No item in cart

# Important Properties of convolution | Signals and Systems | GATE Preparation | ME

Concept of convolution has wide ranging applications such as its usage in digital image processing for the purpose of filtering, improving certain features of images and many other signal processing applications.

Explanation

Convolution is a mathematical operator which relates input and output of an LTI system. It is only with the help of convolution operator that we can generate exact output from input and impulse response. But the only problem is convolution is a little bit complex operator. As an alternative to convolution, we study transformation theory where we reduce convolution relation between input and impulse response in to multiplication by transferring them in to different domain. After finding the output in that domain we again bring the output back to original domain.

Having said that there is an alternative to convolution given the complex nature of convolution operator, there are some important properties of convolution which are in fact very important shortcuts to conventional method of convolution by which we can easily determine the output.

Following are some important properties of convolution

When discrete time signals x[n] and impulse response h[n] are convolved, the resultant signal y[n] has following properties

Lower limit of y[n] is sum of lower limits of x[n] and that of h[n] and upper limit is sum of upper limits of x[n] and that of h([n] respectively.

Length (l) of y[n] is l = l1+l2-1. Where l1 is length of x[n] and l2 is length of h[n] Sum of samples of y[n] is equal to product of sum of x[n] and that of h[n].

When two continuous time signals x(t) and h(t) are convolved, the resultant signal y(t)

Lower limit of y(t) is sum of lower limits of x(t) and that of h(t) and upper limit of y(t) is sum of upper limits of x(t) and that of h(t) respectively.

Width of y(t) is sum of widths of x(t) and h(t).

Area of y(t) is product of areas of x(t) and h(t).

Keywords: Convolution, Properties of convolution, Transform theory, Impulse response, LTI Systems, Signal processing, Image processing, Analog Filter and Digital Filter

### Testimonials

THE GATE Academy questions covered a wide variety of topics and were similar to GATE paper standard. The online platform replicated the actual GATE test environment and the detailed and video solutions were sufficient to clear all doubts regarding the question. Thanks to THE GATE Academy team to provide such wonderful tests & platform.

Avirup Mullick

AIR 5

AIR 5

In one year’s time, I was able to prepare for GATE exam with the help of THE GATE ACADEMY and faculties. GATE Focused study materials and online mock tests helped me know my strengthen & weakness to prepare accordingly. I wish all the best to all GATE aspirants and suggest them to go through GATE coaching in case the basics are not clear.

Ashish Behera

AIR 1

AIR 1

To begin with, it gives me immense pleasure to Thank,Thank the institute THE GATE ACADEMY for all their help and support.Its a place to learn, explore, grow and succeed.Well it helps you brush-up your engineering knowledge and learn new things and clears your concept in such great details

Raju Kumar

AIR 4

AIR 4

I am Praveen. I got AIR 1 in Instrumentation stream. I want to dedicate this to my parents and to the Gate Academy faculty. Gate Academy coaching helped me tremendously to update myself continuously.I was very impressed with the way they taught each topic in different sessions with separate material for each session.

R.V Praveen

AIR 1

AIR 1

I took up mechanical coaching at THE GATE ACADEMY as there is no separate coaching for Engineering Sciences in India and Mechanical and Engineering sciences have more or less common topics.I feared that cracking GATE would be very difficult because I started my preparations very late but the counsellors and teachers guided me

Sampat Singh Bhati

AIR 1

AIR 1

E Lectures helped me a lot in making a head start in the right direction. It helped whenever I got stuck in any topic. Mock Tests across 50 centers helped me judge my progress both on individual and comparative basis.

VinodDatusliya

AIR 1

AIR 1

### GATE Success Story

- Our students get all India rank 1, 1, 1, 1, 4 and 4
- More than 142 students in top 100.