Unformatted text preview: MEC702 Wk 13 Tutorial Fourier Cosine Transform. Fourier Sine Transform. 1. Find the Fourier cosine transform fˆc (w) and fˆs (w) of 0<x<1
1,
f (x) = −1, 1 < x < 2 0,
x > 2.
2. Find fˆc (w) and fˆs (w) of (
f (x) = 3. Find fˆc (w) and fˆs (w) x, 0 < x < 2
.
0, x > 2 of (
x2 , 0 < x < 1
f (x) =
0,
x > 1.
4. Find Fs (e−ax ), a > 0, by integration. Fourier Transform. DFT. FFT. 1. Find the Fourier transform of (a) (b) (c) (d) f (x) without
(
e2ix , −1 < x < 1
f (x) =
0,
otherwise
(
1, a < x < b
f (x) =
0, otherwise
(
ekx , x < 0 (k > 0)
f (x) =
0,
x>0
(
ex , −a < x < a
f (x) =
0, otherwise 1 using Table. Show all details. 2. Find the transform of a general signal of four values f1
f2 .
f = f3 f4
3. Find the transform (the frequency spectrum) of a general signal of two
values
f1
.
f2 4. Find the inverse matrix of the matrix 1
1
F4 = 1
1 1
−i
−1
i 1
−1
1
−1 and use it to recover the signal 0
1 f =
4 .
9
(Related to the example in the notes) 2 1
i −1
−i ...
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 Winter '16
 Alveen Chand
 Discrete cosine transform, Integral transforms, Fourier cosine transform, Fourier sine transform

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