PULSE CODE MODULATION
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The most common
technique to change an analog signal to digital data (digitization) is called
pulse code Modulation (PCM).
A
PCM encoder has three processes
· The analog
signal is sampled.
The sampled signal is quantized.
The quantized values are encoded as streams of
bits.
Sampling
The
first step in PCM is sampling. The analog signal is sampled every Ts s,
where Ts is the sample interval or period. The inverse of the sampling
interval is called the sampling rate or sampling frequency and denoted by is,
where is = IITs' There are three sampling methods-ideal, natural, and flat-top
· In ideal
sampling, pulses from the analog signal are sampled. This is an ideal sampling method
and cannot be easily implemented.
· In natural
sampling, a high-speed switch is turned on for only the small period of time
when the sampling occurs. The result is a sequence of samples that retains the
shape of the analog signal
· The most common
sampling method, called sample and hold, however, creates flat-top samples
by
using a circuit.
Sampling Rate
· According to the
Nyquist theorem, to reproduce the original analog signal, one necessary
condition is that the sampling rate be at least twice the highest frequency in
the original signal.
· if the signal is
band-limited. In other words, a signal with an infinite bandwidth cannot be
sampled. Second, the sampling rate must be at least 2 times the highest
frequency, not the bandwidth. If the analog signal is low-pass, the bandwidth
and the highest frequency are the same value. If the analog signal is bandpass, the
bandwidth value is lower than the value of the maximum frequency.
Quantization
The result of sampling is a
series of pulses with amplitude values between the maximum and minimum
amplitudes of the signal. The set of amplitudes can be infinite with
nonintegral values between the two limits. These values cannot be used in the
encoding process. The following are the steps in quantization:
1. We assume that the original
analog signal has instantaneous amplitudes between Vmin and Vmax'
2. We divide the range into L zones, each of
height (delta).
Vmax
- Vrnin = -==-:::--=L
3. We assign quantized values of
0 to L
- I to the
midpoint of each zone.
4. We approximate the value of
the sample amplitude to the quantized values.
Quantization Levels
If the amplitude of a signal fluctuates
between two values only, we need only two levels; if the signal, like voice,
has many amplitude values, we need more quantization levels. In audio
digitizing, L
is
normally chosen to be 256; in video it is normally thousands. Choosing lower
values of L
increases
the quantization error if there is a lot of fluctuation in the signal.
Quantization Error
Quantization is an approximation
process. The input values to the quantizer are the real values; the output
values are the approximated values. The output values are chosen to be the
middle value in the zone. If the input value is also at the middle of the zone,
there is no quantization error; otherwise, there is an error.
Encoding
The last step in PCM is encoding.
After each sample is quantized and the number of bits per sample is decided,
each sample can be changed to an llb-bit code word
Original
Signal Recovery
The
recovery of the original signal requires the PCM decoder. The decoder first
uses circuitry to convert the code words into a pulse that holds the amplitude
until the next pulse. After the staircase signal is completed, it is passed
through a low-pass filter to smooth the staircase signal into an analog signal.
The filter has the same cutoff frequency as the original signal at the sender. If the signal has been sampled at (or greater than)
the Nyquist sampling rate and if there are enough quantization levels, the
original signal will be recreated. Note that the maximum and minimum values of
the original signal can be achieved by using amplification. Figure shows
the simplified
process.
THAT 'S THE WHOLE PROCESS OF PULSE CODE MODULATION..
pulse code modulation
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