Procesamiento de señales digitales

The Geometric Series in Digital Signal Processing

In Matlab an array operator “” is required to implement a real exponential sequence of the form:

Over the n1< no < n2 interval. For example, to implement:

We will use the following Matlab function:

xlabel(‘n’); ylabel(‘x[n]’)

This script yields:

Geometric series

A one-side exponential sequence of the form:

Where α is an arbitrary constant. This sequences is called a geometric series.  In DSP, the convergence and expression for the sum of this series are used in many applications. The series converges for:

While this condition is true, the sum of the geometric series components converges to:

From here, we also need an expression for the sum of any finite number of terms of the series, and that is given by:

These two important results will be used deeply throughout DSP.

Complex-valued exponential sequence

Where σ produces an attenuation (if<0) or amplification (if>0)  and ωo is the frequency in radians. The Matlab function exp generates the exponential sequences. For example, for x[n] =exp[(2+j3)n], 0n10, we will use the following script:

n=[0:10]; x=exp(3j*n);

This script yields:


  • Digital Signal Processing Using Matlab, 3erd ed


Literature review by:

Prof. Larry Francis Obando – Technical Specialist – Educational Content Writer

Exercises are solved!!

WhatsApp:  +34633129287  Inmediate Attention!!

Twitter: @dademuch

Copywriting, Content Marketing, Tesis, Monografías, Paper Académicos, White Papers (Español – Inglés)

Escuela de Ingeniería Electrónica de la Universidad Simón Bolívar, USB Valle de Sartenejas.

Escuela de Ingeniería Eléctrica de la Universidad Central de Venezuela, UCV CCs

Escuela de Turismo de la Universidad Simón Bolívar, Núcleo Litoral.

Contacto: España. +34633129287

Caracas, Quito, Guayaquil, Jaén. 

WhatsApp:  +34633129287     

Twitter: @dademuch

FACEBOOK: DademuchConnection


9 comentarios sobre “The Geometric Series in Digital Signal Processing”

Deja un comentario