PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

DTFT, DFT, ZT, and FFT 459

Know the basic standard discrete signals and their transforms

Understand the concept of normalized frequencies for discrete-time systems

Understand the relation between the signal, normalized frequency, and effect of

the sampling frequency

Estimate the spectrum of discrete-time signals and systems

State the differences between FT and DTFT

State the differences between DTFT and DFT

Use a table for the evaluation of DTFT

Know the most important properties of the different discrete-system transforms

Know the standard DFT

Know the meaning and power of FFT

Understand the computational effi ciency of FFT

Understand when and how FFT is used

Use the MATLAB command fft to evaluate DFT

Use the power of MATLAB to analyze a variety of discrete-time signals and sys-

tems, in both the time and frequency domains

5.3 Background

R.5.1 A discrete-time system transforms an input sequence f(n) into an output sequence

g(n) by means of a given algorithm, predefi ned rules, conversion tables, and most

often by a mathematical relation or equation.

Analytically, the preceding statement can be expressed as g(n) = Lf(n), and it is

illustrated by means of a block diagram shown in Figure 5.2.

R.5.2 The most common classifi cation and characterization (also referred to as properties)

of discrete-time systems are stated as follows:

a. Linearity

Let

f 1 (n) → g 1 (n) (where → means transforms to)

and

f 2 (n) → g 2 (n)

Then

a 1 f 1 (n) + a 2 f 2 (n) → a 1 g 1 (n) + a 2 g 2 (n)

• • • • • • • • • • • • • •

FIGURE 5.2

Discrete-system block diagram.

f(n) g(n)

L

Input Output

sequence sequence