DSP First, 2/e. FIR Filters. This Lecture: Lecture 11 FIR Filtering Intro INTRODUCE FILTERING IDEA. Chapter 5, Sects. 5-1, 5-2, 5-3 & 5-4 (partial)

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1 DSP First, /e Lecture FIR Filterig Itro READING ASSIGNENTS Tis Lecture: Capter 5, Sects. 5-, 5-, 5- & 5- (partial) Oter Readig: Net Lecture: C. 5, Sects 5-, 5-6, 5-7 & 5-8 CONVOLUTION Aug 6-6, JH cclella & RW Scafer LECTURE OBJECTIVES DIGITAL FILTERING INTRODUCE FILTERING IDEA Weigted Average Ruig Average FINITE IPULSE RESPONSE FILTERS FIR Filters Sow ow to compute te output t from te iput sigal, (t) A-to-D COPUTER D-to-A Caracterized SIGNALS (Fourier series) Coverted to DIGITAL (samplig) Toda: How to PROCESS tem (DSP)? CONCENTRATE o te COPUTER ALGORITHS, SOFTWARE (ATLAB) ad HARDWARE (DSP cips, VLSI) (t) Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer 5

2 Te TS, 98 Roclad Digital Filter, 97 First PC plug-i board from Atlata Sigal Processors Ic. Cost was about te same as te price of a small ouse. Aug 6-6, JH cclella & RW Scafer 6 Aug 6-6, JH cclella & RW Scafer 7 Digital Cell Poe (ca. ) DISCRETE-TIE TIE SYSTE COPUTER OPERATE o to get WANT a GENERAL CLASS of SYSTES ANALYZE te SYSTE TOOLS: TIE-DOAIN & FREQUENCY-DOAIN SYNTHESIZE te SYSTE Now, digital cameras ad video streamig rel o DSP algoritms Aug 6-6, JH cclella & RW Scafer 8 Aug 6-6, JH cclella & RW Scafer 9

3 D-T SYSTE EXAPLES DISCRETE-TIE TIE SIGNAL SYSTE is a LIST of NUBERS INDEXED b EXAPLES: POINTWISE OPERATORS SQUARING: = () RUNNING AVERAGE RULE: te output at time is te average of tree cosecutive iput values STE PLOT Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer -PT AVERAGE SYSTE INPUT SIGNAL ADD CONSECUTIVE NUBERS Do tis for eac ae a TABLE ( ) ( ) OUTPUT SIGNAL = = Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer

4 PAST, PRESENT, FUTURE ANOTHER -pt AVERAGER SLIDE a WINDOW across is PRESENT TIE Uses PAST VALUES of IPORTANT IF represets REAL TIE WHEN & ARE STREAS ( ) Figure 5- Filter calculatio at te preset time (l = ) uses values witi a slidig widow. Gra sadig idicates te past (l < ); orage sadig, te future (l > ). Here, te slidig widow ecompasses values from bot te future ad te past. Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer 5 CAUSAL -pt AVERAGER ( ) GENERAL CAUSAL FIR FILTER FILTER COEFFICIENTS {b } DEFINE THE FILTER For eample, b {,,,} b b Aug 6-6, JH cclella & RW Scafer 6 Aug 6-6, JH cclella & RW Scafer 7

5 GENERAL CAUSAL FIR FILTER FILTER COEFFICIENTS {b } b FILTER ORDER is FILTER LENGTH is L = + NUBER of FILTER COEFFS is L Aug 6-6, JH cclella & RW Scafer 8 GENERAL CAUSAL FIR FILTER SLIDE a WINDOW across b b b b - Aug 6-6, JH cclella & RW Scafer 9 FILTERED STOCK SIGNAL SPECIAL INPUT SIGNALS INPUT OUTPUT = SINUSOID FREQUENCY RESPONSE (LATER) as ol oe NON-ZERO VALUE UNIT-IPULSE 5-pt Averager Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer

6 UNIT IPULSE SIGNAL Sequece Represetatio Eample: is NON-ZERO We its argumet is equal to ZERO 6 6 Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer UNIT IPULSE RESPONSE FIR filter descriptio usuall give i terms of coefficiets b b Ca we describe te filter usig a SIGNAL istead? Wat tappes ifiput tis a uit itimpulse? Aug 6-6, JH cclella & RW Scafer Eample: -pt AVERAGER CAUSAL SYSTE: USE PAST VALUES ( ) INPUT = UNIT IPULSE SIGNAL = OUTPUT is called IPULSE RESPONSE Deoted = we = Aug 6-6, JH cclella & RW Scafer 5

7 Uit Impulse Respose U p s sp s 5 Aug 6-6, JH cclella & RW Scafer 6 SU of Sifted Impulses SU of Sifted Impulses Aug 6-6, JH cclella & RW Scafer 7 FIR IPULSE RESPONSE FIR IPULSE RESPONSE b b Aug 6-6, JH cclella & RW Scafer 9 Was to Represet te FIR filter FIR filter U SHIFTED IPULSES t it Use SHIFTED IPULSES to write : Plot te values } { b : List te values Aug 6-6, JH cclella & RW Scafer },,,, { b True for a sigal,

8 Aug 6-6, JH cclella & RW Scafer LONGER OUTPUT FILTERING EXAPLE 7-poit AVERAGER 7 Removes cosie B maig its amplitude (A) smaller 6 7 -pt AVG EXAPLE Iput : (.) cos( /8 / ) for -poit AVERAGER Cages A sligtl USE PAST VALUES Aug 6-6, JH cclella & RW Scafer Aug 6-6, JH cclella & RW Scafer 7-pt FIR EXAPLE (AVG) Iput : (.) cos( /8 / ) for CAUSAL: Use Previous