INTRODUCTION Most of the signals we deal with in real life getcorrupteed in some way or another by someunwanted signals. For the purpose of signal processing and analysis, it isimperative to get rid of these interferences, or at leastreduce their effects. This is achieved through applying Signal Filteringtechniques.
A Filter is an electronic circuit that removes /attenuates, from a signal, some unwanted componentor feature. Filter Application Eliminate background noise Radio tuning to a specific frequency Direct particular frequencies to different speakers Modify digital images Remove specific frequencies in data analysis
FILTER CHARACTERISTICS:To understand the basics of filtering, it is firstnecessary to learn some important terms used todefine filter characteristics. Cut-Off Frequency (fc): Also referred to as thecorner frequency, this is the frequency orfrequencies that define the limits of the filterrange.
Stop Band: The range of frequencies that is filtered out.Pass Band: The range of frequencies which is letthrough and recorded.Transition Band: Region that Separates the pass bandand stop band.
LOW-PASS FILTER: A low-pass filter is an electronic filter that passeslow-frequency signals and attenuates (reducesthe amplitude of) signals with frequencies higherthan the cutoff frequency. The actual amount ofattenuation for each frequency varies from filter tofilter. It is sometimes called a high-cut filter, or treble cutfilter when used in audio applications.
There are two basic kinds of circuits capable ofaccomplishing this objective, and many variations ofeach one: The inductive low-pass filter The capacitive low-pass filter
THE INDUCTIVE LOW-PASS FILTERThe inductors impedance increases with increasingfrequency. This high impedance in series tends toblock high-frequency signals from getting to the load.
THE RESPONSE OF AN INDUCTIVE LOW-PASS FILTER FALLSOFF WITH INCREASING FREQUENCY.
THE CAPACITIVE LOW-PASS FILTER The capacitors impedance decreases with increasingfrequency. This low impedance in parallel with theload resistance tends to short out high-frequencysignals, dropping most of the voltage across seriesresistor R1.
THE RESPONSE OF A CAPACITIVE LOW-PASS FILTER FALLSOFF WITH INCREASING FREQUENCY.
All low-pass filters are rated at a certain cutofffrequency. The cutoff frequency for a low-pass filteris that frequency at which the output (load) voltageequals 70.7% of the input (source) voltage. Thiscutoff percentage of 70.7 is not really arbitrary, allthough it may seem so at first glance. In a simplecapacitive/resistive low-pass filter, it is the frequencyat which capacitive reactance in ohms equalsresistance in ohms. In a simple capacitive low-passfilter (one resistor, one capacitor), the cutofffrequency is given as:
A simple filter will be two elements - a capacitor orinductor and a resistor. A capacitor will tend to "trap"low frequencies. In the case of a low pass filter made of a capacitorand resistor, the output voltage will be measuredacross the capacitor. Inductors are the opposite, so the output would beacross the resistor.
There are a great many different types of filtercircuits, with different responses to changingfrequency. The frequency response of a filter isgenerally represented using a Bode plot.• First-order filter• Second-order filter• Third and Higher order filters
First-order filter:A first-order filter, will reduce the signal strength byhalf (about −6 dB) every time the frequency doubles.The magnitude Bode plot for a first-order filter lookslike a horizontal line below the cutoff frequency, and adiagonal line above the cutoff frequency.
SECOND-ORDER FILTER A second-order filter does a better job of attenuatinghigher frequencies. The Bode plot for this type offilter resembles that of a first-order filter, except thatit falls off more quickly. For example, a second-order filter will reduce thesignal strength to one fourth its original level everytime the frequency doubles.