O'Reilly logo

Digital Signal Processing and Applications with the TMS320C6713 and TMS320C6416 DSK, 2nd Edition by Donald Reay, Rulph Chassaing

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

4

Finite Impulse Response Filters

  • Introduction to the z-transform
  • Design and implementation of finite impulse response (FIR) filters
  • Programming examples using C and TMS320C6x code

The z-transform is introduced in conjunction with discrete-time signals. Mapping from the s-plane, associated with the Laplace transform, to the z-plane, associated with the z-transform, is illustrated. FIR filters are designed with the Fourier series method and implemented by programming a discrete convolution equation. Effects of window functions on the characteristics of FIR filters are covered.

4.1 INTRODUCTION TO THE z-TRANSFORM

The z-transform is utilized for the analysis of discrete-time signals, similar to the Laplace transform for continuous-time signals. We can use the Laplace transform to solve a differential equation that represents an analog filter or the z-transform to solve a difference equation that represents a digital filter. Consider an analog signal x(t) ideally sampled,

(4.1)

img

where δ(tkT) is the impulse (delta) function delayed by kT and T = 1/Fs is the sampling period. The function xs(t) is zero everywhere except at t = kT. The Laplace transform of xs(t) is

(4.2)

img

From the property of the impulse function

Xs(s) in (4.2) becomes

(4.3)

Let in (4.3) , which becomes

(4.4)

Let the ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required