17-09-2012, 12:44 PM
Sampling Theory
Sampling.ppt (Size: 757.5 KB / Downloads: 210)
Frequency domain
Present recurring phenomena as amplitude vs. frequency
Same sine wave looks like –
Fourier Analysis
The eardrum responds to a sum of all the waves arriving at a particular instant. Yet the individual sounds are “heard.”
Any waveform is composed of an infinite number of simple sine waves of various frequencies and amplitudes.
Shannon-Nyquist's Sampling Theorem
A sampled time signal must not contain components at frequencies above half the sampling rate (The so-called Nyquist frequency)
The highest frequency which can be accurately represented is one-half of the sampling rate
Range of Human Hearing
20 – 20,000 Hz
We lose high frequency response with age
Women generally have better response than men
To reproduce 20 kHz requires a sampling rate of 40 kHz
Below the Nyquist frequency we introduce aliasing
Effect of Aliasing
Fourier Theorem states that any waveform can be reproduced by sine waves.
Improperly sampled signals will have other sine wave components.
http://www2.egr.uh.edu/~glover/applets/S...pling.html
Digital Voice Telephone Transmission
Voice data for telephony purposes is limited to frequencies less than 4,000 Hz.
According to Nyquist, it would take 8,000 samples (2 times 4,000) to capture a 4,000 Hz signal perfectly.
Generally, one byte is recorded per sample (256 levels). One byte is eight bits of binary data.
(8 bits * 8,000 samples per second = 64K bps) over a circuit.
T-1 Transmisson
T carrier circuits are designed around this requirement, since they are primarily designed to carry analog voice signals that have been digitalized.
For example, look at the DS-1 signal which passes over a T-1 circuit. For DS-1 transmissions, each frame contains 8 bits per channel and there are 24 channels. Also, 1 "framing bit" is required for each of the 24 channel frames.