Project 1: Noise Effects

  Homework Exams Lecture Projects

This project consists of two sections. The first section explores different noise models and their means and variances, probability density functions, and the effects of filtering on the noise distribution. The second

Notes on Part 1

Part 1: Noise Models and Linear Systems

A. Means and Variances of Random Signals

1. Open the system mean_value.svu. This system generates three different signals

Gaussian (or normally) distributed noise
Uniformly distributed noise
Random Binary Sequence

Run the system. Go to the SystemView Analysis window and look at the square version of each signal. View all six windows simultaneously by tiling the windows using the toolbar button. Use the statistics toolbar button (looks like a bell curve) to extract information about the signal. Fill out the table given below for each noise source. (In the "design" columns enter the theoretical values from the signal source parameters and in the "analysis" columns enter the time time average values you calculated in the SystemView Analysis windows.) Remember that variance is the square of the standard deviation.

Signal Type Gaussian Uniform Binary
  Design Analysis Design Analysis Design Analysis
Mean Value            
Mean Squared Value            
Standard Deviation            

The goal is to look at how different types of noise vary in time and in their power spectral densities. Compare the noise statistics and the Power Spectral Densities(PSDs). Calculate the PSD of each signal using the analysis toolbox (Fourier transform of  signal squared) Submit pictures of the PSDs of the noise.

2. Return to the design space and change:

mean of the Gaussian noise to 2
range of the uniform noise from 2 to 4
Offset of the random binary signal to 2. 

Rerun the system and complete the table below.

Signal Type Gaussian Uniform Binary
  Design Analysis Design Analysis Design Analysis
Mean Value            
Mean Squared Value            
Standard Deviation            

Comment on the changes between parts one and two.

B. Open the system res-cap-filter.svu. This system simulates an RC circuit that implements a low-pass filter. Its transfer function is: H(f) = 1/(1+j*2*pi*f*R*C). The cutoff frequency is f_c = 1/(2*pi*f*R*C). In SystemView we can design analog filters by selecting a linear filter system then applying the analog filter design tool. 

The three filters set up in this exercise are identical and represent a first-order lowpass Butterworth filter with a cutoff frequencyof 1 Hz. The response of the first order filter to an impulse, noise and a 1 sec duration square pulse is simulated.

Run the simulation and use the analysis window to verify that the cutoff frequency is 1 Hz. Verify this by observing the magnitude of the spectrum using |FFT| of the RC impulse response.
In the analysis window, calculate the magnitude of the response to the filtered noise. Compare this result to the magnitude of the impulse response. Explain your results using the impulse response and the PSD of the noise. How does the LPF change the statistics and PSD of the noise?
Run the simulation for different square pulse widths. Comment on your results.

Part 2: Noise Effects in AM and FM Systems

THe purpose of this part of the project is to compare the effect of additive Gaussian noise on DSB-AM and FM communication systems. You will assess this effect quantitatively using the output SNR and qualitatively using your ears. The output signal to noise ratio will be calculated analytically using the equation:

s_n is the n-th sample of the output signal when no noise is input to the system. s' is the output with noise added to the system.

Compare the output of the AM and FM systems for three different SNR levels for a range of signal qualities. What is the lowest SNR that yields an acceptable signal for both the AM and FM systems?

Add in sinks to look at the signal at different spots in the circuit.

SystemView Models:
8 bit mono wav file for sound (Clip from Laika and the Cosmonauts)
FM system
AM system  New file (12/3/01)

What you should hand in:

Answer all questions in parts 1 and 2, fill in tables
Pictures of the signal spectrums to illustrate what is happening.
DISCUSSION of your results concentrating on what is happening and why (VERY IMPORTANT).

 

Page last updated 12/03/2001