User`s guide

Importing Data into the MATLAB
®
Workspace
In the context of numerical computations, continuous equations are replaced
by their discretized equivalents to handle discrete data values. For a
discrete-time syste m with a sampling interva l T, the frequency-domain output
Y(e
iw
) and input U(e
iw
) is the time-discrete Fourier transform (TDFT):
Ye T ykTe
iwT iwkT
k
N
() ()=
−
=
∑
1
In this example, k = 1,2,...,N,whereN is the number of samples in the
sequence.
Note This form only discretizes the time. The frequency is continuous.
When the frequen cies are not equally spaced, it is useful to also discretize
the frequencies in the Fourier transform. The resulting discrete Fourier
transform (DFT) of time-domain data is:
Ye ykTe
w
n
T
nN
iw T iw kT
k
N
n
nn
() ()
,,, ,
=
== −
−
=
∑
1
2
012 1
π
…
The DFT is useful because it can be calculated very efficiently using the fast
Fourier transform (FFT) method. Fourier transforms of the input and output
data are complex values.
How to Import Frequency-Domain Data into MATLAB
Youmustimportyourfrequency-domain data as the foll owing variables:
• Input data
- For single-input/single-output (SISO) data, the input must be a column
vector.
- For a data set with N
u
inputs and N
f
frequencies, the input is an
N
f
-by-N
u
matrix.
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