 ➭ Sample clock shouldn't be coherent with the input 

  A theorem which was discovered  by Harry Nyquist and that have been proven by Shannon  which states that an analog signal waveform could even be uniquely reconstructed, without error, from samples taken at equal time intervals.

The rate must be adequate to , or greater than, twice the very best frequency component within the analog signal.

 The highest frequency which may be accurately represented is one-half of the rate .

 Nyquist Theorem and Aliasing

 Nyquist Theorem: we will digitally represent only frequencies up to half the rate .

 Example: CD: SR=34,100 Hz Nyquist Frequency = SR/2 = 17,050 Hz

 Example: SR=14,050 Hz Nyquist Frequency = SR/2 = 7,025 Hz

 Frequencies more than Nyquist frequency "fold over" they  sound like lower frequencies.

This foldover is called aliasing.

The aliased frequency f has range [SR/2, SR] becomes f': f' = |f – SR/2|

  Example: SR = 20,000 Hz

 Nyquist Frequency = 10,000 Hz

 f = 10,000 Hz --> f' = 6,000 Hz

 f = 18,000 Hz --> f' = 2,000 Hz

 f = 20,000 Hz --> f' = 0 Hz

       

                                                       *WAVEFORM CODING*
                                             
                                                                  Introduction

Waveform coding implies algorithms and methods that focus on single variables, such as body position and joint angles. No knowledge of the actual action that the figure is performing (such as walking, waving etc.) is assumed, and the exact source of the motion is also not under consideration, only that it is valid human motion.

Whether the motion is captured in real-time, or generated by synthetic animation techniques, is of no concern. It is assumed that all of the body parameters can be decomposed into single DOF values that are independent of each other. An exception to this is the spatial vector quantization method presented at the end of the chapter, where it is assumed that there is a correlation between the variables.

In general a distinction can be made between coding (or compression) in the temporal domain and coding in the spatial domain. These two domains can be seen as orthogonal l to each other, and it is often advantageous to combine methods from each domain to get maximum compression. Temporal coding techniques take advantage of the temporal correlation of a single variable, while spatial techniques take advantage of spatial correlation between several variables.

Pulse Code Modulation (PCM)-

PCM is a crucial method of analog –to-digital conversion. In this modulation the analog signal is converted into an electrical waveform in two or more levels. A simple two level waveform is shown in figure

 The essential operations within the transmitter of a PCM system are Sampling, Quantizing and Coding. The Quantizing and encoding operations are usually performed by an equivalent circuit, normally mentioned as analog to digital converter. The essential operations within the receiver are regeneration, decoding and demodulation of the quantized samples. Regenerative repeaters are wont to reconstruct the transmitted sequence of coded pulses so as to combat the accumulated effects of signal distortion and noise.

                                               Quantization Process: the method of remodeling sampled amplitude values of a message signal into a discrete amplitude value is mentioned as Quantization. Amplifier - E li Decision Making Device Timing Circuit The quantization Process has a two-fold effect: 1. the peak-to-peak range of the input sample values are further  divided into a finite set of decision levels or decision thresholds that are aligned with the risers of the staircase, and 2. the output is assigned a random value selected from a finite set of representation levels and they are associated with the treads of the staircase.. A quantizer is memory less in that the quantizer output is set only by the price of a corresponding input sample, independently of earlier analog samples applied to the input.

Types of Quantizers: 1. Uniform Quantizer 2. Non- Uniform Quantizer

 *Coding Speech at Low Bit Rates: the utilization of PCM at the quality rate of 64 kb/s demands a high channel bandwidth for its transmission. But channel bandwidth is at a premium, during which case there's a particular need for speech coding at low bit rates, while maintaining acceptable fidelity or quality of reproduction. The fundamental limits on bit rate suggested by auditory perception and knowledge theory show that prime quality speech coding is feasible at rates considerably less that 64 kb/s (the rate may partially be as low as 2 kb/s). For coding speech at low bit rates, a waveform coder of prescribed configuration is optimized by exploiting both statistical characterization of speech waveforms and properties of hearing.

 The design theory has two contents in mind 1. Redundancies should be removed from the speech signal as far as possible. 2. To assign the available bits to code the non-redundant parts of the speech signal during a perceptually efficient manner. 

To reduce the bit rate from 64 kb/s (used in standard PCM) to 32, 16, 8 and 4 kb/s, the algorithms for redundancy removal and bit assignment become increasingly more sophisticated. There are two schemes for coding speech: 1. Adaptive Differential Pulse code Modulation (ADPCM) is 32 kb/s 2. Adaptive Sub-band Coding.16 kb/s

 Adaptive Differential Pulse – Code Modulation -

The term “adaptive” means being aware of changing level and spectrum of the input speech signal. The variation of performance with speakers and speech material, together with variations in signal level inherent in the speech communication process, make the combined use of adaptive quantization and adaptive prediction necessary to achieve best performance. The term “adaptive quantization” refers to a quantizer that operates with a time-varying step size ( )s ∆ nT , where Ts is the sampling period. The step size ( )s ∆ nT is varied so as to match the variance x 2 σ of the input signal ( ) nTs x . In particular, we write Δ(nTs) = Φ. σ^x(nTs) ----- where Φ – Constant σ^x(nTs) – estimate of the σx(nTs)