Biomedical Engineering Reference
In-Depth Information
EXAMPLE PROBLEM 11.13
Find and plot the magnitude of the discrete Fourier transform of the signal
x
ðÞ¼
sin
ðp=
4
n
Þþ
2
cos
ðp=
3
n
Þ
in MATLAB.
Solution
n
¼
1:1024; %Discrete Time Axis
¼
þ
x
sin(pi/4*n)
2*cos(pi/3*n); %Generating the signal
¼
X
fft(x,1024*16)/1024; %Computing 16k point Fast Fourier Transform
Freq
(1:1024*16)/(1024*16)*2*pi; %Normalizing Frequencies
between 0-2*pi
plot(Freq,abs(X),'k') %Plotting
axis([0.7 1.15 0 1.2])
xlabel('Frequency (rad/s)')
ylabel('Fourier Magnitude')
¼
Results are shown in Figure 11.14.
1.2
1
0.8
0.6
0.4
0.2
0
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
Frequency (rad/s)
FIGURE 11.14
Fast Fourier transform magnitude for the sum of two sinusoids. Dominant energy peaks are
located at the signal frequencies
p
/3 and
p
/4 rad/s.
11.5.7 The z-Transform
The
transform provides an alternative tool for analyzing discrete signals in the frequency
z-
2p
m
N
.
z
¼
e
j
domain. This transform is essentially a variant of the DFT, where we allow
