In: Electrical Engineering

For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the Fast Fourier Transform using signal flow graph. (Use decimation in Time Algorithm).

For a signal x(n)=sin(2*pi*n/5) defined for n=0to7, evaluate the
Fast Fourier Transform using signal flow graph. (Use decimation in
Time
Algorithm).

4.
For a signal x(n)=sin(4*pi*n/5) defined for n=0to7, evaluate the
Fast Fourier Transform using signal flow graph. (Use decimation in
Time
Algorithm).

4.
For a
signal x(n)=sin(2*pi*n/3) defined for n=0to7, evaluate the Fast
Fourier Transform using signal flow graph. (Use decimation in
frequency Algorithm)

What is the effect of the filter on the Fast Fourier Transform
of voice signal?
Is quantization visible? How can you tell?

USING MATLAB....
a.) Create anonymous functions:
fa(x)=sin(x^2)
fb(x)=sin^2(x)
b.) Evaluate them both at x=1/2 pi
c.)Evaluate them both at x=(0,1,2,...,10)^T
d.) Calculate fa(fb(2)) and fb(fa(2))

Find the Fourier series expansion of f(x)=sin(x) on [-pi,pi].
Show all work and reasoning.

Find the real Fourier series of the piece-wise continuous
periodic function
f(x) = x+sin(x) -pi<=x<pi

1. is sin(pi/4) causal?
2. is sin(pi/4) stable?
3. is delta(n+1) causal?
4. = ?
5. If function w [ n ] is convolved with , what will the result
be?
6. if a system with signal length 4 is convolved with its own
system response, what will the length of that signal be?
7. In an LTI system, x[n] * h[n]= y[n]. What is x[n-3] * h[n-2]
=?

S(x) is a cubic spline for the function f(x) = sin(pi x/2) +
cos(pi x/2) at the nodes x0 = 0 ,
x1 = 1 , x2 = 2
and satisfies the clamped boundary conditions. Determine the
coefficient of x3 in S(x) on [0,1] ans. pi/2 -3/2

Find the Fourier Series for the function defined over -5 < x
< 5
f(x) = -2 when -5<x<0 and f(x) = 3 when 0<x<5
You can use either the real or complex form but must show
work.
Plot on Desmos the first 10 terms of the series along with the
original
function.

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