Microwave Essay

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What is a filter? Digital Filters Take input and create output Programs are filters People are filters Physics is filters That’s too general. 2 Filters Filters shape the frequency spectrum of a sound signal. Filters generally do not add frequency components to a signal that are not there to begin with. Boost or attenuate selected frequency regions Which of the Following is not a Filter? Graphic Equalizer on a stereo system Tone control on a stereo system Microphone Mixing Board Loudspeaker Vocal Tract Ear 4 3 Definition A filter is any operation on a signal (From Rabiner et al, “Terminology in Digital Signal Processing.” Linear Time-Invariant Filters 95% of what we need will be: Linear If filter(x) = y then filter(a*x)=a*y Homogeneity: Input and output scales at the same rate. (a is a real number) Commonly, we limit the term filter to devices (hardware or software) that were designed specifically to boost or attenuate regions of a signal spectrum. 5 Superposition: The sum of two inputs is the sum of two outputs. Time Invariant If filter(x1)=y1 and filter(x2)=y2 then filter(x1+x2)=y1+y2 Time delayed inputs yield time delayed output without change of the filter If filter(x(now))=y(now)then filter(x(now+time))=y(now+time) 6 1 Filter types: frequency response Functions which take one sequence of numbers (the input signal) and produces a new sequence of numbers (the filtered output signal) The Four Basic Types 1. 2. 3. 4. Lowpass lets through low frequencies Stops high frequencies Lowpass Highpass Bandpass Band reject cutoff frequency 7 8 Highpass lets through high frequencies Stops low frequencies Bandpass combinations of lowpass and highpass filters lets through only frequencies above a certain point and below another, so there is a band of frequencies that get through 9 10 Band Reject

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