cs lec4,5 11feb
TRANSCRIPT
review
Signals
Complex Waves and HarmonicsSine Wave
Square Wave
Saw tooth Wave
Conversion/Signal Formatting
Character Coding
2
Formatting
• Character coding
• Sampling
• Quantization
• Pulse Code Modulation(PCM)• Pulse Code Modulation(PCM)
4
2. Analog to Digital Conversion (Codec)
First Step: Pulse Amplitude Modulation (PAM)
• According to Nyquist theorem, the sampling rate must be at least two times the frequency to ensure the accurate reproduction of the original signal.
K. Salah
First Step: Pulse Amplitude Modulation (PAM)
Third Step: Pulse Code Modulation
(PCM)
K. Salah
Out of each sample, Telephone companies only uses the upper 7 bits. The lower bit (bit 0) is always assumed to be 0. For example, sampling values:
+024 � +024, +038 � +038,
+025 � +024, +039 � +038
This is not affecting sampling values much.
In transmission, the most significant bit is used for control purposes, as we will see later.
Remember this
Sample Theorem
Need for sampling:
In analog signal, distortion is produced, and it
is difficult to recover the signal, However it is
easy to do so in digital signal.easy to do so in digital signal.
13
Impulse Sampling
Use of Impulse:
At a particular point, we get a sample.
When any function is multiplied by impulse When any function is multiplied by impulse function at t=xsec, we get a sample of that function at x sec.
If we want to recover complete signal we have to multiply by impulse train.
16
Aliasing
Aliasing refers to an effect that causes different
signals to become indistinguishable (or aliases
of one another) when sampled. It also refers to
the distortion that results when the signalthe distortion that results when the signal
reconstructed from samples is different from the
original continuous signal.
28
Converting bit into samples
• Quantizing
• Similar concept to pixelization.
• Breaks wave into pieces, assigns a value in a
particular rangeparticular range
• 8-bit range allows for 256 possible sample
levels
• More bits means greater detail, fewer bits
means less detail
PCM
PCM uses a sampling rate of 8000 samples per
second.
Each sample is an 8 bit sample resulting in a Each sample is an 8 bit sample resulting in a
digital rate of 64,000 bps (8 x 8000).
Quantization Error
• Analog voice data must be translated into a series of binary digits before they can be transmitted.
• With Pulse Code Modulation (PCM), the amplitude of the sound wave is sampled at amplitude of the sound wave is sampled at regular intervals and translated into a binary number.
• The difference between the original analog signal and the translated digital signal is called quantizing error.
Structure of Telephone System
• End office, known also as local central office
• Local loops (twisted pairs, analog signaling)
• Trunks (fiber optics or microwave, mostly digital)
• Intermediate switches
K. Salah
Question of Lecture
• What is the difference between time and frequency domain?
• Any complex waveform is composed of?
• A square wave is composed of?
• A saw tooth wave is composed of?
• Prove that sine wave is composed of main frequency and all • Prove that sine wave is composed of main frequency and all harmonics using Fourier series?
• Prove that square wave is composed of main frequency and all odd harmonics using Fourier series?
• Read what is ASCII coding?
• What is M-ary pulse modulation
58
Asssignment#1
Due Date: 21Feb, 2014
1. Prove through Fourier series that sine waveform is a fundamental waveform?is a fundamental waveform?
2. What is the harmonic composition of a square wave?
3. Draw and explain the basic communication system taking PSTN as an exemplary network?
4. What is m-ary pulse modulation?
59