Analog Communication Suresh P. Nair [AIE, ME, (PhD)] MIEEE Professor & Head Department of Electronics and Communication Engineering Royal College of Engineering and Technology Chiramanangad PO, Akkikkavu, Thrissur, Kerala, India

Module 4:

Module 4 NOISE P. Suresh Venugopal 2 Analog Communication - NOISE

Topics to be covered:

Topics to be covered Noise Sources of noise Thermal Noise, Shot Noise, Flicker noise and White noise Noise Parameters Signal to noise ratio Noise factor Noise equivalent band width Effective noise temperature P. Suresh Venugopal 3 Analog Communication - NOISE

Topics to be covered:

Topics to be covered Narrow band noise Representation of narrowband noise in terms of In phase and Quadrature Components Noise in CW modulation Systems Noise in linear Receivers using Coherent detection Noise in AM Receivers using Envelope detection Noise in FM Receivers P. Suresh Venugopal 4 Analog Communication - NOISE

Noise Sources:

Noise Sources Introduction to Noise Shot Noise Thermal Noise Flicker Noise White Noise P. Suresh Venugopal 5 Analog Communication - NOISE

Noise - Introduction:

Noise - Introduction Noise – Unwanted Signals that tend to disturb the Transmission and Processing of Signals in Communication System and over which we have incomplete control. Noise is a general term which is used to describe an unwanted signal which affects a wanted signal. These unwanted signals arise from a variety of sources. P. Suresh Venugopal 6 Analog Communication - NOISE

Sources of Noise:

Sources of Noise Sources of noise may be: External Internal Naturally occurring external noise sources include: Atmosphere disturbance (e.g. electric storms, lighting, ionospheric effect etc), so called ‘Sky Noise’ Cosmic noise which includes noise from galaxy, solar noise ‘Hot spot’ due to oxygen and water vapour resonance in the earth’s atmosphere. P. Suresh Venugopal 7 Analog Communication - NOISE

Sources of Noise:

Sources of Noise Noise performance by external sources is shown below.

Sources of Noise:

Sources of Noise Internal Noise is an important type of noise that arises from the SPONTANEOUS FLUCTUATIONS of Current or Voltage in Electrical Circuits. This type of noise is the basic limiting factor of employing more complex Electrical Circuits in Communication System. Most Common Internal Noises are: Shot Noise Thermal Noise P. Suresh Venugopal 9 Analog Communication - NOISE

Shot Noise:

Shot Noise Shot Noise arises in Electronic Components like Diodes and Transistors . Due to the discrete nature of Current flow In these components. Take an example of Photodiode circuit . Photodiode emits electrons from the cathode when light falls on it. The circuit generates a current pulse when an electron is emitted. P. Suresh Venugopal 10 Analog Communication - NOISE

Shot Noise:

Shot Noise The electrons are emitted at Random times, Ʈ k where -∞ < k < ∞ and assume this random emission have been gone for a long time. Thus the Total Current flowing through the Photodiode may be modeled as the sum of these Current Pulses. This process X(t) is Stationary and is called SHOT NOISE P. Suresh Venugopal 11 Analog Communication - NOISE

Thermal Noise:

Thermal Noise Thermal Noise is the name given to the Electrical Noise arising from the Random motion of electrons n a conductor. It is also called Jonson Noise or Nyquist Noise. Let V TN is the Thermal Noise Voltage appearing across the two terminals of a resistor. Let the applied voltage have a bandwidth or frequency), ∆f. Then the Mean Square value of V TN is given by: P. Suresh Venugopal 12 Analog Communication - NOISE

Thermal Noise:

Thermal Noise Where k = Boltzmann’s constant = 1.38 x 10 -23 Joules per o K T = absolute temperature in o K R = resistance in ohms P. Suresh Venugopal 13 Analog Communication - NOISE

Jonson Noise or Nyquist Noise:

Jonson Noise or Nyquist Noise P. Suresh Venugopal 14 Analog Communication - NOISE

Thermal Noise:

Thermal Noise We can model a noisy resistor using the Thevenin and Norton Equivalent Circuit as shown below:

Thermal Noise:

Thermal Noise The number of electrons inside a resistor is very large and their random motions inside the resistors are statistically independent. The Central Limiting Theorem indicates that thermal Noise is a Gaussian Distribution with Zero mean. P. Suresh Venugopal 16 Analog Communication - NOISE

Low Frequency or Flicker Noise:

Low Frequency or Flicker Noise Active devices, integrated circuit, diodes, transistors etc also exhibits a low frequency noise, which is frequency dependent (i.e. non uniform) known as flicker noise . It is also called ‘one – over – f’ noise or 1/f noise because of its low-frequency variation . Its origin is believed to be attributable to contaminants and defects in the crystal structure in semiconductors, and in the oxide coating on the cathode of vacuum tube devices P. Suresh Venugopal 17 Analog Communication - NOISE

Low Frequency or Flicker Noise:

Low Frequency or Flicker Noise Flicker Noise is found in many natural phenomena such as nuclear radiation, electron flow through a conductor, or even in the environment. The noise power is proportional to the bias current , and, unlike Thermal and Shot Noise, Flicker Noise decreases with frequency. An exact mathematical model does not exist for flicker noise because it is so device-specific. However, the inverse proportionality with frequency is almost exactly 1/f for low frequencies, whereas for frequencies above a few kilohertz, the noise power is weak but essentially flat. P. Suresh Venugopal 18 Analog Communication - NOISE

Low Frequency or Flicker Noise:

Low Frequency or Flicker Noise Flicker Noise is essentially random, but because its frequency spectrum is not flat , it is not a white noise. It is often referred to as pink noise because most of the power is concentrated at the lower end of the frequency spectrum. Flicker Noise is more prominent in FETs (smaller the channel length, greater the Flicker Noise), and in bulky carbon resistors. The objection to carbon resistors mentioned earlier for critical low noise applications is due to their tendency to produce flicker noise when carrying a direct current. In this connection, metal film resistors are a better choice for low frequency, low noise applications. P. Suresh Venugopal 19 Analog Communication - NOISE

White Noise:

White Noise The Noise Analysis of Communication System is done on the basis of an idealized form of noise called WHITE NOISE . Its power spectral density is independent on operating frequency. White – White light contain equal amount of all frequencies in visible spectrum. P. Suresh Venugopal 20 Analog Communication - NOISE

White Noise:

White Noise Power spectral density is given by: The 1/2 here emphasizes that the spectrum extends to both positive and negative frequencies. P. Suresh Venugopal 21 Analog Communication - NOISE

Power Spectral Density of White Noise:

Power Spectral Density of White Noise A random process W(t) is called white noise if it has a flat power spectral density , i.e., S W (f) is a constant c for all f . P. Suresh Venugopal 22 Analog Communication - NOISE

Ideal Low Pass Filtered White Noise:

Ideal Low Pass Filtered White Noise Let w(t) = White Gaussian Noise applied to the LPF B = Bandwidth of LPF n(t) = noise appearing at the output of LPF S N (f) = Power Spectral Density of n(t) R N (Ʈ) = Auto Correlation function of n(t) P. Suresh Venugopal 23 Analog Communication - NOISE

Ideal Low Pass filtered White Noise:

Ideal Low Pass filtered White Noise P. Suresh Venugopal 24 Analog Communication - NOISE

Noise Parameters:

Noise Parameters Signal to noise ratio Noise factor Noise equivalent band width Effective noise temperature P. Suresh Venugopal 25 Analog Communication - NOISE

Signal to Noise Ratio (SNR):

Signal to Noise Ratio (SNR) where: P S is the signal power in watts P N is the noise power in watts Hartley-Shannon Theorem (also called Shannon’s Limit) states that the maximum data rate for a communications channel is determined by a channel’s bandwidth and SNR. A SNR of zero dB means that noise power equals the signal power. P. Suresh Venugopal 26 Analog Communication - NOISE

Noise Figure / Factor (NF or F or Fn):

Noise Figure / Factor (NF or F or F n ) Electrical noise is defined as electrical energy of random amplitude, phase, and frequency. It is present in the output of every radio receiver. The noise is generated primarily within the input stages of the receiver system itself. Noise generated at the input and amplified by the receiver's full gain greatly exceeds the noise generated further along the receiver chain. P. Suresh Venugopal 27 Analog Communication - NOISE

Noise Figure / Factor (NF or F or Fn):

Noise Figure / Factor (NF or F or F n ) The noise performance of a receiver is described by a figure of merit called the noise figure (NF). where G = Antenna Gain P. Suresh Venugopal 28 Analog Communication - NOISE

Noise equivalent band width:

Noise equivalent band width P. Suresh Venugopal 29 Analog Communication - NOISE

Effective noise temperature:

Effective noise temperature T = environmental temperature (Kelvin) N = noise power (watts) K = Boltzmann’s constant (1.38 10 -23 J/K) B = total noise factor (hertz) T e = equivalent noise temperature F = noise factor (unitless) P. Suresh Venugopal 30 Analog Communication - NOISE

Narrowband Noise:

Narrowband Noise Introduction to Narrowband Noise Representation of narrowband noise in terms of In phase and Quadrature Components P. Suresh Venugopal 31 Analog Communication - NOISE

Narrow band noise:

Narrow band noise Preprocessing of received signals Preprocessing done by a Narrowband Filter Narrowband Filter – Bandwidth large enough to pass the modulated signal. Noise also pass through this filter. The noise appearing at the output of this NB filter is called NARROWBAND NOISE. P. Suresh Venugopal 32 Analog Communication - NOISE

Narrow band noise:

Narrow band noise Fig (a) – spectral components of NB Noise concentrates about + f c Fig (b) – shows that a sample function n(t) of such process appears somewhat similar to a sinusoidal wave of frequency f c

Narrow band noise:

Narrow band noise We need a mathematical representation to analyze the effect of this NB Noise. There are 2 specific representation of NB Noise (depending on the application) P. Suresh Venugopal 34 Analog Communication - NOISE

Representation of narrowband noise in terms of In phase and Quadrature Components:

Representation of narrowband noise in terms of In phase and Quadrature Components Let n(t) is the Narrowband Noise with Bandwidth 2B centered at f c We can represent n(t) in canonical (standard) form as: We can extract n I (t) (In Phase Component) and n Q (t) (Quadrature Component) from n(t). P. Suresh Venugopal 35 Analog Communication - NOISE

Extraction of nI(t) and nQ(t) from n(t) :

Extraction of n I (t) and n Q (t) from n(t) Each LPF have bandwidth ‘B’ This is known as NARROWBAND NOISE ANALYSER

Generation of n(t) from nI(t) and nQ(t):

Generation of n(t) from n I (t) and n Q (t) This is known as NARROWBAND NOISE SYNTHESISER P. Suresh Venugopal 37 Analog Communication - NOISE

Important properties of nI(t) and nQ(t):

Important properties of n I (t) and n Q (t)

Important properties of nI(t) and nQ(t):

Important properties of n I (t) and n Q (t) P. Suresh Venugopal 39 Analog Communication - NOISE

Noise in CW modulation Systems:

Noise in CW modulation Systems Noise in linear Receivers using Coherent detection Noise in AM Receivers using Envelope detection Noise in FM Receivers P. Suresh Venugopal 40 Analog Communication - NOISE

Gaussian process:

Gaussian process Let X(t) denote a random process for an interval that starts at time t = 0 and lasts until t = T. The random variable Y is a linear functional of the random process X(t) if: where g(t) is an arbitrary function By definition: The random process X(t) is a Gaussian process if every linear functional of X(t ) is a Gaussian random variable. P. Suresh Venugopal 41 Analog Communication - NOISE

Main virtues of the Gaussian process::

Main virtues of the Gaussian process: Gaussian process has many properties that make results possible in analytic form Random processes produced by physical phenomena (see thermal noise as an example) are often such that they may be modeled by the Gaussian process If the input to a linear time invariant (LTI) system is Gaussian then its output is also Gaussian P. Suresh Venugopal 42 Analog Communication - NOISE

Thermal noise:

Thermal noise Is generated by each resistor. Used to model channel noise in analysis the of communication systems. It is an ergodic, Gaussian process with the mean of zero. P. Suresh Venugopal 43 Analog Communication - NOISE

Gaussian distribution:

Gaussian distribution Main virtue of the Gaussian process: Two parameters, the mean and variance are enough to fully characterize a Gaussian distribution. P. Suresh Venugopal 44 Analog Communication - NOISE

Power spectral density (PSD) of a random process:

Power spectral density (PSD) of a random process By definition, the power spectral density S X (t) and autocorrelation function R X (Ʈ) of an ergodic random process X(t) form a Fourier transform pair with Ʈ and f as the variables of interest. The power of an ergodic random process X(t) is equal to the total area under the graph of power spectral density. The power spectral density is that characteristic of a random process which is easy to measure and which is used in communication engineering to characterize noise. 45

White Gaussian Noise:

White Gaussian Noise Gaussian means Gaussian process. A measurable consequence: Measured instantaneous values of a thermal noise give a Gaussian distribution. White means that the autocorrelation function consists of a delta function weighted by the factor N0=2 and occurring a Ʈ = 0. Power spectral density of white noise is: P. Suresh Venugopal 46 Analog Communication - NOISE

White Gaussian Noise:

White Gaussian Noise P. Suresh Venugopal 47 Analog Communication - NOISE

White Gaussian Noise:

White Gaussian Noise Thermal noise is a white Gaussian noise. It is an ergodic Gaussian process with mean of zero, its power is given by the variance σ 2 . Its power spectral density is: where k is the Boltzmann’s constant and Te is the equivalent noise temperature. Note: Power of white noise is infinite. Only the bandlimited white noise has a finite power! P. Suresh Venugopal 48 Analog Communication - NOISE

Noisy Receiver Model:

Noisy Receiver Model where the receiver noise is included in N 0 given by: the bandwidth and center frequency of ideal band-pass channel filter are identical to the transmission bandwidth B T and the center frequency of modulated waveform , respectively. P. Suresh Venugopal 49 Analog Communication - NOISE

Noisy Receiver Model:

Noisy Receiver Model The filtered noisy received signal x(t) available for demodulation is defined by: Note: Noise n(t) is the band-pass filtered version of w(t) P. Suresh Venugopal 50 Analog Communication - NOISE

Power spectral density (PSD) of band-pass filtered noise:

Power spectral density (PSD) of band-pass filtered noise The average noise power may be calculated from the power spectral density . The average power N of filtered Gaussian white noise is: P. Suresh Venugopal 51 Analog Communication - NOISE

Signal to Noise Ratio (SNR):

Signal to Noise Ratio (SNR) A measure of the degree to which a signal is contaminated with additive noise is the signal-to-noise ratio (SNR) P. Suresh Venugopal 52 Analog Communication - NOISE

Figure of Merit Of CW Modulation Schemes:

Figure of Merit Of CW Modulation Schemes Goal: Compare the performance of different CW modulation schemes. Signal-to-noise ratio (SNR) is a measure of the degree to which a signal is contaminated by noise. Assume that the only source of degradation in message signal quality is the additive noise w(t ). Noisy receiver model: 53

Figure of Merit Of CW Modulation Schemes:

Figure of Merit Of CW Modulation Schemes The signal-to-noise ratio at the demodulator input : The signal-to-noise ratio at the demodulator output : P. Suresh Venugopal 54 Analog Communication - NOISE

Figure of Merit Of CW Modulation Schemes:

Figure of Merit Of CW Modulation Schemes (SNR) O is well defined only if the recovered message signal and noise appear additively at demodulator output. This condition is: Always valid for coherent demodulators But is valid for noncoherent demodulators only if the input signal to- noise ratio (SNR) I is high enough Output signal-to-noise ratio (SNR) O depends on: Modulation scheme Type of demodulator P. Suresh Venugopal 55 Analog Communication - NOISE

Figure of Merit Of CW Modulation Schemes:

Figure of Merit Of CW Modulation Schemes Conditions of comparison To get a fair comparison of CW modulation schemes and receiver configurations , it must be made on an equal basis. Modulated signal s(t) transmitted by each modulation scheme has the same average power Channel and receiver noise w(t) has the same average power measured in the message bandwidth W According to the equal basis, the channel signal-to-noise ratio is defined as: 56

Figure of Merit Of CW Modulation Schemes:

Figure of Merit Of CW Modulation Schemes Noise performance of a given CW modulation scheme and a given type of demodulator is characterized by the figure of merit. By definition, the figure of merit is: The higher the value of the figure of merit, the better the noise performance P. Suresh Venugopal 57 Analog Communication - NOISE

SNRs & Figure of Merit:

SNRs & Figure of Merit P. Suresh Venugopal 58 Analog Communication - NOISE

Noise in AM DSB-FC Receivers:

Noise in AM DSB-FC Receivers 59

Noise in AM DSB-FC Receivers:

Noise in AM DSB-FC Receivers P. Suresh Venugopal 60 Analog Communication - NOISE

Threshold effect:

Threshold effect The threshold is a value of carrier-to-noise ratio below which the noise performance of a demodulator deteriorates much more rapidly than proportionately to the carrier-to-noise ratio. Every noncoherent detector exhibits a threshold effect, below the threshold the restored message signal becomes practically useless. P. Suresh Venugopal 61 Analog Communication - NOISE

Noise in AM DSB-FC Receivers:

Noise in AM DSB-FC Receivers Figure of merit for DSB modulation: where P denotes the average power of message signal m(t) and ka is the amplitude sensitivity of AM modulator. The best figure of merit is achieved if the modulation factor is µ = k a A m = 1 DSB system using envelope detection must transmit three times as much average power as a suppressed-carrier system P. Suresh Venugopal 62 Analog Communication - NOISE

Threshold effect:

Threshold effect Physical explanation: If the carrier-to-noise ratio is high enough then the signal dominates and the noise causes only a small unwanted AM and PM. However, if the carrier-to-noise ratio is small then the noise dominates which results in a complete loss of information. As a result, the demodulator output does not contain the message signal at all. P. Suresh Venugopal 63 Analog Communication - NOISE

Threshold effect:

Threshold effect Threshold Effect : loss of message in an envelope detector that operates at a low CNR. 64

Noise in AM DSB-SC Receivers:

Noise in AM DSB-SC Receivers P. Suresh Venugopal 65 Analog Communication - NOISE

Noise in AM DSB-SC Receivers:

Noise in AM DSB-SC Receivers P. Suresh Venugopal 66

Noise in AM DSB-SC Receivers:

Noise in AM DSB-SC Receivers Finding (SNR) O P. Suresh Venugopal 67 Analog Communication - NOISE

Noise in AM DSB-SC Receivers:

Noise in AM DSB-SC Receivers Finding (SNR) O P. Suresh Venugopal 68 Analog Communication - NOISE

Noise performance of AM receivers:

Noise performance of AM receivers Note: For high value of (SNR) C , the noise performance of coherent and noncoherent DSB are identical. But noncoherent DSB has a threshold effect . Coherent AM detectors have no threshold effect ! P. Suresh Venugopal 69 Analog Communication - NOISE

Comparison of noise performance of AM modulation schemes:

Comparison of noise performance of AM modulation schemes Remarks Curve I: DSB modulation and envelope detector with modulation factor µ = 1 Curve II: DSB–SC and SSB with coherent demodulator Note the threshold effect that appears at about 10 dB P. Suresh Venugopal 70 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers w(t): zero mean white Gaussian noise with PSD = No/2 s(t): carrier = f c , BW = B T BPF: [f C - B T /2 - f C + B T /2] Amplitude limiter: remove amplitude variation. Discriminator Slope network : varies linearly with frequency Envelope detector P. Suresh Venugopal 71 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers FM signal: Filtered noise n(t): P. Suresh Venugopal 72 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers Phasor diagram interpretation of noisy demodulator input: Due to the PM generated by the noise, noise appears at the demodulator output. But the FM demodulator is sensitive to the instantaneous frequency of the input signal . The instantaneous frequency is the first derivative of the phase of input signal. P. Suresh Venugopal 73 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers The instantaneous frequency is the first derivative of the phase of input signal. Derivation in the time domain corresponds to multiplication by ( j2 π f ) in the frequency domain. Multiplication by (j2 π f) means that the frequency response of derivation is: Recall , power spectral density of the output process equals to the PSD of the input process multiplied by the squared magnitude of the frequency response H(f ) of the LTI two-port. P. Suresh Venugopal 74 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers Recall , power spectral density of the output process equals to the PSD of the input process multiplied by the squared magnitude of the frequency response H(f ) of the LTI two-port. Therefore, the PSD S N 0 (f) of noise at an FM receiver output has a square-law dependence on the operating frequency. The high-frequency noise is dominant at the output of an FM receiver P. Suresh Venugopal 75 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers Discriminator output P. Suresh Venugopal 76 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers P. Suresh Venugopal Analog Communication - NOISE 77

Noise in FM Receivers:

Noise in FM Receivers P. Suresh Venugopal Analog Communication - NOISE 78

Noise in FM Receivers:

Noise in FM Receivers P. Suresh Venugopal Analog Communication - NOISE 79

Noise in FM Receivers:

Noise in FM Receivers P. Suresh Venugopal Analog Communication - NOISE 80

Noise in FM Receivers:

Noise in FM Receivers Figure of merit for frequency modulation If the (SNR) C is high enough and exceeds the threshold level then: where P denotes the average power of message signal m(t), k f is the frequency sensitivity of FM modulator and W denotes the bandwidth of message signal. Since: and for wide-band FM we may write: P. Suresh Venugopal 81 Analog Communication - NOISE

Noise in FM Receivers:

Noise in FM Receivers Figure of merit for frequency modulation we obtain by substituting: where β is the Modulation Index. Note : An increase in the transmission bandwidth BT provides a corresponding quadratic increase in the output signal-to-noise ratio (or in the figure of merit) of the FM system . P. Suresh Venugopal 82 Analog Communication - NOISE

FM threshold effect:

FM threshold effect The figure of merit discussed above is valid only if the carrier-to-noise ratio ( SNR) C is high compared with unity . It has been found experimentally that as (SNR) C is decreased below a threshold , each FM demodulator, either coherent or noncoherent , breaks: At first isolated clicks are heard and if the (SNR) C is decreased further, the clicks rapidly merge into a crackling. sound P. Suresh Venugopal 83 Analog Communication - NOISE

FM threshold effect:

FM threshold effect A qualitative explanation If (SNR) C is small then the noise becomes dominant and the phasor representation and the decomposition of noise into a PM and AM are not valid any more. The phase of noise is a random variable and it may take any value. Recall , the FM demodulator is sensitive to the derivate of phase. When the phase of demodulator input varies suddenly by 2 π due to the noise then an impulse, i.e., click appears at the receiver output. P. Suresh Venugopal 84 Analog Communication - NOISE

Pre-emphasis and de-emphasis in FM systems:

Pre-emphasis and de-emphasis in FM systems Recall: The power spectral density S N 0 (f) of noise at an FM receiver output has a square law dependence on the operating frequency. The high-frequency noise is dominant at the output of an FM receiver. The power spectral density of message signals usually falls off at higher frequencies . Generally , the most part of a message signal is in the low-frequency region. These facts may be exploited to improve the noise performance of FM systems P. Suresh Venugopal 85 Analog Communication - NOISE

Pre-emphasis and de-emphasis in FM systems:

Pre-emphasis and de-emphasis in FM systems Basic idea Apply a filter at the demodulator output which reduces the high frequency content of the output spectrum. To compensate this attenuation, a pre-emphasis must be applied to the high-frequency signals at the transmitter Pre-emphasis at the transmitter : A filter that artificially emphasize the high-frequency components of the message signal prior to the modulation. P. Suresh Venugopal 86 Analog Communication - NOISE

Pre-emphasis and de-emphasis in FM systems:

Pre-emphasis and de-emphasis in FM systems De-emphasis at the receiver : An inverse operation performed by a filter placed after the demodulation . The de-emphasis filter restores the original signal by de-emphasizing the high-frequency components. Effects of pre-emphasis and de-emphasis filters cancel each other: P. Suresh Venugopal 87 Analog Communication - NOISE

Use of pre-emphasis and de-emphasis in an FM system:

Use of pre-emphasis and de-emphasis in an FM system P. Suresh Venugopal 88 Analog Communication - NOISE

Comparison of noise performance of CW systems:

Comparison of noise performance of CW systems Note: Threshold problem is more serious in FM modulation than in AM. The higher the β , the better the FM noise performance. But the price to be paid is the wider transmission bandwidth P. Suresh Venugopal 89 Analog Communication - NOISE

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