Signals and Systems For Dummies

Chapter 11

The Discrete-Time Fourier Transform for ­Discrete-Time Signals

In This Chapter

Checking out the Fourier transform of sequences

Getting familiar with the characteristics and properties specific to the DTFT

Working with LTI system relationships in the frequency domain

Using the convolution theorem

If you’re hoping to find out how the discrete-time Fourier transform (DTFT) operates on discrete-time signals and systems to produce spectra and frequency response representations with units of radians/sample, you’re in the right place! And I hope it wasn’t too hard to find; Fourier theory is covered in four different chapters.

The Fourier transform (FT) (explored in Chapter 9) has the same capabilities as the DTFT, but it applies to the continuous-time cousins in the lands of continuous frequency. If you’re looking for a Fourier transform that’s discrete in both time and frequency, you need the discrete Fourier transform (DFT), which is the subject of Chapter 12. The Fourier series (covered in Chapter 8) applies to continuous-time periodic signals with a discrete frequency-domain ...