READING ASSIGNMENTS. Signal Processing First LECTURE OBJECTIVES TIME & FREQUENCY. This Lecture: Lecture 13 Digital Filtering of Analog Signals

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1 Sigal Procssig First Lctur Digital Filtrig of Aalog Sigals READING ASSIGNENTS This Lctur: Chaptr 6, Sctios 6-6, 6-7 & 6-8 Othr Radig: Rcitatio: Chaptr 6 FREQUENCY RESPONSE EXAPLES Nt Lctur: Chaptr 7 /6/, J ccllla & RW Schafr /6/, J ccllla & RW Schafr LECTURE OBJECTIVES Two Domais: Tim & Frquc Track th spctrum of thru a FIR Filtr: Siusoid-IN givs Siusoid-OUT UNIFICATION: ow dos Frquc Rspos affct t to produc t? t FIR t /6/, J ccllla & RW Schafr 4 TIE & FREQUENCY k b k k k h k k FIR DIFFERENCE EQUATION is th TIE-DOAIN h h k /6/, J ccllla & RW Schafr 5 h k h k h

2 E: DELAY b SYSTE DELAY b SYSTE Fid h ad h for b k {,, } h δ /6/, J ccllla & RW Schafr 6 Fid h ad δ for k δ k k k ONLY /6/, J ccllla & RW Schafr 7 GENERAL DELAY PROPERTY Fid h ad h δ d δ k k d k ONLY ONE o-zero TER for k at k d for /6/, J ccllla & RW Schafr 8 d d FREQ DOAIN --> TIE?? START with ad fid h or b h h? 7 /6/, J ccllla & RW Schafr 9 k cos

3 FREQ DOAIN --> TIE cos EULER s Formula h.5δ.5δ b k {,.5,,.5} PREVIOUS LECTURE REVIEW SINUSOIDAL INPUT SIGNAL OUTPUT has SAE FREQUENCY DIFFERENT Amplitud ad Phas FREQUENCY RESPONSE of FIR AGNITUDE vs. Frquc PASE vs. Frq PLOTTING AG PASE /6/, J ccllla & RW Schafr /6/, J ccllla & RW Schafr FREQ. RESPONSE PLOTS PLOT of FREQ RESPONSE b k } { {,,} DENSE GRID ww from - to ww -pi:pi/:pi; frqzbb,,ww VECTOR bb cotais Filtr Cofficits DSP-First: frkzbb,,ww k k /6/, J ccllla & RW Schafr b k cos RESPONSE at radias /6/, J ccllla & RW Schafr

4 /6/, J ccllla & RW Schafr 4 EXAPLE 6. cos / 4 ad is kow wh Fid /6/, J ccllla & RW Schafr 5 / 4 wh Fid EXAPLE 6. aswr / at valuat O Stp - cos / 4 / / / 6 /6/, J ccllla & RW Schafr 6 EXAPLE: COSINE INPUT cos ad is kow wh Fid 4 cos /6/, J ccllla & RW Schafr 7 EX: COSINE INPUT as- cos wh Fid 4 cos / 4 / 4 4 / 4 / 4

5 EX: COSINE INPUT as- Fid wh cos 4 / 4 / 6cos cos / 4 / 4 / 4 /6/, J ccllla & RW Schafr 8 / SINUSOID thru FIR IF ultipl th agituds Add th Phass Acos φ A * cos φ /6/, J ccllla & RW Schafr 9 LTI Dmo with Siusoids FILTER DIGITAL FILTERING t t SPECTRU of t SU of SINUSOIDS SPECTRU of Is ALIASING a PROBLE? SPECTRU FIR Gai or Nulls Th, OUTPUT t SU of SINUSOIDS /6/, J ccllla & RW Schafr /6/, J ccllla & RW Schafr

6 FREQUENCY SCALING -pt AVERAGER Eampl t TIE SAPLING: IF NO ALIASING: FREQUENCY SCALING t /6/, J ccllla & RW Schafr t T s T s f s t k k 5 z? si 5 5 z t cos 5 t cos 5 t t /6/, J ccllla & RW Schafr si D-A FREQUENCY SCALING TRACK th FREQUENCIES t t t t TIE SAPLING: t T t s f s 5 z z RECONSTRUCT up to.5f s FREQUENCY SCALING f s 5 z.5 Fs z.5.5 NO w frqs 5 z /6/, J ccllla & RW Schafr 4 /6/, J ccllla & RW Schafr 5

7 -pt AVERAGER. 5 NULLS or ZEROS. 5 /6/, J ccllla & RW Schafr 6 EVALUATE Frq. Rspos At. 5 si si si.5 si.5 5 /6/, J ccllla & RW Schafr 7 si.75 si EVALUATE Frq. Rspos DIGITAL FILTER f s 5 / 5/ AG SCALE PASE CANGE EFFECTIVE RESPONSE LOW-PASS FILTER /6/, J ccllla & RW Schafr 8 /6/, J ccllla & RW Schafr 9

8 FILTER TYPES B & W IAGE LOW-PASS FILTER LPF BLURRING ATTENUATES IG FREQUENCIES IG-PASS FILTER PF SARPENING for IAGES BOOSTS TE IGS REOVES DC BAND-PASS FILTER BPF /6/, J ccllla & RW Schafr /6/, J ccllla & RW Schafr B&W IAGE with COSINE FILTERED B&W IAGE FILTERED: -pt AVG LPF: BLUR /6/, J ccllla & RW Schafr /6/, J ccllla & RW Schafr

9 ROW of B&W IAGE FILTERED ROW of IAGE BLACK 55 WITE ADJUSTED DELAY b 5 sampls /6/, J ccllla & RW Schafr 4 /6/, J ccllla & RW Schafr 5