7/27/2019 Chapter 1_ Basic Concepts of Digital Filtering and Types of Digital Filters

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9/22/13 Chapter 1: Basic concepts of digital fi ltering and types of digital fi lters - Digital Filter Design - mikroElektronika

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TOC Chapter 1 Chapter 2 Chapter 3

Digital Filter Design

Chapter 1: Introduction

1.1. Basic concepts of digital filtering1.2. Types of digital filters

1.1 Basic concepts of digital filtering

Digital filtering has specific characteristics that you need to pay special attention to. The analog input signal mus t satisfy certain

requirements. Furthermore, on converting an output digital signal into analog form, it is necess ary to perform additional signal processing

in order to obtain the appropriate result.

Figure 1-1 shows the block diagram of digital filtering process.

Figure 1-1. Digital filtering

The process of converting an analog s ignal into digital form is performed by sampling with a finite sam pling frequency fs. If an input signal

contains frequency components higher than half the sampling frequency (fs/2), it will cause distortion to the original spectrum. This is the

reason why it is first necessary to perform filtering of an input signal us ing a low-pas s filter that eliminates high-frequency components

from input frequency spectrum. This filter is called anti-aliasing filter as it prevents aliasi ng.

After the process of filtering and sampl ing, a digital s ignal is ready for further process ing which, in this case, is filtering using the

appropriate digital filter. The output signal is also a digital s ignal which, in som e cases , needs to be converted back into analog form. After

digital-to-analog conversion, signal contains som e frequency components higherthan fs/2 that mus t be eliminated. Again, it is neces sary

to use a low-pass filter with the sampling frequency fs/2. The specific characteristics of conversion affecting the signal a re beyond the

scope of this book.

Digital filter attenuation is usually expressed in terms of the logarithmic decibel scale (dB). The attenuation measured in decibels can be

found using the following expression:

a = 20 * log(H(f))

Cut-off frequencies are us ed for filter specification, which will be discussed later. The cut-off frequency of the passband is a frequency at

which the transition of the passband to the transition region occurs. The cut-off frequency of the s topband is a frequency at which the

transition of the transition region to the stopband occurs. These two frequencies are equivalent only for the ideal filter which is not poss ible

to realize in practice. In other words, they are always different.

1.2.Types of digital filters

Filters can be class ified in several different groups, depending on what criteria are used for class ification. The two major types o f digital

filters are finite impuls e respons e digital filters (FIR filters) and infinite impulse respons e digital filters (IIR).

Both types have some advantages and disadvantages that should be carefully considered when designing a filter. Besides, it is necess ary

to take into account all fundamental characteristics of a s ignal to be filtered as these are very important when deciding which filter to use. In

mos t cases, it is only one characteristic that really matters and it is whether it is necess ary that filter has linear phase characteristic or not.

Speech signal, for example, can be processed in the systems with non-linear phase characteristic. The phase characteristic of a speech

signal is not of the ess ence and as s uch can be neglected, which results in the poss ibility to use much wider range of systems for its

prosessing.

There are also signa ls for which the phase characteristic is of the essence. A typical example are s ignals obtained from various sensors

in indus try. Therefore, it is neces sary that a filter has linear phase characteristic to prevent loosing important information.

When a s ignal to be filtered is analysed in this way, it is easy to decide which type of digital filter is bes t to use. Accordingly, if the phas e

characteristic is of the essence, FIR filters s hould be us ed as they have linear phase characteristic. Such filters are of higher order and

more com plex, therefore. Otherwise, when it is only frequency respons e that matters, it is preferable to use IIR digital filters which have far

lower order, i.e. are less complex, and thus much eas ier to realize.

The basic characteristics of Finite Impulse Response (FIR) filters are:

linear phase characteristic;

high filter order (more complex circuits); and

stability.

The basic characteristics of Infinite Impulse Respons e (IIR) are:

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9/22/13 Chapter 1: Basic concepts of digital fi ltering and types of digital fi lters - Digital Filter Design - mikroElektronika

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table of contents | next chapter

non-linear phase characteristic;

low filter order (less complex circuits); and

resulting digital filter has the potential to become unstable.

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