# 3.1 Blind source separation via ica: implementation

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This module details the implementation of a blind source separation system using fast ICA.

#### Implementation

In order to implement our design to enable the separation of two audio signals, we require two microphones and a processing computer with audio output capabilities. When two microphones are present in an environment with two sources, then they will record a mixing of both these signals, weighted by coefficients base on distance away from the microphone (remember that as a signal is further away from a recording source, the quieter it will be).

The mixed signal inputs of these microphones must then be imported into a processing computer that is able to run code based in C or MatLab (or potentially any other language, but the most efficient algorithm is run in MatLab and C).

The model for these mixed signals can be represented in matrix notation by:

x = A s

As we can see, the signal vector is multiplied by some mixing matrix A. Therefore to isolate the signals s based on the mixed signals x we must find an inverse matrix A-1. To do this we implement a piece of Matlab code known as FastICA . The math behind the algorithm is explained elsewhere but the most important piece of code, the iteration to find the inverse mixing matrix, is displayed here:

`% Take a random initial vector of length 1 and orthogonalize it`

`% with respect to the other vectors.`

`if initialStateMode == 0`

`w = randn (vectorSize, 1);`

`elseif initialStateMode == 1`

`w=whiteningMatrix*guess(:,round);`

`end`

`w = w - B * B' * w;`

`w = w / norm(w);`

`wOld = zeros(size(w));`

`wOld2 = zeros(size(w));`

`% This is the actual fixed-point iteration loop.`

`% for i = 1 : maxNumIterations + 1`

`i = 1;`

`gabba = 1;`

`while i<= maxNumIterations + gabba`

`if (usedDisplay>0)`

`drawnow;`

`end`

`% Project the vector into the space orthogonal to the space`

`% spanned by the earlier found basis vectors. Note that we can do`

`% the projection with matrix B, since the zero entries do not`

`% contribute to the projection.`

`w = w - B * B' * w;`

`w = w / norm(w);`

`if notFine`

`if i == maxNumIterations + 1`

`if b_verbose`

`fprintf('\nComponent number %d did not converge in %d iterations.\n', round, maxNumIterations);`

`end`

`round = round - 1;`

`numFailures = numFailures + 1;`

`if numFailures>failureLimit`

`if b_verbose`

`fprintf('Too many failures to converge (%d). Giving up.\n', numFailures);`

`end`

`if round == 0`

`A=[];`

`W=[];`

`end`

`return;`

`end`

`% numFailures>failurelimit`

`break;`

This iteration will guess a row of the demixing matrix (w in the code) and then run through a loop until it finds a projection that agrees with the statistical analysis behind the decoding.

After running on the supplied mixed signals, the program will output what it thinks are the two original sources and the demixing matrix. We can then use these outputs to complete a variety of tasks such as removing noise from the original signals, matching the original signals with other signals to detect base elements of the mixed signal, or even just simply outputting the original signals through a speaker system.

#### Questions & Answers

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what is a economy planning?
what is demand
demand means desire for a commodity backed by willingness & ability to pay for that commodity
Rajesh
what is supply
Akoheni
supply means suppliers supplying more commodities when price's high or less when price's low to satisfy human want
Prince
the coefficient of price elasticity of supply is the measure of percentage change in the quantity supplied of a good due to a given percentage change in its price.
Khushiba
Please what is Economics of Scales?
Prince
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Khushiba
Cardinal utility is the satisfaction derived by the consumers from the consumption of goods and services while ordinal is ranked in terms of preference.
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Khushiba
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Prince
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Prince
economics scales I don't know but I know laws of returns to scale
Khushiba
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TIMAH
hello
Khushiba
can someone help explain to me what is fairly inelastic dd
TIMAH
Economics Economics - The study of how people use their limited resources to try to satisfy unlimited wants
Abdullah
Economic integration has been one of the main economic developments affecting international trade in the last years. Countries have wanted to engage in economic cooperation to use their respective resources more effectively and to provide large markets for member-countries of the resulting integrate
Abdullah
Inelastic Demand When consumers are relatively unresponsive to price changes. A PED coefficient of less than one means that a particular change in the price of a good will be met by a proportionally smaller change in the quantity demanded.
Abdullah
what is development planning?
What is economics?
economics is study of scarcity and how humans make decisions.
reason for development planning in West Africa
Emmanuel
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Emmanuel
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when a person is part 50% rational and the other part of him is 50% focused on money as an incentive
Yahir
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BELDON
must find out the problems originating from and take remedy for it.
Rigved
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more explanation on GDP
it is a country total out put of goods and services divided by the total population of the country.I think it can also be derived from the country labour force,,because it mostly depend on the labour force and the level of technology .
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labour force and technological progress leads to greater production increases the GDP
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Jessica
degree of responsiveness of demand to changes in price and other factors that influence demand.
OBIAJULUM
It is the degree of responsiveness of demand and supply to a little change in price of a goods and services
Ibrahim
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by this time
Emmanuel
It is a social science that analyses production,distribution and consumption of goods and services
Emmanuel
A social science that study human behavior in relationship with decision making
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Charllote
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the science in which we study about the investement of our wealth.
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a competitive demand is also known as substitute demand .the moment the price of the commodity increase consumers will purchase the other other commodity which it's price is low and the vice versa. an example is milo and bournvita
Yussif
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Moses
equilibrium is a situation where market is stable there is no entry nor exit. demand is the willingness to pay Which is backed by law.
Yussif
list and explain three implication of balance of payment disequilibrium?
Jayson
Economics is a social science that study's human behaviour as a relationship between ends and scares means which have alternative uses
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What are the typical patterns of GDP for a high-income economy like the United States in the long run and the short run?
What are the limitation and significant of macroeconomic
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