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# 2. In a certain concert hall, echoes of the original signal

### Resolved Question:

2. In a certain concert hall, echoes of the original signal x(n) are generated due to the reflections at the walls and ceiling. The audio signal experienced by the listener y(n) is a combination of x(n) and its echoes. Let y(n) = x(n) + α x(n-k) where k is the amount of delay in samples and α is its relative strength.
Let x(n) = cos (0.2πn) + 0.5 cos (0.6πn), α = 0.1, k = 50. Generate 200 samples of y(n)
and plot them. Also obtain the system function.
Submitted: 4 years ago.
Category: Homework
Expert:  akch2002 replied 4 years ago.
Can you explain what is nn in x(n) = cos (0.2πn) + 0.5 cos (0.6πn)? Is it n^2?
I will use Excel to generate 200 samples of y from y1 to y200.
Customer: replied 4 years ago.
not nn,it is pi n
Expert:  akch2002 replied 4 years ago.
x(n) = cos (0.2pi*n) + 0.5 cos (0.6pi*n)

Hence, y(n) = cos (0.2pi*n) + 0.5 cos (0.6pi*n)+0.1x(n-50)
n ≥ 50

Is it correct?
Customer: replied 4 years ago.
n greaer than or equal to 50 not given.rest is correct

This is a digital signal processing question.Iwant it fast within 2 hours
Expert:  akch2002 replied 4 years ago.
Do we have to calculate y(1), y(2),.........y(200)?

If, yes; we will have y(1) = cos (0.2pi*1) + 0.5 cos (0.6pi*1)+0.1x(-49)

and x(-49) = cos (0.2pi*-49) + 0.5 cos (0.6pi*-49).
Putting this, we can find out y1 and other values y(2),y(3),y4,......y(200). Is this what you want?
I can reply in 2 hours after you clarify my doubt.
Expert:  akch2002 replied 4 years ago.
Are you there?
Expert:  akch2002 replied 4 years ago.
excel file
Customer: replied 4 years ago.
should be done in matlab
Expert:  akch2002 replied 4 years ago.
Expert:  akch2002 replied 4 years ago.
MATLAB code and plot is given below.
n = 0:1:50;
y = cos(0.2*pi*n)+0.5*cos(0.6*pi*n) +0.1*cos(0.2*pi*(n-50)) +0.05*cos(0.6*pi*(n-50));
plot(n,y)
Customer: replied 4 years ago.