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Nâng Cao Xử Lý Số Tín Hiệu - Special Topics on ADSP

Chapter 2:

Noise and Distortion in terms of signals

Lectured by Assoc. Prof. Dr. Thuong Le-Tien

February 2015

• Noise can be defined as an unwanted signal that inteferenceswith the communication or measurement of another signal.

• The sources of noise a re many, and vary from low to ultra high frequency

• Noise and distortion are the main limiting factors in communication and measurement systems

1. INTRODUCTIONDepending on its source, noise can be classified asa. Acoustic noise: moving cars, air conditioners, computer fans,

traffic, people talking, wind, rain, etc.b. Electromagnetic noise: present in all frequencies, particular at

the radio frequencies.c. Electrostatic noise: by presence of a voltage with/without

current flow. Fluorescent lighting is one of the more common sources of this electrostatic noise

d. Channel distortion, echo and fading: due to non-ideal characteristic of communication channels. Radio channels scuh as cellular phone operators, radio networks, etc.

e. Processing noise: results from the analog/digital signal processing,e.g. quantization noise, lost data packets in data communications, etc.

Depending on its frequencies or time characteristics, a noise Process can be classified as:

a. Narrowband noise: such as 50/60z from electricity supplyb. White noise: purely random noise, flat power spectrum in

all frequencies.c. Band-limited white noise: flat spectrum, limited BW cover

limited spectrum of devices or signal interestd. Colored noise: non-white noise or any wideband noise, non-flat

shape of spectrum, e.g. pink noise, brown noise, autoregressive noise

e. Impulsive noise: short-duration pulses of random amplitude and duration.

f. Transient noise pulses: relatively long duration noise pulses.

2. WHITE NOISE

White noise Autocorrelation Spectrum

The constant power spectrum

The spectrum of band-limited white noise

Ts is the sampling period, and when Nyquist sampling rate

Then the auto-corrrelation function is a delta function

3. COLORED NOISERefered to broad band noise with a non-white spectrumExamples: most audio noise, moving car noise, computer fan noise, electric drill noise. Two classic colored noise are pink and brown noise

4. IMPULSES NOISE

Short duration on/off noise: switching noise

5. TRANSIENT NOISE PULSES

Short sharp initial pulse followed by decaying low-frequency oscillations

A typical scratch pulse waveform in the figure exhibits two distinct regions

6. THERMAL NOISE

Referred as Johnson noiseFor a metallic resistor, the mean square value of the instantaneous Voltage due to the thermal noise is

T is absolute temperature in Kelvin degree, B is bandwidth

The spectral density of thermal noise

7. SHOT NOISEA shot noise arose from the analysis of random variations in theemission of electron from the cathode of a vacuum tube

Consider an electric current as the flow of discrete electric charges.If the charges act independently of each other the fluctuating current is given

B is measurement Bandwidth

8. ELECTROMAGNETIC NOISE

Every electrical devices that generates, consumes or transmits power is a potential source of electromagnetic noise and interference for other systems. The common sources of electromagnetic noise are transformers, radio and television transmitters, mobile phones, Microwave transmitters, ac power lines, oscillators, electrical storms

9. CHANNEL DISTORTION

There are two main manifestation distortion: Magnitude and phase distortion

10. MODELING NOISEThe objective of modeling is to characterize the structures and the patterns in a signal or a noise process

The figure is an example of the spectra of car noise recorded from a BMW and Volvo. The noise in a car is nostationary, varied and may include the following sources:

10.1. Additive white Gaussian noise model (AWGN)In communication theory, it is assumed that the noise is a stationary AWGN process.

10.2 Hidden Markov model for noise (HMM)Most noise process a re non-stationary, e.g. the statistical parametersof the noise, such as mean, variance and power spectrum, vary with

Time. Non stationary processes may be modeled using the HMM

(a) An impulse noise sequence, (b) A binary state model of impulse noise

• An Hidden Markov Model is essentially a finite state Markov chain of stationary sub-processes

• Note that a stationary noise process can be modeled by a single state HMM• A non-stationary noise, a multi state HMM can model the time variations

of the noise process with a finite number of stationary states.• For non-Gaussian noise, a mixture Gaussian density model can be used to

model the space of the noise within each state.• In general, the number of states per model and number of mixtures per

state required to accurately model a noise process depends on the non-stationary character of the noise.