Signals and Systems - Electrical Engineering

10.4 Discrete Fourier Transform 627

FIGURE 10.18
FIR filtering of disturbed
signal. Comparison of results
usingconvandfft
functions. (a) Actual and
noisy signal (plotted as a
continuous signal using black
lines); (b) denoised signal
(notice the delay caused by
the FIR filter); (c) impulse
response and magnitude
response of low-pass FIR
filter; and (d) error signal
[n]=y[n]−y 1 [n]between
output fromconv- and
fft-based filtering.

0 10 20 30 40

−0.2

0

0.2

0.4

0.6

0.8

1

n

h

[n

]

0 20 40 60 80 100 120 140

− 1

−0.5

0

0.5

1

n

y

[n

]

0 20 40 60 80 100 120 140

− 2

0

2

4

n

× 10 −16

ε[

n]

0 10 20 30 40 50 60 70 80 90 100

− 1

−0.5

0

0.5

1

n

x[

n],

x^1

[n

]

0 1 2 3

0

0.2

0.4

0.6

0.8

1

ω

|H

(e

jω

)|

(a)

(c)

(b)

(d)