 REGISTER NUMBER : 727822TUEC147
 NAME : B.RAMYARAAHASHRI
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 EXPERIMENT NUMBER: 01
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 DATE : 31.05.2023
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 QUESTION NO : 1
For the given discrete time signal represented by the sequence of samples [2, 4, 6, 8] compute and
plot the magnitude and phase spectrum of the Fourier Transform of the signal.
In[34]:=
signal = {2, 4, 6, 8};
fourier = Fourier[signal];
ListPlotAbs[fourier], PlotRange → All,
FrameLabel → "Frequency (k)", "Magnitude",
PlotLabel → "Fourier Transform Magnitude Spectrum"
Out[36]=
Fourier Transform Magnitude Spectrum
10
8
6
4
2
1.5
2.0
2.5
3.0
3.5
4.0
2
In[85]:=
signal = {2, 4, 6, 8};
fourier = Fourier[signal];
ListPlotArg[fourier], PlotRange → All,
FrameLabel → "Frequency (k)", "Phase",
PlotLabel → "Fourier Transform Phase Spectrum"
Out[87]=
Fourier Transform Phase Spectrum
3
2
1
1.5
2.0
2.5
3.0
3.5
4.0
-1
-2
In[60]:=
 QUESTION NO : 2
Find Fourier transforms of e ^ - a ^ 2 * x ^ 2, a < 0.
In[17]:=
y = (1 / Sqrt[2 * pi])
y1 = y * IntegrateExp (- a ^ 2 * x ^ 2) * ExpI s x, {x, - I, I}
Out[17]=
1
2
pi
Out[18]=
ⅈ
2 a2 Exp - 2 s Cosh[s] + 2 + s2 Sinh[s]
pi s3
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 QUESTION NO : 3
Given a time domain signal represented by the function f(x)={a^2-x^2 for |x|<a
{0
for |x|>a
3
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y = (1 / Sqrt[2 * π])
y1 = y * Integratea ^ 2 - x ^ 2 ExpI s x, {a, - I, I}
Out[11]=
1
2π
Out[12]=
-
2ⅈ
- 2 ⅈ ⅇⅈ s x x2
3
2π
In[67]:=
 QUESTION NO : 4
Find Fourier transform of f (x) = cos t.
In[23]:=
y = (1 / Sqrt[2 * pi])
y1 = y * Integrate(Cos[t]) * ExpI s x, {x, - I, I}
Out[23]=
1
2
pi
Out[24]=
ⅈ
2 Cos[t] Sinh[s]
pi s